the effect of text based math task on dynamic stability control during stair descent abstract stair descent imposes a significant challenge for dynamic stability among young adults the effect of a concurrent text based math task on dynamic stability control remains unclear during stair descent when considering the influence of gait velocity twenty six participants performed three successful stair descent trials under texting or no texting conditions at their preferred speed synchronous kinematics and kinetics were collected by an eight camera vicon infrared motion capture system and two force platforms repeated measures analysis of covariance and wilcoxon signed rank test were used to analyze the differences between the two different task conditions with gait velocity as a covariate the outcomes indicated that under texting condition sagittal margin of stability increased at right foot landing step cadence double support percentage sagittal and frontal joint moment decreased and sagittal and frontal joint angles were also modified it is concluded that concurrent texting impaired sagittal and frontal stability control during stair descent despite slowing down the step cadence knee and ankle joint adjustment strategies were mainly adopted in response to stability control in the sagittal plane with the interference of texting whereas the hip joint adjustment strategy was adopted in the frontal plane in conclusion texting behaviors on mobile phones should be minimized during stair descent

direct adaptive controller for nonaffine nonlinear systems using self structuring neural networks a direct adaptive state feedback controller is proposed for highly nonlinear systems we consider uncertain or ill defined nonaffine nonlinear systems and employ a neural network nn with flexible structure i e an online variation of the number of neurons the nn approximates and adaptively cancels an unknown plant nonlinearity a control law and adaptive laws for the weights in the hidden layer and output layer of the nn are established so that the whole closed loop system is stable in the sense of lyapunov moreover the tracking error is guaranteed to be uniformly asymptotically stable uas rather than uniformly ultimately bounded uub with the aid of an additional robustifying control term the proposed control algorithm is relatively simple and requires no restrictive conditions on the design constants for the stability the efficiency of the proposed scheme is shown through the simulation of a simple nonaffine nonlinear system

dynamic margins of stability during human walking in destabilizing environments understanding how humans maintain stability when walking particularly when exposed to perturbations is key to preventing falls here we quantified how imposing continuous pseudorandom anterior posterior ap and mediolateral ml oscillations affected the control of dynamic walking stability twelve subjects completed five 3 minute walking trials in the computer assisted rehabilitation environment caren system under each of 5 conditions no perturbation nop ap platform app or visual apv or ml platform mlp or visual mlv oscillations we computed ap and ml margins of stability mos for each trial mean mosml were consistently slightly larger during all perturbation conditions than during nop p 0 038 mean mosap for the app mlp and mlv oscillations were significantly smaller than during nop p 0 0005 variability of both mosap and mosml was significantly greater during the mlp and mlv oscillations than during nop p 0 0005 we also directly quantified how the mos on any given step affected the mos on the following step using first return plots there were significant changes in step to step mosml dynamics between experimental conditions p 0 0005 these changes suggested that subjects may have been trying to control foot placement and consequently stability during the perturbation conditions quantifying step to step changes in margins of dynamic stability may be more useful than mean mos in assessing how individuals control walking stability

reduced knee joint moment in acl deficient patients at a cost of dynamic stability during landing abstract the current study aimed to examine the effect of anterior cruciate ligament deficiency acld on joint kinetics and dynamic stability control after a single leg hop test slht twelve unilateral acld patients and a control subject group n 13 performed a slht over a given distance with both legs the calculation of joint kinetics was done by means of a soft tissue artifact optimized rigid full body model margin of stability mos was quantified by the difference between the base of support and the extrapolated center of mass during landing the acld leg showed lower external knee flexion moments but demonstrated higher moments at the ankle and hip compared to controls p 0 05 the main reason for the joint moment redistribution in the acld leg was a more anterior position of the ground reaction force grf vector which affected the moment arms of the grf acting about the joints p 0 05 for the acld leg trunk angle was more flexed over the entire landing phase compared to controls p 0 05 and we found a significant correlation between moment arms at the knee joint and trunk angle r 2 0 48 p 0 01 the consequence of this altered landing strategy in acld legs was a more anterior position of the center of mass reducing the mos p 0 05 the results illustrate the interaction between trunk angle joint kinetics and dynamic stability during landing maneuvers and provide evidence of a feedforward adaptive adjustment in acld patients i e more flexed trunk angle aimed at reducing knee joint moments at the cost of dynamic stability control

diagrammatic derivation of gradient algorithms for neural networks deriving gradient algorithms for time dependent neural network structures typically requires numerous chain rule expansions diligent bookkeeping and careful manipulation of terms in this paper we show how to derive such algorithms via a set of simple block diagram manipulation rules the approach provides a common framework to derive popular algorithms including backpropagation and backpropagation through time without a single chain rule expansion additional examples are provided for a variety of complicated architectures to illustrate both the generality and the simplicity of the approach

a new adaptive backpropagation algorithm based on lyapunov stability theory for neural networks a new adaptive backpropagation bp algorithm based on lyapunov stability theory for neural networks is developed in this paper it is shown that the candidate of a lyapunov function v k of the tracking error between the output of a neural network and the desired reference signal is chosen first and the weights of the neural network are then updated from the output layer to the input layer in the sense that deltav k v k v k 1 0 the output tracking error can then asymptotically converge to zero according to lyapunov stability theory unlike gradient based bp training algorithms the new lyapunov adaptive bp algorithm in this paper is not used for searching the global minimum point along the cost function surface in the weight space but it is aimed at constructing an energy surface with a single global minimum point through the adaptive adjustment of the weights as the time goes to infinity although a neural network may have bounded input disturbances the effects of the disturbances can be eliminated and asymptotic error convergence can be obtained the new lyapunov adaptive bp algorithm is then applied to the design of an adaptive filter in the simulation example to show the fast error convergence and strong robustness with respect to large bounded input disturbances

a stable neural network based observer with application to flexible joint manipulators a stable neural network nn based observer for general multivariable nonlinear systems is presented in this paper unlike most previous neural network observers the proposed observer uses a nonlinear in parameters neural network nlpnn therefore it can be applied to systems with higher degrees of nonlinearity without any a priori knowledge about system dynamics the learning rule for the neural network is a novel approach based on the modified backpropagation bp algorithm an e modification term is added to guarantee robustness of the observer no strictly positive real spr or any other strong assumption is imposed on the proposed approach the stability of the recurrent neural network observer is shown by lyapunov s direct method simulation results for a flexible joint manipulator are presented to demonstrate the enhanced performance achieved by utilizing the proposed neural network observer

body weight support impacts lateral stability during treadmill walking body weight support bws systems are a common tool used in gait rehabilitation bws systems may alter the requirements for an individual to actively stabilize by 1 providing lateral restoring forces that reduce the requirements for the nervous system to actively stabilize and 2 decreasing the stabilizing gravitational moment in the frontal plane which could increase the requirements to actively stabilize the goal of the current study was to quantify the interaction between bws and lateral stability we hypothesized that when able bodied people walk with bws 1 the lateral restoring forces provided by bws would reduce the requirements to stabilize in the frontal plane when comparing dynamically similar gaits and 2 increasing bws would decrease the stabilizing gravitational moment in the frontal plane and increase the requirements to stabilize when speed is constrained our findings partly support these hypotheses but indicate a complex interaction between bws and lateral stability with bws subjects significantly decreased step width variability and significantly increased step width p 0 05 for both the dynamically similar and speed matched conditions the decrease in step width variability may be attributable to a combination of lateral restoring forces decreasing the mechanical requirements to stabilize and an enhanced sense of position that could have improved locomotor control increases in step width when walking with high levels of bws could have been due to decreases in the gravitational moment about the stance limb which may challenge the control of stability in multiple planes

peaking free output feedback adaptive neural control under a nonseparation principle high gain observers have been extensively applied to construct output feedback adaptive neural control anc for a class of feedback linearizable uncertain nonlinear systems under a nonlinear separation principle yet due to static gain and linear properties high gain observers are usually subject to peaking responses and noise sensitivity existing adaptive neural network nn observers cannot effectively relax the limitations of high gain observers this paper presents an output feedback indirect anc strategy under a nonseparation principle where a hybrid estimation scheme that integrates an adaptive nn observer with state variable filters is proposed to estimate plant states by applying a single lyapunov function candidate to the entire system it is proved that the closed loop system achieves practical asymptotic stability under a relatively low observer gain dominated by controller parameters our approach can completely avoid peaking responses without control saturation while keeping favourable noise rejection ability simulation results have shown effectiveness and superiority of this approach

high gain observers in the state and estimation of robots having elastic joints the paper deals with the state and parameter estimation of robots having elastic joints the estimation of the unknown parameters of the robot is reduced to the estimation of its state variables by a state space immersion the luenberger observer is used in the state estimation of the extended robot model the use of high gains is studied in the cancellation of nonlinearities in order to simplify the observer design the high gain induces a time scale separation between the robot model and the observer and therefore the singular perturbation theory can be used in the stability analysis of the estimate error dynamics in particular it is shown that the error dynamics reaches the stable equilibrium in a very fast transient ensuring that the slow dynamics of the observer is just that of the given robot

gait stability variability and complexity on inclined surfaces this study evaluated the gait stability variability and complexity of healthy young adults on inclined surfaces a total of 49 individuals walked on a treadmill at their preferred speed for 4min at inclinations of 6 8 and 10 in upward up and downward down conditions and in horizontal 0 condition gait variability was assessed using average standard deviation trunk acceleration between strides var gait stability was assessed using margin of stability mos and maximum lyapunov exponent s and gait complexity was assessed using sample entropy sen trunk variability var increased in the medial lateral ml anterior posterior and vertical directions for all inclined conditions the sen values indicated that movement complexity decreased almost linearly from down to up conditions reflecting changes in gait pattern with longer and slower steps as inclination increased the down conditions were associated with the highest variability and lowest stability in the mos ml but not in s stability was lower in up conditions which exhibited the largest s values the overall results support the hypothesis that inclined surfaces decrease gait stability and alter gait variability particularly in up conditions

modelling the dynamic margins of stability for use in evaluations of balance following a support surface perturbation the dynamic margin of stability provides a method that captures the center of mass com state position velocity in relation to the base of support bos however the model upon which this concept was derived does not consider how the inertial characteristics of forced support surface perturbations would influence balance control within the current article the inverted pendulum model was restructured to account for fixed piecewise accelerations of the bos from this logic two variations of the adjusted margin of stability each maintaining a similar definition of extrapolated com are proposed one ignoring horizontal ground contact and inertial forces applied to the bos the other incorporating these forces unique within the proposed models is the time variant bos boundaries that depend on the perturbation applied verification of the solution for each model is provided along with a comparison of obtained values to previous methods of defining com position velocity stability metrics using a computational model and optimal control for the simpler model variation ignoring forces we also assessed how com position and perturbation parameter selection over underestimate the predicted maximal permissible velocity the results of these analyses suggest that factors which increase the acceleration impulse decrease the difference between the two models the opposite was observed for factors increasing displacements between the com and bos boundary lastly use of the proposed adjusted margin of stability within an experimental data set highlights the ability of our model to predict instability stepping strategies negative margin of stability relative to the use of the extrapolated com alone

center of mass velocity position predictions for balance control the purposes of this analysis were to predict the feasible movements during which balance can be maintained based on environmental contact force anatomical foot geometry and physiological muscle strength constraints and to identify the role of each constraint in limiting movement an inverted pendulum model with a foot segment was used with an optimization algorithm to determine the set of feasible center of mass cm velocity position combinations for movement termination the upper boundary of the resulting feasible region ran from a velocity of 1 1 s 1 normalized to body height at 2 4 foot lengths behind the heel to 0 45 s 1 over the heel to zero over the toe and the lower boundary from a velocity of 0 9 s 1 at 2 7 foot lengths behind the heel to zero over the heel forward falls would be initiated if states exceeded the upper boundary and backward falls would be initiated if the states fell below the lower boundary under normal conditions the constraint on the size of the base of support bos determined the upper and lower boundaries of the feasible region however friction and strength did limit the feasible region when friction levels were less than 0 82 when dorsiflexion was reduced more than 51 or when plantar flexion strength was reduced more than 35 these findings expand the long held concept that balance is based on cm position limits i e the horizontal cm position has to be confined within the bos to guarantee stable standing to a concept based on cm velocity position limits

travelling waves of the diffusive nicholson s blowflies equation with strong generic delay kernel and non local effect abstract in this paper we consider travelling wave solutions for the diffusive nicholson s blowflies equation incorporating time delay and diffusion special attention is paid to the modelling of the time delay to incorporate associated non local spatial terms which account for the drift of individuals to their present position from their possible positions at previous times for the strong generic delay kernel we show that travelling wave solutions exist provided that the delay is sufficiently small using the geometric singular perturbation theory

dirichlet problem for the diffusive nicholson s blowflies equation abstract the object of this paper is to consider the asymptotic behavior of solutions of the diffusive nicholson s blowflies equation under dirichlet boundary condition a new approach is developed to study the global attractivity of the positive steady state for a reaction diffusion equation with time delay when monotone or quasi monotone conditions fail to apply this approach should be applicable to other dirichlet problems as well even though our analysis is tailored to the diffusive nicholson s blowflies equation

common nature of learning between back propagation and hopfield type neural networks for generalized matrix inversion with simplified models in this paper two simple structure neural networks based on the error back propagation bp algorithm i e bp type neural networks bpnns are proposed developed and investigated for online generalized matrix inversion specifically the bpnn l and bpnn r models are proposed and investigated for the left and right generalized matrix inversion respectively in addition for the same problem solving task two discrete time hopfield type neural networks hnns are developed and investigated in this paper similar to the classification of the presented bpnn l and bpnn r models the presented hnn l and hnn r models correspond to the left and right generalized matrix inversion respectively comparing the bpnn weight updating formula with the hnn state transition equation for the specific i e left or right generalized matrix inversion we show that such two derived learning expressions turn out to be the same in mathematics although the bp and hopfield type neural networks are evidently different from each other a great deal in terms of network architecture physical meaning and training patterns numerical results with different illustrative examples further demonstrate the efficacy of the presented bpnns and hnns for online generalized matrix inversion and more importantly their common natures of learning

nonlinear adaptive wavelet control using constructive wavelet networks in this paper an adaptive wavelet network based control approach is proposed for highly nonlinear uncertain dynamical systems wavelet network as a kind of universal approximator has two novel properties orthonormality and multiresolution the orthonormal property ensures that adding a new resolution new wavelets does not affect the existing wavelet network that may have been well tuned in the sequel the online adjustment of the structure of the nonlinear adaptive wavelet controller awc can be done in a constructive manner by gradually increasing the network resolution the multiresolution property on the other hand assures a guaranteed improvement of the approximation precision when a new resolution is added in real life problems we are unable to know the adequate size of a network either a neural network nn or a wavelet network to produce the required approximation precision by virtue of the novel wavelet network properties a coarse or very simple structure can be selected first if the system fails to converge after the elapse of a dwell time a new wavelet resolution is considered to be necessary and added directly in this manner the awc can be easily constructed and tuned from the coarse to finer levels until the performance requirement is satisfied the trial and error way of selecting the network structure which may lead to either an inadequate or a highly redundant structure can be avoided in this paper the proposed adaptive wavelet network is applied first to a class of nonlinear dynamical systems with a partially known model and an affine in input structure then the adaptive wavelet network is applied to a class of nonlinear nonaffine dynamical systems

optimal design for robust control of uncertain flexible joint manipulators a fuzzy dynamical system approach abstracta novel fuzzy dynamical system approach to the control design of flexible joint manipulators with mismatched uncertainty is proposed uncertainties of the system are assumed to lie within p

an actuated dissipative spring mass walking model predicting human like ground reaction forces and the effects of model parameters abstract simple models are widely used to understand the mechanics of human walking the optimization based minimal biped model and spring loaded inverted pendulum slip model are two popular models that can achieve human like walking patterns however ground reaction forces grf from these two models still deviate from experimental data in this paper we proposed an actuated dissipative spring mass model by integrating these two models to realize more human like grf patterns we first explored the function of stiffness damping and weights of both energy cost and force cost in the objective function and found that these parameters have distinctly different influences on the optimized gait and grf profiles the stiffness and objective weight affect the number and size of peaks in the vertical grf and stance time the damping changes the relative size of the peaks but has little influence on stance time based on these observations these parameters were manually tuned at three different speeds to approach experimentally measured vertical grf and the highest correlation coefficient can reach 0 983 these results indicate that the stiffness damping and proper objective functions are all important factors in achieving human like motion for this simple walking model these findings can facilitate the understanding of human walking dynamics and may be applied in future biped models

a new development for the tikhonov theorem in nonlinear singular perturbation systems abstract this paper deals with the exponential stability of nonlinear perturbation systems under a new condition a novel criterion of exponential stability of nonlinear systems is firstly given in a general form in this criterion a new kind of characteristic value is introduced which makes the exponential stability measurable based on this criterion a new development for the tikhonov theorem in nonlinear singular perturbation systems is presented

traveling waves of a diffusive predator prey model with nonlocal delay and stage structure abstract in this paper a diffusive predator prey model with nonlocal delay and stage structure is investigated by using the cross iteration method and schauder s fixed point theorem we reduce the existence of traveling wave solutions to the existence of a pair of upper lower solutions numerical simulations are carried out to illustrate the theoretical results

the discriminant capabilities of stability measures trunk kinematics and step kinematics in classifying successful and failed compensatory stepping responses by young adults abstract this study evaluated the discriminant capability of stability measures trunk kinematics and step kinematics to classify successful and failed compensatory stepping responses in addition the shared variance between stability measures step kinematics and trunk kinematics is reported the stability measures included the anteroposterior distance d between the body center of mass and the stepping limb toe the margin of stability mos as well as time to boundary considering velocity ttb v velocity and acceleration ttb a and mos ttb mos kinematic measures included trunk flexion angle and angular velocity step length and the time after disturbance onset of recovery step completion fourteen young adults stood on a treadmill that delivered surface accelerations necessitating multiple forward compensatory steps thirteen subjects fell from an initial disturbance but recovered from a second identical disturbance trunk flexion velocity at completion of the first recovery step and trunk flexion angle at completion of the second step had the greatest overall classification of all measures 92 3 ttb v and ttb a at completion of both steps had the greatest classification accuracy of all stability measures 80 8 the length of the first recovery step r 0 70 and trunk flexion angle at completion of the second recovery step r 0 54 had the largest correlations with stability measures although ttb v and ttb a demonstrated somewhat smaller discriminant capabilities than trunk kinematics the small correlations between these stability measures and trunk kinematics r 0 52 suggest that they reflect two important yet different aspects of a compensatory stepping response

adaptive control of nonlinear systems using neural networks layered networks are used in a nonlinear adaptive control problem the plant is an unknown feedback linearizable discrete time system represented by an input output model a state space model of the plant is obtained to define the zero dynamics which are assumed to be stable a linearizing feedback control is derived in terms of some unknown nonlinear functions to identify these functions it is assumed that they can be modelled by layered neural networks the weights of the networks are updated and used to generate the control a local convergence result is given computer simulations verify the theoretical result

online stabilization of block diagonal recurrent neural networks deals with a discrete time recurrent neural network dtrnn with a block diagonal feedback weight matrix called the block diagonal recurrent neural network bdrnn that allows a simplified approach to online training and to address network and training stability issues the structure of the bdrnn is exploited to modify the conventional backpropagation through time bptt algorithm to reduce its storage requirement by a numerically stable method of recomputing the network state variables the network and training stability is addressed by exploiting the bdrnn structure to directly monitor and maintain stability during weight updates by developing a functional measure of system stability that augments the cost function being minimized simulation results are presented to demonstrate the performance of the bdrnn architecture its training algorithm and the stabilization method

moving beyond quiet stance applicability of the inverted pendulum model to stooping and crouching postures background currently it is unknown whether the inverted pendulum model is applicable to stooping or crouching postures therefore the aim of this study was to determine the degree of applicability of the inverted pendulum model to these postures via examination of the relationship between the centre of mass com acceleration and centre of pressure cop com difference methods ten young adults held static standing stooping and crouching postures each for 20 s for both the anterior posterior ap and medio lateral ml directions the time varying com acceleration and the cop com were computed and the relationship between these two variables was determined using pearson s correlation coefficients additionally in both directions the average absolute com acceleration average absolute cop com signal and the inertial component i e i wh were compared across postures results pearson correlation coefficients revealed a significant negative relationship between the com acceleration and cop com signal for all comparisons regardless of the direction p 0 001 while no effect of posture was observed in the ap direction p 0 463 in the ml direction the correlation coefficients for stooping were different i e stronger than standing p 0 008 regardless of direction the average absolute com acceleration for both the stooping and crouching postures was greater than standing p 0 002 conclusion the high correlations indicate that the inverted pendulum model is applicable to stooping and crouching postures due to their importance in completing activities of daily living there is merit in determining what type of motor strategies are used to control such postures and whether these strategies change with age

neural network observer based optimal control for unknown nonlinear systems using adaptive dynamic programming in this paper an observer based optimal control scheme is developed for unknown nonlinear systems using adaptive dynamic programming adp algorithm first a neural network nn observer is designed to estimate system states then based on the observed states a neuro controller is constructed via adp method to obtain the optimal control in this design two nn structures are used a three layer nn is used to construct the observer which can be applied to systems with higher degrees of nonlinearity and without a priori knowledge of system dynamics and a critic nn is employed to approximate the value function the optimal control law is computed using the critic nn and the observer nn uniform ultimate boundedness of the closed loop system is guaranteed the actor critic and observer structures are all implemented in real time continuously and simultaneously finally simulation results are presented to demonstrate the effectiveness of the proposed control scheme

an algorithm for determining gravity line location from posturographic recordings abstract in posturographic recordings the center of pressure cop displacement does not accurately reflect migration of the gravity line gl the vertical line passing through the body s center of gravity cog since the horizontal ground reaction force f x is proportional to the horizontal acceleration of the cog its second integral does represent the horizontal position of the gravity line glp however the initial constants of integration initial velocity and position are not known in this note a technique for estimating these integration constants is suggested zero point to zero point integration this method is based on a postulation that when f x 0 the glp and cop coincide by integrating f x from one zero point to another zero point both the instantaneous glp and its velocity are determined a validation of the suggested algorithm was performed using optical methods to determine the glp during a one legged standing tasks cross correlation values of glp determined via videography and the suggested algorithm ranged from 0 79 to 0 96 these results suggest that the zero point to zero point integration is an acceptable technique for determining glp from posturographic recordings

neural network adaptive control for nonlinear nonnegative dynamical systems nonnegative and compartmental dynamical system models are derived from mass and energy balance considerations that involve dynamic states whose values are nonnegative these models are widespread in engineering and life sciences and typically involve the exchange of nonnegative quantities between subsystems or compartments wherein each compartment is assumed to be kinetically homogeneous in this paper we develop a full state feedback neural adaptive control framework for adaptive set point regulation of nonlinear uncertain nonnegative and compartmental systems the proposed framework is lyapunov based and guarantees ultimate boundedness of the error signals corresponding to the physical system states and the neural network weighting gains in addition the neural adaptive controller guarantees that the physical system states remain in the nonnegative orthant of the state space for nonnegative initial conditions

impulsive stabilization of high order hopfield type neural networks with time varying delays this paper studies the problems of global exponential stability for impulsive high order hopfield type neural networks nns with time varying delays by employing the lyapunov razumikhin technique some criteria ensuring global exponential stability are derived our results are then used to obtain some sufficient conditions under which some nns can be forced to converge by impulsive control numerical examples are also discussed to illustrate our results

influence of gait speed on the control of mediolateral dynamic stability during gait initiation this study investigated the influence of gait speed on the control of mediolateral dynamic stability during gait initiation thirteen healthy young adults initiated gait at three self selected speeds slow normal and fast the results indicated that the duration of anticipatory postural adjustments apa decreased from slow to fast i e the time allocated to propel the centre of mass com towards the stance leg side was shortened likely as an attempt at compensation the peak of the anticipatory centre of pressure cop shift increased however cop compensation was not fully efficient since the results indicated that the mediolateral com shift towards the stance leg side at swing foot off decreased with gait speed consequently the com shift towards the swing leg side at swing heel contact increased from slow to fast indicating that the mediolateral com fall during step execution increased as gait speed rose however this increased com fall was compensated by greater step width so that the margin of stability the distance between the base of support boundary and the mediolateral component of the extrapolated centre of mass at heel contact remained unchanged across the speed conditions furthermore a positive correlation between the mediolateral extrapolated com position at heel contact and step width was found indicating that the greater the mediolateral com fall the greater the step width globally these results suggest that mediolateral apa and step width are modulated with gait speed so as to maintain equivalent mediolateral dynamical stability at the time of swing heel contact

output feedback control of a class of discrete mimo nonlinear systems with triangular form inputs in this paper adaptive neural network nn control is investigated for a class of discrete time multi input multi output mimo nonlinear systems with triangular form inputs each subsystem of the mimo system is in strict feedback form first through two phases of coordinate transformation the mimo system is transformed into input output representation with the triangular form input structure unchanged by using high order neural networks honns as the emulators of the desired controls effective output feedback adaptive control is developed using backstepping the closed loop system is proved to be semiglobally uniformly ultimate bounded sguub by using lyapunov method the output tracking errors are guaranteed to converge into a compact set whose size is adjustable and all the other signals in the closed loop system are proved to be bounded simulation results show the effectiveness of the proposed control scheme

asymptotic behavior and traveling wave solutions for parabolic functional differential equations on presente une generalisation de la theorie des equations kpp et de diffusion bistables non lineaires on montre que des solutions onde de propagation existent pour des equations fonctionnelles paraboliques non lineaires

stability normalised walking speed a new approach for human gait perturbation research 2019 in gait stability research neither self selected walking speeds nor the same prescribed walking speed for all participants guarantee equivalent gait stability among participants furthermore these options may differentially affect the response to different gait perturbations which is problematic when comparing groups with different capacities we present a method for decreasing inter individual differences in gait stability by adjusting walking speed to equivalent margins of stability mos eighteen healthy adults walked on a split belt treadmill for two minute bouts at 0 4 m s up to 1 8 m s in 0 2 m s intervals the stability normalised walking speed mos 0 05 m was calculated using the mean mos at touchdown of the final 10 steps of each speed participants then walked for three minutes at this speed and were subsequently exposed to a treadmill belt acceleration perturbation a further 12 healthy adults were exposed to the same perturbation while walking at 1 3 m s the average of the previous group large ranges in mos were observed during the prescribed speeds 6 10 cm across speeds and walking speed significantly p 0 001 affected mos the stability normalised walking speeds resulted in mos equal or very close to the desired 0 05 m and reduced between participant variability in mos the second group of participants walking at 1 3 m s had greater inter individual variation in mos during both unperturbed and perturbed walking compared to 12 sex height and leg length matched participants from the stability normalised walking speed group the current method decreases inter individual differences in gait stability which may benefit gait perturbation and stability research in particular studies on populations with different locomotor capacities preprint https doi org 10 1101 314757

center of pressure control for balance maintenance during lateral waist pull perturbations in older adults when balance is disturbed location of the center of pressure cop contributes to a person s ability to recover from a perturbation this study investigated cop control prior to first step lift off fslo during lateral perturbations in older non fallers and fallers 38 non fallers and 16 fallers received lateral waist pulls at 5 different intensities crossover stepping responses at the intensity level where the largest number of subjects responded with crossover steps were analyzed whole body center of mass com and cop positions in the medio lateral ml direction with respect to the base of support bos and cop velocity were calculated an inverted pendulum model was used to define the bos stability boundary at fslo which was also adjusted using the cop position at fslo functional boundary no significant differences were found in the cop velocities between fallers and non fallers p 093 however the cop positions for fallers were located significantly more medial at fslo p 01 resulting in a significantly reduced functional boundary although the stability margins measures of stability based on the bos were significantly larger than zero for fallers p 004 they were not significantly different from zero for the functional boundary i e reaching the functional stability limit fallers had reduced functional limits of stability in the ml direction which would predispose them to more precarious stability conditions than non fallers this could be a cause for taking more steps than non fallers for balance recovery as we observed the functional boundary estimation may be a more sensitive marker of balance instability than the bos boundary

predicting dynamic postural instability using center of mass time to contact information our purpose was to determine whether spatiotemporal measures of center of mass motion relative to the base of support boundary could predict stepping strategies after upper body postural perturbations in humans we expected that inclusion of center of mass acceleration in such time to contact ttc calculations would give better predictions and more advanced warning of perturbation severity ttc measures were compared with traditional postural variables which do not consider support boundaries and with an inverted pendulum model of dynamic stability developed by hof et al 2005 the condition for dynamic stability journal of biomechanics 38 1 8 a pendulum was used to deliver sequentially increasing perturbations to 10 young adults who were strapped to a wooden backboard that constrained motion to sagittal plane rotation about the ankle joint subjects were instructed to resist the perturbations stepping only if necessary to prevent a fall peak center of mass and center of pressure velocity and acceleration demonstrated linear increases with postural challenge in contrast boundary relevant minimum ttc values decreased nonlinearly with postural challenge enabling prediction of stepping responses using quadratic equations when ttc calculations incorporated center of mass acceleration the quadratic fits were better and gave more accurate predictions of the ttc values that would trigger stepping responses in addition ttc minima occurred earlier with acceleration inclusion giving more advanced warning of perturbation severity our results were in agreement with ttc predictions based on hof s model and suggest that ttc may function as a control parameter influencing the postural control system s decision to transition from a stationary base of support to a stepping strategy

an approximate observer for a class of nonlinear systems abstract for a class of nonlinear multi input multi output systems an approximate observer is derived the design utilizes a change of coordinates by which the error differential equation is transformed in the observable canonical form neglecting higher order terms with respect to the set of operating points the note is completed by an example referred to elastic robots

stepping boundary of external force controlled perturbations of varying durations comparison of experimental data and model simulations abstract this study investigated the stepping boundary the force that can be resisted without stepping for force controlled perturbations of different durations twenty two healthy young adults 19 37 years old were instructed to try not to step in response to 86 different force time combinations of forward waist pulls the forces at which 50 of subjects stepped f50 were identified for each tested perturbation durations results showed that f50 decreased hyperbolically when the perturbation s duration increased and converged toward a constant value about 10 bw for longer perturbations over 1500 ms the effect of perturbation duration was critical for the shortest perturbations less than 1 s in parallel a simple function was proposed to estimate this stepping boundary considering the dynamics of a linear inverted pendulum foot model and simple balance recovery reactions we could express the maximum pulling force that can be withstood without stepping as a simple function of the perturbation duration when used with values of the main model parameters determined experimentally this function replicated adequately the experimental results this study demonstrates for the first time that perturbation duration has a major influence on the outcomes of compliant perturbations such as force controlled pulls the stepping boundary corresponds to a constant perturbation force duration product and is largely explained by only two parameters the reaction time and the displacement of the center of pressure within the functional base of support future work should investigate pathological populations and additional parameters characterizing the perturbation time profile such as the time derivative of the perturbation

a new neuro fds definition for indirect adaptive control of unknown nonlinear systems using a method of parameter hopping the indirect adaptive regulation of unknown nonlinear dynamical systems is considered in this paper the method is based on a new neuro fuzzy dynamical system neuro fds definition which uses the concept of adaptive fuzzy systems afss operating in conjunction with high order neural network functions fhonnfs since the plant is considered unknown we first propose its approximation by a special form of an fds and then the fuzzy rules are approximated by appropriate honnfs thus the identification scheme leads up to a recurrent high order neural network rhonn which however takes into account the fuzzy output partitions of the initial fds the proposed scheme does not require a priori experts information on the number and type of input variable membership functions making it less vulnerable to initial design assumptions once the system is identified around an operation point it is regulated to zero adaptively weight updating laws for the involved honnfs are provided which guarantee that both the identification error and the system states reach zero exponentially fast while keeping all signals in the closed loop bounded the existence of the control signal is always assured by introducing a novel method of parameter hopping which is incorporated in the weight updating law simulations illustrate the potency of the method and comparisons with conventional approaches on benchmarking systems are given also the applicability of the method is tested on a direct current dc motor system where it is shown that by following the proposed procedure one can obtain asymptotic regulation

adaptational responses in dynamic stability during disturbed walking in the elderly the purpose of this study was to examine the age related predictive and feedback adaptive locomotor improvements in the components of dynamic stability control during disturbed walking thirteen old 62 74 yrs and ten young 23 30 yrs male subjects performed a gait protocol on a gangway which included one covered element by exchanging this element the subjects walked either solely over hard surface or experienced a perturbation of the gait on the soft surface element the gait protocol consisted of a baseline on hard surface and an adaptation phase with 19 trials on soft or hard 2nd 8th and 19th surface the investigation of dynamic stability was made by using the margin of stability ms which was calculated as the difference between the base of support and the extrapolated center of mass cm horizontal velocity of cm and its vertical projection in anterior posterior direction as well as the eigenfrequency of an inverted pendulum generate the extrapolated cm as a result of the first unexpected disturbance ms was decreased in the step following the perturbation compared to baselines in both age groups this decrease was higher for the old participants compared to the young ones indicating a more unstable position in the step after the perturbation for the elderly in the following adaptation phase ms returned to baseline values in both age groups in the hard trial after the first unexpected perturbation both age groups increased ms at touchdown of the disturbed leg compared to baseline reflecting fast predictive adjustments our findings show that the well known age related biological impairments did not inhibit the adaptive improvements in the components of dynamic stability in the elderly however the feedback corrections after the first unexpected perturbation were less effective for the elderly this may increase the risk of falling

the condition for dynamic stability the well known condition for standing stability in static situations is that the vertical projection of the centre of mass com should be within the base of support bos on the basis of a simple inverted pendulum model an extension of this rule is proposed for dynamical situations the position of the vertical projection of the com plus its velocity times a factor rootl g should be within the bos l being leg length and g the acceleration of gravity it is proposed to name this vector quantity extrapolated centre of mass position xcom the definition suggests as a measure of stability the margin of stability b the minimum distance from xcom to the boundaries of the bos an alternative measure is the temporal stability margin tau the time in which the boundary of the bos would be reached without intervention some experimental data of subjects standing on one or two feet flatfoot and tiptoe are presented to give an idea of the usual ranges of these margins of stability example data on walking are also presented c 2004 elsevier ltd all rights reserved

active arm swing and asymmetric walking leads to increased variability in trunk kinematics in young adults abstract fall induced injuries are a leading cause for occupational injuries with the majority originating from challenging same level walking surfaces despite current perturbation and fall prevention paradigms occupational fall prevalence remains stable typically these paradigms do not account for arm swing which has been demonstrated to affect the center of mass movement during walking this study examined the effect of different arm swing on postural control during symmetric and asymmetric walking fifteen healthy young adults age 23 4 2 8 walked symmetrically and asymmetrically with three arm motions normal held and active on a split belt treadmill caren extended system motek medical amsterdam nl mean standard deviation and maximal values of trunk linear and angular velocity and whole body angular momentum were calculated in all three axes additionally step length time and width mean and coefficient of variation margin of stability and harmonic ratios were calculated compared to normal and held conditions active arm increased trunk linear and angular velocity standard deviation max velocity values mean step length and time as well as the coefficient of variation for step length time and width furthermore whole body angular momentum increased as a function of arm swing amplitude active arm swing further reduced harmonic ratios in the mediolateral and anteroposterior directions asymmetric walking increased average step time and width as well as increased the coefficient of variation for step length and time but reduced left average step length and step width coefficient of variation further asymmetric walking increased mediolateral margin of stability and reduced anteroposterior and mediolateral harmonic ratios finally results demonstrated that actively increasing arm swing increases trunk linear and angular velocity variability in healthy young adults during symmetric and asymmetric treadmill walking findings may be due to active arm swing and asymmetric walking causing a disproportional contribution to trunk and center of mass movement causing participants to modify their base of support to maintain stability

a novel error observer based adaptive output feedback approach for control of uncertain systems we develop an adaptive output feedback control methodology for nonaffine in control of uncertain systems having full relative degree given a smooth reference trajectory the objective is to design a controller that forces the system measurement to track it with bounded errors a neural network with linear parameters is introduced as an adaptive signal a simple linear observer is proposed to generate an error signal for the adaptive laws ultimate boundedness is shown through lyapunov s direct method simulations of a nonlinear second order system illustrate the theoretical results

robust single hidden layer feedforward network based pattern classifier in this paper a new robust single hidden layer feedforward network slfn based pattern classifier is developed it is shown that the frequency spectrums of the desired feature vectors can be specified in terms of the discrete fourier transform dft technique the input weights of the slfn are then optimized with the regularization theory such that the error between the frequency components of the desired feature vectors and the ones of the feature vectors extracted from the outputs of the hidden layer is minimized for the linearly separable input patterns the hidden layer of the slfn plays the role of removing the effects of the disturbance from the noisy input data and providing the linearly separable feature vectors for the accurate classification however for the nonlinearly separable input patterns the hidden layer is capable of assigning the dfts of all feature vectors to the desired positions in the frequency domain such that the separability of all nonlinearly separable patterns are maximized in addition the output weights of the slfn are also optimally designed so that both the empirical and the structural risks are well balanced and minimized in a noisy environment two simulation examples are presented to show the excellent performance and effectiveness of the proposed classification scheme

rcmac hybrid control for mimo uncertain nonlinear systems using sliding mode technology a hybrid control system integrating principal and compensation controllers is developed for multiple input multiple output mimo uncertain nonlinear systems this hybrid control system is based on sliding mode technique and uses a recurrent cerebellar model articulation controller rcmac as an uncertainty observer the principal controller containing an rcmac uncertainty observer is the main controller and the compensation controller is a compensator for the approximation error of the system uncertainty in addition in order to relax the requirement of approximation error bound an estimation law is derived to estimate the error bound the taylor linearization technique is employed to increase the learning ability of rcmac and the adaptive laws of the control system are derived based on lyapunov stability theorem and barbalat s lemma so that the asymptotical stability of the system can be guaranteed finally the proposed design method is applied to control a biped robot simulation results demonstrate the effectiveness of the proposed control scheme for the mimo uncertain nonlinear system

relating real time backpropagation and backpropagation through time an application of flow graph interreciprocity we show that signal flow graph theory provides a simple way to relate two popular algorithms used for adapting dynamic neural networks real time backpropagation and backpropagation through time starting with the flow graph for real time backpropagation we use a simple transposition to produce a second graph the new graph is shown to be interreciprocal with the original and to correspond to the backpropagation through time algorithm interreciprocity provides a theoretical argument to verify that both flow graphs implement the same overall weight update

designing and implementation of stable sinusoidal rough neural identifier a rough neuron is defined as a pair of conventional neurons that are called the upper and lower bound neurons in this paper the sinusoidal rough neural networks sr nns are used to identify the discrete dynamic nonlinear systems ddnss with or without noise in series parallel configuration in the identification of periodic nonlinear systems sinusoidal activation functions provide more efficient neural networks than the sigmoidal activation functions based on the lyapunov stability theory an online learning algorithm is developed to train the sr nns the asymptotically convergence of the identification error to zero and the boundedness of parameters as well as predictions are proved sr nns are used to identify some ddnss and the cement rotary kiln crk crk is a complex nonlinear system in the cement factory which produces the cement clinker the experiments show that the sr nns in the identification of nonlinear systems have better performances than multilayer perceptrons mlps sinusoidal neural networks and rough mlps particularly in the presence of noise

adaptive control of uncertain nonaffine nonlinear systems with input saturation using neural networks this paper presents a tracking control methodology for a class of uncertain nonlinear systems subject to input saturation constraint and external disturbances unlike most previous approaches on saturated systems which assumed affine nonlinear systems in this paper tracking control problem is solved for uncertain nonaffine nonlinear systems with input saturation to deal with the saturation constraint an auxiliary system is constructed and a modified tracking error is defined then by employing implicit function theorem mean value theorem and modified tracking error updating rules are derived based on the well known back propagation bp algorithm which has been proven to be the most relevant updating rule to control problems however most of the previous approaches on bp algorithm suffer from lack of stability analysis by injecting a damping term to the standard bp algorithm uniformly ultimately boundedness of all the signals of the closed loop system is ensured via lyapunov s direct method furthermore the presented approach employs nonlinear in parameter neural networks hence the proposed scheme is applicable to systems with higher degrees of nonlinearity using a high gain observer to reconstruct the states of the system an output feedback controller is also presented finally the simulation results performed on a duffing holmes chaotic system a generalized pendulum type system and a numerical system are presented to demonstrate the effectiveness of the suggested state and output feedback control schemes

function approximation using generalized adalines this paper proposes neural organization of generalized adalines gadalines for data driven function approximation by generalizing the threshold function of adalines we achieve the k state transfer function of gadalines which responds a unitary vector of k binary values to the projection of a predictor on a receptive field a generative component that uses the k state activation of a gadaline to trigger k posterior independent normal variables is employed to emulate stochastic predictor oriented target generation the fitness of a generative component to a set of paired data mathematically translates to a mixed integer and linear programming since consisting of continuous and discrete variables the mathematical framework is resolved by a hybrid of the mean field annealing and gradient descent methods following the leave one out learning strategy the obtained learning method is extended for optimizing multiple generative components the learning result leads to parameters of a deterministic gadaline network for function approximation numerical simulations further test the proposed learning method with paired data oriented from a variety of target functions the result shows that the proposed learning method outperforms the mlp and rbf learning methods for data driven function approximation

effects of walking speed on the step by step control of step width abstract young healthy adults walking at typical preferred speeds use step by step adjustments of step width to appropriately redirect their center of mass motion and ensure mediolateral stability however it is presently unclear whether this control strategy is retained when walking at the slower speeds preferred by many clinical populations we investigated whether the typical stabilization strategy is influenced by walking speed twelve young neurologically intact participants walked on a treadmill at a range of prescribed speeds 0 2 1 2 m s the mediolateral stabilization strategy was quantified as the proportion of step width variance predicted by the mechanical state of the pelvis throughout a step calculated as r2 magnitude from a multiple linear regression our ability to accurately predict the upcoming step width increased over the course of a step the strength of the relationship between step width and pelvis mechanics at the start of a step was reduced at slower speeds however these speed dependent differences largely disappeared by the end of a step other than at the slowest walking speed 0 2 m s these results suggest that mechanics dependent adjustments in step width are a consistent component of healthy gait across speeds and contexts however slower walking speeds may ease this control by allowing mediolateral repositioning of the swing leg to occur later in a step thus encouraging slower walking among clinical populations with limited sensorimotor control

can stability really predict an impending slip related fall among older adults the primary purpose of this study was to systematically evaluate and compare the predictive power of falls for a battery of stability indices obtained during normal walking among community dwelling older adults one hundred and eighty seven community dwelling older adults participated in the study after walking regularly for 20 strides on a walkway participants were subjected to an unannounced slip during gait under the protection of a safety harness full body kinematics and kinetics were monitored during walking using a motion capture system synchronized with force plates stability variables including feasible stability region measurement margin of stability the maximum floquet multiplier the lyapunov exponents short and long term and the variability of gait parameters including the step length step width and step time were calculated for each subject sensitivity of predicting slip outcome fall vs recovery was examined for each stability variable using logistic regression results showed that the feasible stability region measurement predicted fall incidence among these subjects with the highest sensitivity 68 4 except for the step width with an sensitivity of 60 2 no other stability variables could differentiate fallers from those who did not fall for the sample included in this study the findings from the present study could provide guidance to identify individuals at increased risk of falling using the feasible stability region measurement or variability of the step width

spatial structures and periodic travelling waves in an integro differential reaction diffusion population model an integro differential reaction diffusion equation is proposed as a model for populations where local aggregation is advantageous but intraspecific competition increases as global populations increase it is claimed that this is inherently more realistic than the usual kind of reaction diffusion model for mobile populations three kinds of bifurcation from the uniform steady state solution are considered i to steady spatially periodic structures ii to periodic standing wave solutions and iii to periodic travelling wave solutions these correspond to aggregation and motion of populations

asymptotic stability of traveling wave fronts in nonlocal reaction diffusion equations with delay abstract this paper is concerned with the asymptotic stability of traveling wave fronts of a class of nonlocal reaction diffusion equations with delay under monostable assumption we prove that the traveling wave front is exponentially stable by means of the technical weighted energy method when the initial perturbation around the wave is suitable small in a weighted norm the exponential convergent rate is also obtained finally we apply our results to some population models and obtain some new results which recover complement and or improve a number of existing ones

an observer for flexible joint robots the problem of state observation of robots that have elastic joints is discussed outputs are assumed to be the global link coordinates and their time derivatives and a nonlinear observer is proposed which asymptotically reconstructs all the robot state variables the dynamic behaviour of the observation algorithm is illustrated by simulation tests referred to a manipulator with three revolute elastic joints to verify the observer robustness the previous simulation tests were repeated by using the same observer designed for a nominal payload of 5 kg and actual robot payloads of 0 and 10 kg the differences with respect to the nominal case are not appreciable however the steady state joint errors which were about 10 sup 6 rad in the nominal case became about 10 sup 4 rad

on robust tracking with non linear model predictive control in this paper a class of stabilizing model predictive control algorithms based on an optimization problem with two different horizons control and prediction is considered particular attention is devoted to the tracking problem for reference signals constant beyond a prescribed future horizon for such a problem it is pointed out the necessity of an output feedback scheme to guarantee robust steady state zero error regulation moreover an additional constraint is introduced in the optimization problem for the robust fulfilment of the constraints on the control variable the potentiality of this approach is shown through some simulation experiments on a highly non linear chemical reactor

stable neurovisual servoing for robot manipulators in this paper we propose a stable neurovisual servoing algorithm for set point control of planar robot manipulators in a fixed camera configuration an show that all the closed loop signals are uniformly ultimately bounded uub and converge exponentially to a small compact set we assume that the gravity term and jacobian matrix are unknown radial basis function neural networks rbfnns with online real time learning are proposed for compensating both gravitational forces and errors in the robot jacobian matrix the learning rule for updating the neural network weights similar to a back propagation algorithm is obtained from a lyapunov stability analysis experimental results on a two degrees of freedom manipulator are presented to evaluate the proposed controller

predicted threshold against backward balance loss in gait the purpose of this study was to determine the minimum forward center of mass com velocity required to prevent backward loss of balance in gait as function of the initial com position we hypothesized that these threshold values would be different from those previously published for standing because of the postural differences between gait and standing to investigate this issue we constructed a seven link nine degree of freedom biomechanical model and employed dynamic optimization to estimate these threshold values under two initial postural conditions 1 the posture at the beginning of swing phase i e at toe off and 2 symmetric bipedal standing in particular for a range of possible com positions posterior to the base of support bos simulated annealing was used to search for the minimum velocity that could carry the com into the bos and avoid backward loss of balance we found that the stability boundary against backward balance loss in walking had a similar overall trend as that previously published for standing in general the minimal com velocity necessary to prevent a backward loss of balance in walking was greater than that in symmetric bipedal standing and the difference could approach 30 or more when the com started 0 5 and 1 0 foot lengths behind the bos these discrepancies suggest that simpler biomechanical models while being more efficient and easier to employ may not always be adequate for exploring stability limits of humans

qualitative theory of compartmental systems dynamic models of many processes in the biological and physical sciences which depend on local mass balance conditions give rise to systems of ordinary differential equations many nonlinear that are called compartmental systems in this paper the authors define compartmental systems specify their relations to other nonnegative systems and discuss examples of applications the authors review the qualitative results on linear and nonlinear compartmental systems including their relation to cooperative systems they review the results for linear compartmental systems and then integrate and expand the results on nonlinear compartmental systems providing a framework for unifying them under a few general theorems in the course of that they complete the solution of a problem posed by bellman and show that closed nonlinear autonomous n compartment systems can show the full gamut of possible behaviors of systems of odes finally to provide additional structure to this study the authors show how to partiti

single and multiple step balance recovery responses can be different at first step lift off following lateral waist pull perturbations in older adults abstract an inability to recover lateral balance with a single step is predictive of future falls in older adults this study investigated if balance stability at first step lift off fslo would be different between multiple and single stepping responses to lateral perturbations 54 healthy older adults received left and right waist pulls at 5 different intensities levels 1 5 crossover stepping responses at and above intensity level 3 that induced both single and multiple steps were analyzed whole body center of mass com and center of pressure cop positions in the medio lateral direction with respect to the base of support were calculated an inverted pendulum model was used to define the lateral stability boundary which was also adjusted using the cop position at fslo functional boundary no significant differences were detected in the cop positions between the responses at fslo p 0 075 indicating no difference in the functional boundaries between the responses significantly smaller stability margins were observed at first step landing for multiple steps at all levels p 0 024 while stability margins were also significantly smaller at fslo for level 3 and 4 p 0 048 these findings indicate that although reduced stability at first foot contact would be associated with taking additional steps stepping responses could also be attributable to the com motion state as early as first step lift off preceding foot contact perturbation based training interventions aimed at improving the reactive control of stability would reduce initial balance instability at first step lift off and possibly the consequent need for multiple steps in response to balance perturbations

stability properties of equilibria of classes of cooperative systems this note deals with the constant control problem for homogeneous cooperative and irreducible systems these systems serve as models for positive systems a necessary and sufficient condition for global asymptotic stability of the zero solution of this class of systems is known adding a constant control allows to shift the equilibrium point from zero to a point in the first orthant we prove that for every nontrivial nonnegative control vector a unique nontrivial equilibrium point is achieved which is globally asymptotically stable if the zero solution of the uncontrolled system is globally asymptotically stable in addition a converse result is provided finally a stability result for a particular class of kolmogorov systems is established we compare our main results to those in the literature

robust output feedback control of nonlinear stochastic systems using neural networks we present an adaptive output feedback controller for a class of uncertain stochastic nonlinear systems the plant dynamics is represented as a nominal linear system plus nonlinearities in turn these nonlinearities are decomposed into a part obtained as the best approximation given by neural networks plus a remaining part which is treated as uncertainties modeling approximation errors and neglected dynamics the weights of the neural network are tuned adaptively by a lyapunov design the proposed controller is obtained through robust optimal design and combines together parameter projection control saturation and high gain observers high performances are obtained in terms of large errors tolerance as shown through simulations

traveling waves for the diffusive nicholson s blowflies equation we consider traveling wave front solutions for the diffusive nicholson s blowflies equation on the real line the existence of such solutions is proved using the technique developed by j wu and x zou j dyn differ equations 13 3 2001 some numerical simulation using the iteration formula of wu and zou 7 is also provided

nl sub q theory checking and imposing stability of recurrent neural networks for nonlinear modeling it is known that many discrete time recurrent neural networks such as e g neural state space models multilayer hopfield networks and locally recurrent globally feedforward neural networks can be represented as nl sub q systems sufficient conditions for global asymptotic stability and input output stability of nl sub q systems are available including three types of criteria 1 diagonal scaling 2 criteria depending on diagonal dominance 3 condition number factors of certain matrices the paper discusses how narendra s 1990 1991 dynamic backpropagation procedure which is used for identifying recurrent neural networks from i o measurements can be modified with an nl sub q stability constraint in order to ensure globally asymptotically stable identified models an example illustrates how system identification of an internally stable model corrupted by process noise may lead to unwanted limit cycle behavior and how this problem can be avoided by adding the stability constraint

multilayer potts perceptrons with levenberg marquardt learning this paper presents learning multilayer potts perceptrons mlpotts for data driven function approximation a potts perceptron is composed of a receptive field and a k state transfer function that is generalized from sigmoid like transfer functions of traditional perceptrons an mlpotts network is organized to perform translation from a high dimensional input to the sum of multiple postnonlinear projections each with its own postnonlinearity realized by a weighted k state transfer function mlpotts networks span a function space that theoretically covers network functions of multilayer perceptrons compared with traditional perceptrons weighted potts perceptrons realize more flexible postnonlinear functions for nonlinear mappings numerical simulations show mlpotts learning by the levenberg marquardt lm method significantly improves traditional supervised learning of multilayer perceptrons for data driven function approximation

representations of non linear systems the narmax model abstract input output representations of non linear discrete time systems are discussed it is shown that the narmax non linear autoregressive moving average with exogenous inputs model is a general and natural representation of non linear systems and contains as special cases several existing non linear models the problem of approximating non linear input output systems is also addressed and several properties of non linear models are highlighted using simple examples