the primal dual active set strategy as a semismooth newton method this paper addresses complementarity problems motivated by constrained optimal control problems it is shown that the primal dual active set strategy which is known to be extremely efficient for this class of problems and a specific semismooth newton method lead to identical algorithms the notion of slant differentiability is recalled and it is argued that the max function is slantly differentiable in lp spaces when appropriately combined with a two norm concept this leads to new local convergence results of the primal dual active set strategy global unconditional convergence results are obtained by means of appropriate merit functions

point island dynamics under fixed rate deposition abstract we consider the dynamics of point islands during submonolayer deposition in which the fragmentation of subcritical size islands is allowed to understand asymptotics of solutions we use methods of centre manifold theory and for globalisation we employ results from the theories of compartmental systems and of asymptotically autonomous dynamical systems we also compare our results with those obtained by making the quasi steady state assumption

a moving finite element method with error estimation and refinement for one dimensional time dependent partial differential equations we discuss a moving finite element method for solving vector systems of time dependent partial differential equations in one space dimension the mesh is moved so as to equidistribute the spatial component of the discretization error in h 1 we present a method of estimating this error by using p hierarchic finite elements the error estimate is also used in an adaptive mesh refinement procedure to give an algorithm that combines mesh movement and refinement we discretize the partial differential equations in space using a galerkin procedure with piecewise linear elements to approximate the solution and quadratic elements to estimate the error a system of ordinary differential equations for mesh velocities are used to control element motions we use existing software for stiff ordinary differential equations for the temporal integration of the solution the error estimate and the mesh motion computational results using a code based on our method are presented for several examples

adaptive numerical analysis in primal elastoplasticity with hardening the quasi static viscoplastic resp elastoplastic evolution problem with isotropic or kinematic hardening is considered with emphasis on optimal convergence and adapted mesh refining in the spatial discretization within one time step of an implicit time discretization the finite element method leads to a minimisation problem for non smooth convex functions on discrete subspaces for piecewise constant resp affine ansatz functions the stress resp displacement approximations are experimentally and theoretically shown to converge linearly an a posteriori error estimate then justifies an automatic adaptive mesh refining algorithm numerical examples support the superiority of the adapted mesh

on the decay rate of discrete time linear delay systems with cone invariance this technical note is concerned with the decay rate constrained stability analysis for linear delay systems that possess cone invariant property in order to capture the decay rate of such systems we introduce a nondecreasing positive function whose reciprocal represents the decay rate under mild assumptions on the growth rate of this function an explicit condition is given to ensure that a cone preserving linear system with unbounded time varying delays is asymptotically stable with a given decay rate as typical cases necessary and sufficient conditions are given to characterize the decay rate when the delay is restricted by a linear sublinear or logarithmic growth rate finally some numerical examples are given to illustrate the effectiveness of the theoretical results

large assemblies of stochastic oscillators this paper studies the occurrence of stochastic synchronization and phase locking in large assemblies of coupled stochastic oscillators which are modelled as phaseangle stochastic processes attention will be restricted to the case of discrete phaseangle spaces these are technically much simpler than processes over continuous phase spaces and yet show an interesting range of properties stochastic synchronization occurs if the oscillator assembly obeys a large deviation principle and if the deterministic limit dynamics possesses a stable periodic orbit all relevant concepts are reviewed in section section 1 2 and the appendix in section 4 general necessary and sufficient conditions for stochastic synchronization are obtained weak and robust types of synchronization are distinguished a describing function method is formulated which is very convenient for checking the general conditions in concrete examples separate treatments of feedback gain feedback type i e positive or negative and feedback sources lead to investigations of how the occurrence of stochastic synchronization depends on any one of those feedback aspects in a sequence of gradually more realistic models section 3 4b 5a the general results are applied to assemblies of stochastic fireflies the first of these models section 3 is mathematically instructive in that it provides a good example of how the liapunov function character of large deviation rate functions can be exploited to study global properties of the corresponding deterministic limit ode the analysis of firefly assemblies culminates in a proof of stochastic firefly synchronization this result is the precise stochastic analogue of the well known proof of deterministic firefly synchronization given by mirollo strogatz 1990 in section 5 the general results of section 4 are applied to neuronal assemblies particular attention is paid to the dependence of neuronal synchronization on the feedback type that is excitatory or inhibitory signalling we find it natural and instructive to distinguish between external and internal variants of inhibition the latter in particular in the form of graded refractoriness of neurons is shown to be crucial for stochastic synchronization within one neural assembly whereas the former is instrumental for phase locking between distinct assemblies these findings are summarized and sharpened in a number of concrete predictions for real biological networks of neurons except for some topical aspects of large deviation theory reviewed in the appendix the mathematics employed in this paper are straightforward

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

continuously deforming finite elements a general class of time dependent co ordinate transformations is introduced in a variational formulation for evolution problems the variational problem is posed with respect to both solution and transformation field variables an approximate analysis using finite elements is developed from the continuous variational form modified forms of the variational functional are considered to ensure the deforming mesh is not top irregular ode system integrators are utilized to integrate the resulting semidiscrete systems in part i we consider the formulation for problems in one spatial dimension and time including in particular convection dominated flows described by the convection diffusion burgers and buckley leverett equations in part ii the extension of the method to two dimensions and supporting numerical experiments are presented

on the minus partial order in control systems abstract in this paper the minus matrix partial order is considered to introduce the concept of minus partial ordered control systems the transmission of the reachability property under this binary relation is investigated furthermore the analysis of compartmental systems leads us to consider block triangular matrices hence the existence and computation of partially ordered matrices having a similar block structure are studied these results are applied to compartmental systems to get via feedback related systems with the same block structure and ordered under the minus partial order

a combined smoothing and regularization method for monotone second order cone complementarity problems the second order cone complementarity problem soccp is a wide class of problems containing the nonlinear complementarity problem ncp and the second order cone programming problem socp recently fukushima luo and tseng siam j optim 12 2001 pp 436 460 extended some merit functions and their smoothing functions for ncp to soccp moreover they derived computable formulas for the jacobians of the smoothing functions and gave conditions for the jacobians to be invertible in this paper we propose a globally and quadratically convergent algorithm which is based on smoothing and regularization methods for solving monotone soccp in particular we study strong semismoothness and jacobian consistency which play an important role in establishing quadratic convergence of the algorithm furthermore we examine the effectiveness of the algorithm by means of numerical experiments

realization of continuous time positive linear systems positive linear systems are used in biomathematics economics and other research areas for discrete time positive linear systems part of the realization problem has been solved in this paper the solution of the corresponding problem for continuous time positive linear systems will be presented which can be deduced from that of the discrete time case by a transformation sufficient and necessary conditions for the existence of a positive realization are presented to solve the problem of minimality the solution of the factorization of positive matrices is needed

composite systems with uncertain couplings of fixed structure scaled riccati equations and the problem of quadratic stability we consider large scale systems consisting of a finite number of separate uncertain subsystems which interact via uncertain couplings of arbitrarily prescribed structure the couplings are viewed as structured perturbations of the block diagonal system representing the collection of the separate nominal subsystems the nominal system we define spectral value sets and stability radii for these time invariant structured perturbations and derive formulas for their computation scaled riccati equations are introduced to obtain explicit formulas for the stability radii with respect to time varying and possibly nonlinear perturbations of the given structure from these we derive necessary and sufficient conditions under which the stability radii with respect to time invariant and time varying perturbations are equal these results are obtained by constructing joint quadratic liapunov functions of optimal robustness with their help we prove necessary and sufficient conditions for quadratic stability and sufficient conditions for the validity of a generalized aizerman conjecture

survey constrained model predictive control stability and optimality model predictive control is a form of control in which the current control action is obtained by solving at each sampling instant a finite horizon open loop optimal control problem using the current state of the plant as the initial state the optimization yields an optimal control sequence and the first control in this sequence is applied to the plant an important advantage of this type of control is its ability to cope with hard constraints on controls and states it has therefore been widely applied in petro chemical and related industries where satisfaction of constraints is particularly important because efficiency demands operating points on or close to the boundary of the set of admissible states and controls in this review we focus on model predictive control of constrained systems both linear and nonlinear and discuss only briefly model predictive control of unconstrained nonlinear and or time varying systems we concentrate our attention on research dealing with stability and optimality in these areas the subject has developed in our opinion to a stage where it has achieved sufficient maturity to warrant the active interest of researchers in nonlinear control we distill from an extensive literature essential principles that ensure stability and use these to present a concise characterization of most of the model predictive controllers that have been proposed in the literature in some cases the finite horizon optimal control problem solved on line is exactly equivalent to the same problem with an infinite horizon in other cases it is equivalent to a modified infinite horizon optimal control problem in both situations known advantages of infinite horizon optimal control accrue

stabilizing predictive control of nonlinear arx models in this paper a predictive control algorithm for nonlinear discrete time systems is presented starting from a state space model conditions for the asymptotic tracking of constant reference signals in a neighbourhood of a given equilibrium are first derived then it is shown that the system under control can be locally described in terms of a suitable narx nonlinear arx model which in practice can be identified by means of well established techniques for the narx model a receding horizon predictive control algorithm is proposed which guarantees local stability and robust asymptotic tracking in the neighbourhood of the equilibrium conditions for local stability and tracking are given in terms of reachability observability and transmission zeros of the linearization of the original state space system around the equilibrium an example is reported to illustrate the effectiveness of the proposed method

continuation newton methods severely nonlinear problems can only be solved by some homotopy continuation method an example of a homotopy method is the continuous newton method which however must be discretized which leads to the damped step version of newton s method the standard newton iteration method for solving systems of nonlinear equations f u 0 must be modified in order to get global convergence i e convergence from any initial point the control of steplengths in the damped step newton method can lead to many small steps and slow convergence furthermore the applicability of the method is restricted in as much as it assumes a nonsingular and everywhere differentiable mapping f classical continuation methods are surveyed then a new method in the form of a coupled newton and load increment method is presented and shown to have a global convergence already from the start and second order of accuracy with respect to the load increment step and with less restrictive regularity assumptions than for the standard newton method the method is applied for an elastoplastic problem with hardening

smoothing methods and semismooth methods for nondifferentiable operator equations we consider superlinearly convergent analogues of newton methods for nondifferentiable operator equations in function spaces the superlinear convergence analysis of semismooth methods for nondifferentiable equations described by a locally lipschitzian operator in rn is based on rademacher s theorem which does not hold in function spaces we introduce a concept of slant differentiability and use it to study superlinear convergence of smoothing methods and semismooth methods in a unified framework we show that a function is slantly differentiable at a point if and only if it is lipschitz continuous at that point an application to the dirichlet problems for a simple class of nonsmooth elliptic partial differential equations is discussed

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

non smooth multisurface plasticity and viscoplasticity loading unloading conditions and numerical algorithms rate independent plasticity and viscoplasticity in which the boundary of the elastic domain is defined by an arbitrary number of yield surfaces intersecting in a non smooth fashion are considered in detail it is shown that the standard kuhn tucker optimality conditions lead to the only computationally useful characterization of plastic loading on the computational side an unconditionally convergent return mapping algorithm is developed which places no restrictions aside from convexity on the functional forms of the yield condition flow rule and hardening law the proposed general purpose procedure is amenable to exact linearization leading to a closed form expression of the so called consistent algorithmic tangent moduli for viscoplasticity a closed form algorithm is developed based on the rate independent solution the methodology is applied to structural elements in which the elastic domain possesses a non smooth boundary numerical simulations are presented that illustrate the excellent performance of the algorithm

consistent tangent operators for rate independent elastoplasticity abstract it is shown that for problems involving rate constitutive equations such as rate independent elastoplasticity the notion of consistency between the tangent stiffness operator and the integration algorithm employed in the solution of the incremental problem plays a crucial role in preserving the quadratic rate of asymptotic convergence of iterative solution schemes based upon newton s method within the framework of closest point projection algorithms a methodology is presented whereby tangent operators consistent with this class of algorithms may be systematically developed to wit associative j 2 flow rules with general nonlinear kinematic and isotropic hardening rules as well as a class of non associative flow rules are considered the resulting iterative solution scheme preserves the asymptotic quadratic convergence characteristic of newton s method whereas use of the socalled elastoplastic tangent in conjunction with a radial return integration algorithm a procedure often employed results in newton type of algorithms with suboptimal rate of convergence application is made to a set of numerical examples which include saturation hardening laws of exponential type

technical communique adaptive control for nonlinear nonnegative dynamical systems nonnegative and compartmental models are widespread in engineering systems and life sciences and play a key role in the understanding of these systems in this paper we develop a direct adaptive control framework for nonlinear uncertain nonnegative and compartmental dynamical systems the proposed framework is lyapunov based and guarantees partial asymptotic set point regulation that is asymptotic set point regulation with respect to part of the closed loop system states associated with the plant in addition the adaptive controller guarantees that the physical system states remain in the nonnegative orthant of the state space

a projected newton algorithm for the dual convex program of elastoplasticity summary in this paper we study a dual optimization problem that arises when taking a mathematical programming approach to incremental state update in nonlinear problems the mathematical programming approach stems from energy based descriptions of constitutive models we describe a projected newton algorithm to solve the dual optimization problem this algorithm requires solution of an unconstrained optimization problem at the integration point level rather than a constrained one as carried out by classical return mapping schemes especially implementation of multi surface plasticity models is no more involved than that of single surface models we explore characteristics and performance of the projected newton algorithm through numerical examples insights gained from such a further exploration of mathematical programming algorithms are likely to aid in development of successive convex programming approaches to geometric nonlinear and other non convex problems such as non associated flow models copyright 2014 john wiley sons ltd

optimal moving grids for time dependent partial differential equations abstract various adaptive moving grid techniques for the numerical solution of time dependent partial differential equations have been proposed the precise criterion for grid motion varies but most techniques will attempt to give grids on which the solution of the partial differential equation can be well represented we investigate moving grids on which the solutions of the linear heat conduction and viscous burgers equation in one space dimension are optimally approximated precisely we report the results of numerical calculations of optimal moving grids for piecewise linear finite element approximation of pde solutions in the least squares norm

receding horizon control of nonlinear systems the receding horizon control strategy provides a relatively simple method for determining feedback control for linear or nonlinear systems the method is especially useful for the control of slow nonlinear systems such as chemical batch processes where it is possible to solve sequentially open loop fixed horizon optimal control problems online the method has been shown to yield a stable closed loop system when applied to time invariant or time varying linear systems it is shown that the method also yields a stable closed loop system when applied to nonlinear systems

input to state stability of efficient robust h mpc scheme for nonlinear systems propose an efficient constrained h nmpc with guaranteed iss w r t bounded disturbances use piecewise affine h control and augmented pldi models to decrease conservatism of nmpc use pldi method to turn the non convex min max problem into a semi definite programming present a sufficient condition in form of lmis to ensure the iss of the proposed nmpc scheme apply the proposed nmpc to some fast systems such as mass carts and vehicular platoon in this work we present an efficient h model predictive control mpc scheme with guaranteed input to state stability iss for constrained nonlinear systems subject to unknown but bounded disturbances the nonlinear system is represented by using some given inclusion polytope the notion of iss is introduced to derive the sufficient condition in terms of linear matrix inequalities lmis which ensures the iss of the closed loop system in order to reduce the online computational demand of mpc the non convex min max optimization problem is converted to a minimization problem in form of lmis a suboptimal mpc algorithm is then addressed to further decrease the computational demand the applicability of the proposed results is illustrated by two numerical examples of a mass cart and a vehicular platoon

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

equidistributing principles in moving finite element methods abstract recently miller and his co workers proposed a moving finite element method based on a least squares principle this was followed by a similar method by the present authors using a petrov galerkin approach in this paper the two methods are compared in particular it is shown that both methods move their nodes according to an approximate equidistributing principle this observation leads to a criterion for the placement of the nodes it is also shown that the penalty function designed by miller may also be used with the petrov galerkin method finally numerical examples are given illustrating the performance of the two methods

robust receding horizon control of constrained nonlinear systems we present a method for the construction of a robust dual mode receding horizon controller which can be employed for a wide class of nonlinear systems with state and control constraints and model error the controller is dual mode in a neighborhood of the origin the control action is generated by a linear feedback controller designed for the linearized system outside this neighborhood receding horizon control is employed existing receding horizon controllers for nonlinear continuous time systems which are guaranteed to stabilize the nonlinear system to which they are applied require the exact solution at every instant of an optimal control problem with terminal equality constraints these requirements are considerably relaxed in the dual mode receding horizon controller presented in this paper stability is achieved by imposing a terminal inequality rather than an equality constraint only approximate minimization is required a variable time horizon is permitted robustness is achieved by employing conservative state and stability constraint sets thereby permitting a margin of error the resultant dual mode controller requires considerably less online computation than existing receding horizon controllers for nonlinear constrained systems

stabilizing receding horizon control of nonlinear time varying systems a receding horizon control scheme for nonlinear time varying systems is proposed which is based on a finite horizon optimization problem with a terminal state penalty the penalty is equal to the cost that would be incurred over an infinite horizon by applying a locally stabilizing linear control law to the nonlinear system assuming only stabilizability of the linearized system around the desired equilibrium the new scheme ensures exponential stability of the equilibrium as the length of the optimization horizon goes from zero to infinity the domain of attraction moves from the basin of attraction of the linear controller toward the basin of attraction of the infinite horizon nonlinear controller stability robustness in the face of system perturbations is also established

grading functions and mesh redistribution we consider the problem of determining an appropriate grading of a mesh for piecewise polynomial interpolation and for approximate solution of two point boundary value problems by finite difference or finite element methods an analysis of optimality of the mesh and optimal grading functions in various norms and seminorms for the interpolation problem leads to the formulation of an adaptive mesh redistribution algorithm for boundary value problems in one dimension error estimates are given and numerical results presented to demonstrate the performance of the scheme and compare alternative redistribution criteria

self adjusting grid methods for one dimensional hyperbolic conservation laws it is shown how to automatically adjust the grid to follow the dynamics of the numerical solution of hyperbolic conservation laws the grid motion is determined by averaging the local characteristic velocities of the equations with respect to the amplitudes of the signals the resulting algorithm is a simple extension of many currently popular godunov type methods computer codes using one of these methods can be easily modified to add the moving mesh as an option numerical examples are given that illustrate the improved accuracy of godunov s and roe s methods on a self adjusting mesh

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

moving finite element methods for evolutionary problems i theory abstract in this paper the first of two on the subject we present a unified approach to moving and fixed finite element methods for evolutionary problems in terms of projections the central theoretical results are concerned with moving finite elements for one dimensional scalar problems particularly hyperbolic equations with shocks but the viewpoint extends to general systems in any number of dimensions

an adaptive moving grid method for one dimensional systems of partial differential equations we describe a fully adaptive moving grid method for solving initial boundary value problems for systems of one space dimensional partial differential equations whose solutions exhibit rapid variations in space and time the method based on finite differences is of the lagrangian type and has been derived through a co ordinate transformation which leads to equidistribution in space of the second derivative our technique is intermediate between static regridding methods where nodes remain fixed for intervals of time and continuously moving grid methods where the node movement and the pde integration are fully coupled in our approach the computation of the moving grids and the solution on these grids are carried out separately while the nodes are moved at each time step two error monitors have been implemented one to govern the time step selection and the other to eventually adapt the number of moving nodes the method allows the use of different moving grids for different components in the pde system numerical experiments are presented for a set of five sample problems from the literature including two problems from combustion

spectral conditions for stability and stabilization of positive equilibria for a class of nonlinear cooperative systems nonlinear cooperative systems associated to vector fields that are concave or subhomogeneous describe well interconnected dynamics that are of key interest for communication biological economical and neural network applications for this class of positive systems we provide conditions that guarantee existence uniqueness and stability of strictly positive equilibria these conditions can be formulated directly in terms of the spectral radius of the jacobian of the system if control inputs are available then it is shown how to use state feedback to stabilize an equilibrium point in the interior of the positive orthant

efficient numerical methods for the large scale parallel solution of elastoplastic contact problems parts of the work of the first author were supported by the deutsche forschungsgemeinschaft dfg within priority program 1480 modelling simulation and compensation of thermal effects for complex machining processes through grant number bl 256 11 3 the third author is supported by the national science foundation through award no oci 1148116 the second and third authors are supported in part by the computational infrastructure in geodynamics initiative cig through the national science foundation under award no ear 0949446 and the university of california davis this publication is based in part on the work supported by award no kus c1 016 04 made by king abdullah university of science and technology kaust some computations for this paper were performed on the brazos and hurr clusters at the institute for applied mathematics and computational science iamcs at texas a m university part of brazos was supported by nsf award dms 0922866 hurr is supported by award no kus c1 016 04 made by king abdullah university of science and technology kaust

moving finite elements i we present new and general numerical methods for dealing with problems whose solutions develop sharp transition layers or near shocks these methods allow many nodes automatically to concentrate in the critical regions and move with them for clarity of exposition we concentrate on the space of piecewise linear functions with movable nodes with burgers equation as our test equation but the generalization to much more general spaces and equations including even certain previous moving vorticity blobs of the first author and s doss for the navier stokes equations becomes clear in this paper we present the theoretical and computational details of our scheme along with computational trial runs for burgers equation showing that the nodes do concentrate sharply and move with the shocks as desired the conclusiveness of these preliminary numerical trials is marred somewhat by the fact that we never successfully debugged a newton s method for our implicit stiff ode solver and were thus limited to ver

output tracking of constrained nonlinear processes with offset free input to state stable fuzzy predictive control this paper develops an efficient offset free output feedback predictive control approach to nonlinear processes based on their approximate fuzzy models as well as an integrating disturbance model the estimated disturbance signals account for all the plant model mismatch and unmodeled plant disturbances an augmented piecewise observer constructed by solving some linear matrix inequalities is used to estimate the system states and the lumped disturbances based on the reference from an online constrained target generator the fuzzy model predictive control law can be easily obtained by solving a convex semi definite programming optimization problem subject to several linear matrix inequalities the resulting closed loop system is guaranteed to be input to state stable even in the presence of observer estimation error the zero offset output tracking property of the proposed control approach is proved and subsequently demonstrated by the simulation results on a strongly nonlinear benchmark plant

piecewise smoothness local invertibility and parametric analysis of normal maps this paper is concerned with properties of the euclidean projection map onto a convex set defined by finitely many smooth convex inequalities and affine equalities under a constant rank constraint qualification we show that the projection map is piecewise smooth pc1 hence bouligand differentiable or directionally differentiable and a relatively simple formula is given for the b derivative these properties of the projection map are used to obtain inverse and implicit function theorems for associated normal maps using a new characterization of invertibility of a pc1 function in terms of its b derivative an extension of the implicit function theorem which does not require local uniqueness is also presented degree theory plays a major role in the analysis of both the locally unique case and its extension

on the superlinear convergence in computational elasto plasticity we consider the convergence properties of return algorithms for a large class of rate independent plasticity models based on recent results for semismooth functions we can analyze these algorithms in the context of semismooth newton methods guaranteeing local superlinear convergence this recovers results for classical models but also extends to general hardening laws multi yield plasticity and to several non associated models the superlinear convergence is also numerically shown for a large scale parallel simulation of drucker prager elasto plasticity and an example for the modified cam clay model

solution of one time step problems in elastoplasticity by a slant newton method we discuss a solution algorithm for quasi static elastoplastic problems with hardening such problems can be described by a time dependent variational inequality where the displacement and the plastic strain fields serve as primal variables after discretization in time one variational inequality of the second kind is obtained per time step and can be reformulated as a minimization problem with a convex energy functional which depends smoothly on the displacement and nonsmoothly on the plastic strain there exists an explicit formula for minimizing the energy functional with respect to the plastic strain for a given displacement by substitution the energy functional can be written as a functional depending only on the displacement the theorem of moreau from convex analysis states that the energy functional is differentiable with an explicitly computable first derivative the second derivative of the energy functional does not exist due to the lack of smoothness of the plastic strain across the elastoplastic interface which separates the continuum in elastically and plastically deformed parts a newton like method exploiting slanting functions of the energy functional s first derivative instead of the nonexistent second derivative is applied such a method is called a slant newton method for short the local superlinear convergence of the algorithm in the discrete case is shown and sufficient regularity assumptions are formulated which would guarantee the local superlinear convergence also in the continuous case

stability theory for nonnegative and compartmental dynamical systems with time delay abstract nonnegative and compartmental dynamical system models are derived from mass and energy balance considerations and involve the exchange of nonnegative quantities between subsystems or compartments these models are widespread in biological and physical sciences and play a key role in understanding these processes a key physical limitation of such systems is that transfers between compartments is not instantaneous and realistic models for capturing the dynamics of such systems should account for material in transit between compartments in this paper we present necessary and sufficient conditions for stability of nonnegative and compartmental dynamical systems with time delay specifically asymptotic stability conditions for linear and nonlinear nonnegative dynamical systems with time delay are established using linear lyapunov krasovskii functionals

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

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

brief paper on receding horizon feedback control receding horizon feedback control rhfc was originally introduced as an easy method for designing stable state feedback controllers for linear systems here those results are generalized to the control of nonlinear autonomous systems and we develop a performance index which is minimized by the rhfc inverse optimal control problem previous results for linear systems have shown that desirable nonlinear controllers can be developed by making the rhfc horizon distance a function of the state that functional dependence was implicit and difficult to implement on line here we develop similar controllers for which the horizon distance is an easily computed explicit function of the state

an interior point algorithm for elastoplasticity the problem of small deformation rate independent elastoplasticity is treated using convex programming theory and algorithms a finite step variational formulation is first derived after which the relevant potential is discretized in space and subsequently viewed as the lagrangian associated with a convex mathematical program next an algorithm based on the classical primal dual interior point method is developed several key modifications to the conventional implementation of this algorithm are made to fully exploit the nature of the common elastoplastic boundary value problem the resulting method is compared to state of the art elastoplastic procedures for which both similarities and differences are found finally a number of examples are solved demonstrating the capabilities of the algorithm when applied to standard perfect plasticity hardening multisurface plasticity and problems involving softening copyright 2006 john wiley sons ltd

a duality based path following semismooth newton method for elasto plastic contact problems a fenchel dualization scheme for the one step time discretized contact problem of quasi static elasto plasticity with combined kinematic isotropic hardening is considered the associated path is induced by a coupled moreau yosida tikhonov regularization of the dual problem the sequence of solutions to the regularized problems is shown to converge strongly to the optimal displacement stress strain triple of the original elasto plastic contact problem in the space continuous setting this property relies on the density of the intersection of certain convex sets which is shown as well it is also argued that the mappings associated with the resulting problems are newton or slantly differentiable consequently each regularized subsystem can be solved mesh independently at a local superlinear rate of convergence for efficiency purposes an inexact path following approach is proposed and a numerical validation of the theoretical results is given

convergence of newton type methods in incremental return mapping analysis of elasto plastic problems abstract the incremental finite element algorithm with return mapping stress computation is considered for the solution of problems of elasto plasticity this algorithm performed in load steps leads to the necessity of solving large scale nonlinear systems the properties of these systems are investigated in the presented paper together with two iterative techniques for their solution the main results of the paper are rigorous proofs of the convergence of the inexact initial stiffness method and the local quadratic convergence of the inexact newton method with the consistent tangent operator

a quasi infinite horizon nonlinear model predictive control scheme with guaranteed stability we present in this paper a novel nonlinear model predictive control scheme that guarantees asymptotic closed loop stability the scheme can be applied to both stable and unstable systems with input constraints the objective functional to be minimized consists of an integral square error ise part over a finite time horizon plus a quadratic terminal cost the terminal state penalty matrix of the terminal cost term has to be chosen as the solution of an appropriate lyapunov equation furthermore the setup includes a terminal inequality constraint that forces the states at the end of the finite prediction horizon to lie within a prescribed terminal region if the jacobian linearization of the nonlinear system to be controlled is stabilizable we prove that feasibility of the open loop optimal control problem at time t 0 implies asymptotic stability of the closed loop system the size of the region of attraction is only restricted by the requirement for feasibility of the optimization problem due to the input and terminal inequality constraints and is thus maximal in some sense

handbook of differential equations chapter headings definitions and concepts transformations exact analytical methods exact methods for odes exact methods for pdes approximate analytical methods numerical methods concepts numerical methods for odes numerical methods for pdes list of tables list of programs list of figures subject index

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

transit time and age distributions for nonlinear time dependent compartmental systems many processes in nature are modeled using compartmental systems reservoir pool box systems usually they are expressed as a set of first order differential equations describing the transfer of matter across a network of compartments the concepts of age of matter in compartments and the time required for particles to transit the system are important diagnostics of these models with applications to a wide range of scientific questions until now explicit formulas for transit time and age distributions of nonlinear time dependent compartmental systems were not available we compute densities for these types of systems under the assumption of well mixed compartments assuming that a solution of the nonlinear system is available at least numerically we show how to construct a linear time dependent system with the same solution trajectory we demonstrate how to exploit this solution to compute transit time and age distributions in dependence on given start values and initial age distributions furthermore we derive equations for the time evolution of quantiles and moments of the age distributions our results generalize available density formulas for the linear time independent case and mean age formulas for the linear time dependent case as an example we apply our formulas to a nonlinear and a linear version of a simple global carbon cycle model driven by a time dependent input signal which represents fossil fuel additions we derive time dependent age distributions for all compartments and calculate the time it takes to remove fossil carbon in a business as usual scenario

brief paper componentwise ultimate bound and invariant set computation for switched linear systems we present a novel ultimate bound and invariant set computation method for continuous time switched linear systems with disturbances and arbitrary switching the proposed method relies on the existence of a transformation that takes all matrices of the switched linear system into a convenient form satisfying certain properties the method provides ultimate bounds and invariant sets in the form of polyhedral and or mixed ellipsoidal polyhedral sets is completely systematic once the aforementioned transformation is obtained and provides a new sufficient condition for practical stability we show that the transformation required by our method can easily be found in the well known case where the subsystem matrices generate a solvable lie algebra and we provide an algorithm to seek such transformation in the general case an example comparing the bounds obtained by the proposed method with those obtained from a common quadratic lyapunov function computed via linear matrix inequalities shows a clear advantage of the proposed method in some cases

stability margins of nonlinear receding horizon control via inverse optimality using the nonlinear analog of the fake riccati equation developed for linear systems we derive an inverse optimality result for several receding horizon control schemes this inverse optimality result unifies stability proofs and shows that receding horizon control possesses the stability margins of optimal control laws

a tfeti domain decomposition solver for elastoplastic problems we propose an algorithm for the efficient parallel implementation of elastoplastic problems with hardening based on the so called tfeti total finite element tearing and interconnecting domain decomposition method we consider an associated elastoplastic model with the von mises plastic criterion and the linear isotropic hardening law such a model is discretized by the implicit euler method in time and the consequent one time step elastoplastic problem by the finite element method in space the latter results in a system of nonlinear equations with a strongly semismooth and strongly monotone operator the semismooth newton method is applied to solve this nonlinear system corresponding linearized problems arising in the newton iterations are solved in parallel by the above mentioned tfeti domain decomposition method the proposed tfeti based algorithm was implemented in matlab parallel environment and its performance was illustrated on a 3d elastoplastic benchmark numerical results for different time discretizations and mesh levels are presented and discussed and a local quadratic convergence of the semismooth newton method is observed

on the stability of mesh equidistribution strategies for time dependent partial differential equations abstract we study the stability of several mesh equidistribution schemes for time dependent partial differential equations in one space dimension the schemes move a finite difference or finite element mesh so that a given quantity is uniform over the domain we consider mesh moving methods that are based on solving a system of ordinary differential equations for the mesh velocities and show that some of these methods are unstable with respect to an equidistributing mesh when the partial differential system is dissipative using linear perturbation techniques we are able to develop simple criteria for determining the stability of a particular method and show how to construct stable differential systems for the mesh velocities several examples illustrating stable and unstable mesh motions are presented

the dynamical systems approach to differential equations bulletin new series of the american mathematical society volume 11 number 1 july 1984 the dynamical systems approach to differential equations by morris w hirsch 1 this harmony that human intelligence believes it discovers in nature does it exist apart from that intelligence no without doubt a reality completely independent of the spirit which conceives it sees it or feels it is an impossibility a world so exterior as that even if it existed would be forever inaccessible to us but what we call objective reality is in the last analysis that which is common to several thinking beings and could be common to all this common part we will see can be nothing but the harmony expressed by mathematical laws h poincare la valeur de la science p 9 ignorance of the roots of the subject has its price no one denies that modern formulations are clear elegant and precise it s just that it s impossible to comprehend how any one ever thought of them m spivak a comprehensive introduction to differential geometry introduction the mathematical subject we call dynamical systems was fathered by poin care developed sturdily under birkhoff and has enjoyed a vigorous new growth for the last twenty years as i try to show in chapter i it is interesting to look at this mathematical development as the natural outcome of a much broader theme which is as old as science itself the universe is a sytem which changes in time every mathematician has a particular way of thinking about mathematics but rarely makes it explicit yet such perspectives in any particular field can be of great value to nonexperts who must apply the results of the field or who want to learn them in some fields the points of view of its practitioners cluster around several comparatively clearly defined concepts and insights dynamical systems theory is one of them the basic concepts go back to poincare the main thrust of chapters i and ii is to explain rather discursively some of received by the editors december 14 1983 1980 mathematics subject classification primary 00a25 00a99 01a45 01a55 01a60 34a40 34c35 34d10 34d30 35b05 35b35 35b40 35b50 35b30 35k55 54h20 58f25 58f40 58f12 58f10 58d25 58d07 46a40 46e10 47h07 47h20 92a15 92a17 secondary 06f30 35b65 58f13 35j60 46e05 92 03 90 03 90a16 supported in part by national science foundation and institute for advanced study 1984 american mathematical society 0273 0979 84 1 00 25 per page

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

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

a nonsmooth version of newton s method newton s method for solving a nonlinear equation of several variables is extended to a nonsmooth case by using the generalized jacobian instead of the derivative this extension includes the b derivative version of newton s method as a special case convergence theorems are proved under the condition of semismoothness it is shown that the gradient function of the augmented lagrangian forc2 nonlinear programming is semismooth thus the extended newton s method can be used in the augmented lagrangian method for solving nonlinear programs

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

finite element analysis and algorithms for single crystal strain gradient plasticity summary we provide optimal a priori estimates for finite element approximations of a model of rate independent single crystal strain gradient plasticity the weak formulation of the problem takes the form of a variational inequality in which the primary unknowns are the displacement and slips on the prescribed slip systems as well as the back stress associated with the vectorial microstress it is shown that the return mapping algorithm for local plasticity can be applied element wise to this non local setting some numerical examples illustrate characteristic features of the non local model copyright 2012 john wiley sons ltd

positive linear observers for linear compartmental systems linear compartmental systems are mathematical systems that are frequently used in biology and mathematics the inputs states and outputs of such systems are positive because they denote amounts or concentrations of material for linear dynamic systems the observer problem has been solved the purpose of the observer problem is to determine a linear observer such that the state can be approximated the difference between the state and its estimate should converge to zero the interpretation in terms of a physical system requires that an estimate of the state be positive like the state itself in this paper conditions on the system matrices are presented that guarantee that there exists a positive linear observer such that both the error converges to zero and the estimate is positive

nonlinear complementarity functions for plasticity problems with frictional contact in this paper a unifying framework for the numerical treatment of frictional contact in combination with elastoplasticity with hardening is presented both kinds of problems lead to the mathematical structure of variational inequalities which are discretized by introducing additional variables for the contact stresses or the deviatoric stresses leading to a mixed formulation by defining a family of nonlinear complementarity functions which can be applied to both frictional and plastic yield conditions these inequality constraints are reformulated as equalities combined with the equilibrium equations a system of nonlinear equations is obtained that is solved in terms of a semismooth newton method to obtain a larger domain of convergence and better stability properties the introduction of additional scaling parameters is motivated and their benefit to the convergence of the scheme is demonstrated due to the locality of the contact and plastic constraints the resulting method can be interpreted as a primal dual active set strategy furthermore for linear hardening laws our method is a generalization of the well known radial return algorithm which is obtained for a special suboptimal choice of the plastic scaling parameters the efficiency and the generality of the proposed quasi newton scheme is demonstrated by several numerical examples including the simulation of a three dimensional contact problem with several elastoplastic bodies exponential isotropic hardening and coulomb friction

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