control lyapunov razumikhin functions and robust stabilization of time delay systems motivated by control lyapunov functions and razumikhin theorems on stability of time delay systems we introduce the concept of control lyapunov razumikhin functions clrf the main reason for considering clrfs is construction of robust stabilizing control laws for time delay systems most existing universal formulas that apply to clfs are not applicable to clrfs it turns out that the domination redesign control law applies achieving global practical stability and under an additional assumption global asymptotic stability this additional assumption is satisfied in the practically important case when the quadratic part of a clrf is itself a clrf for the jacobian linearization of the system the clrf based domination redesign possesses robustness to input unmodeled dynamics including an infinite gain margin while in general construction of clrfs is an open problem we show that for several classes of time delay systems a clrf can be constructed in a systematic way

control of an unstable reaction diffusion pde with long input delay abstract a smith predictor like design for compensation of arbitrarily long input delays is available for general controllable possibly unstable lti finite dimensional systems such a design has not been proposed previously for problems where the plant is a pde we present a design and stability analysis for a prototype problem where the plant is a reaction diffusion parabolic pde with boundary control the plant has an arbitrary number of unstable eigenvalues and arbitrarily long delay with an unbounded input operator the predictor based feedback design extends fairly routinely within the framework of infinite dimensional backstepping however the stability analysis contains interesting features that do not arise in predictor problems when the plant is an ode the unbounded character of the input operator requires that the stability be characterized in terms of the h 1 rather than the usual l 2 norm of the actuator state the analysis involves an interesting structure of interconnected pdes of parabolic and first order hyperbolic types where the feedback gain kernel for the undelayed problem becomes an initial condition in a pde arising in the compensator design for the problem with input delay space and time variables swap their roles in an interesting manner throughout the analysis

behaviour of the frobenius map in a noncommutative world abstract we study various properties of the frobenius map x x p on a noncommutative algebra r over a field f of positive characteristic p we call r perfect whenever is surjective more generally we say that r is additively respectively multiplicatively p power closed if for every x y r there exists a positive integer n such that x p n y p n respectively x p n y p n is a p power in r if for example n were a ring homomorphism as when r is commutative then r would be additively and multiplicatively p power closed we show that a finite dimensional unital algebra r is lie nilpotent if and only if r is additively respectively multiplicatively p power closed and each of its simple homomorphic images has schur index 1 since not all finite dimensional perfect division algebras are lie nilpotent the schur index condition cannot be omitted we deduce that similar results hold for the class of all finitely generated pi algebras moreover for this same class we give a positive solution to the following problem reminiscent of the problems of kurosh and levitzki is every finitely generated perfect algebra finite dimensional

estimation of aquifer parameters under transient and steady state conditions 2 uniqueness stability and solution algorithms paper 2 of this three part series starts with a discussion of the question under what conditions is the aquifer inverse problem well posed after defining the terms uniqueness identifiability and stability theoretical considerations and synthetic examples are used to demonstrate that ill posedness can be mitigated by including prior information about the parameters in the estimation criterion to be minimized at the same time the inclusion of such information is shown to be insufficient to guarantee uniqueness and stability in all cases several test problems in the recent literature which have resulted in pessimistic conclusions about the solvability of the aquifer inverse problem are shown to be ill posed a question is thus raised about the validity of these conclusions in the general case various conjugate gradient algorithms coupled with the adjoint state finite element method for computing the gradient of the estimation criterion and with newton s method for determining the optimum step size downgradient are compared a marked improvement in the rate at which these algorithms converge is shown to be achieved by switching from one method to another when the former slows down or fails to converge

robust compensation of delay and diffusive actuator dynamics without distributed feedback this paper deals with robust observer based output feedback stabilization of systems whose actuator dynamics can be described in terms of partial differential equations pdes more specifically delay dynamics first order hyperbolic pde and diffusive dynamics parabolic pde are considered the proposed controllers have a pde observer based structure the main novelty is that stabilization for an arbitrarily large delay or diffusion domain length is achieved while distributed integral terms in the control law are avoided the exponential stability of the closed loop in both cases is proved using lyapunov functionals even in the presence of small uncertainties in the time delay or the diffusion coefficient the feasibility of this approach is illustrated in simulations using a second order plant with an exponentially unstable mode

estimating unsaturated soil hydraulic properties from tension disc infiltrometer data by numerical inversion tension disc infiltrometers are becoming increasingly popular devices for in situ measurement of the unsaturated hydraulic properties of soil tension infiltration data are generally used to evaluate the parametersks and ain gardner s exponential model of the unsaturated hydraulic conductivity either two measurements using different disc diameters or measurements with a single disc but using multiple pressure heads are then used in this paper we describe a parameter estimation procedure which combines the levenberg marquardt nonlinear parameter optimization method involving weighted least squares with a quasi three dimensional numerical model which solves the variably saturatedflow equation by numerical inversion of richards equation the unknown parameters in van genuchten s model of the unsaturated soil hydraulic properties are estimated from observed cumulative infiltration data during transient waterflow additional measurements of the pressure head or water content as well as a penalty function for constraining the unknown parameters to remain in some feasible region bayesian estimation can be optionally included into the parameter estimation procedure the problem of optimal sampling design that is selecting the best points in space and time for making measurements is addressed by studying the sensitivity of the objective function to changes in the optimized hydraulic parameters we calculate objective functions based on available cumulative infiltration pressure head and water content measurements and also on several combinations of these data the behavior of the objective function in three dimensional parameter space is evaluated by means of a series of two dimensional response surfaces the utility of the parameter estimation procedure is demonstrated using numerically generated data the sensitivity of the procedure to different initial estimates of the model parameters is also discussed

estimation of root water uptake parameters by inverse modeling with soil water content data 1 in this paper we have tested the feasibility of the inverse modeling approach to derive root water uptake parameters rwup from soil water content data using numerical experiments for three differently textured soils and for an optimal drying period the rwup of interest are the rooting depth and the bottom root length density in a first step a thorough sensitivity analysis was performed this showed that soil water content dynamics is relatively insensitive to rwup and that the sensitivity depends on the texture of the considered soil for medium fine textured soil the sensitivity is particularly low due to relatively high unsaturated hydraulic conductivity values these ones allow a compensating effect to occur i e vertical unsaturated water fluxes overshadowing in some way the root water uptake in a second step we analyzed the well posedness of the solution stability and nonuniqueness when only rwup are optimized for this case the inverse problem is clearly ill posed except for the estimation of the rooting depth parameter for coarse and the very fine textured soils in a third step we addressed the case where rwup are estimated simultaneously with additional parameters of the system i e with soil hydraulic parameters for this case our study showed that the inverse problem is well posed for the coarse and very fine textured soils allowing for the estimation of both rwup of interest provided that a powerful global optimization algorithm is used on the contrary the estimation of rwup is unfeasible for medium fine textured soil due to the compensating effect of the vertical unsaturated water flows in conclusion we can state that the inverse modeling approach can be applied to derive rwup for some soils coarse and very fine textured and that the feasibility is strongly improved if the rwup are simultaneously optimized with additional parameters nevertheless more detailed research is needed to apply the inverse modeling approach to real cases for which additional issues are likely to be encountered such as soil heterogeneity and root dynamics

new formulation of predictors for finite dimensional linear control systems with input delay we consider a one dimensional controlled reaction diffusion equation where the control acts on the boundary and is subject to a constant delay such a model is a paradigm for more general parabolic systems coupled with a transport equation we prove that this is possible to stabilize in h 1 norm this process by means of an explicit predictor based feedback control that is designed from a finite dimensional subsystem the implementation is very simple and efficient and is based on standard tools of pole shifting our feedback acts on the system as a finite dimensional predictor we compare our approach with the backstepping method

stabilization of an unstable reaction diffusion pde cascaded with a heat equation abstract we consider a control problem of an unstable reaction diffusion parabolic pde cascaded with a heat equation through a boundary where the heat influx of the heat equation is fed into the temperature of the reaction diffusion equation and the control actuator is designed at the another boundary of the heat equation a backstepping invertible transformation is used to design a suitable boundary feedback control so that the closed loop system is equivalent to a cascade of pde pde system which is shown to be exponentially stable in a suitable hilbert space with the dirichlet boundary input from the heat equation the reaction diffusion pde is shown to be exponentially stable in h 1 0 1 numerical simulations are presented to illustrate the convergence of the state of the reaction diffusion equation

closed form boundary state feedbacks for a class of 1 d partial integro differential equations in this paper a problem of boundary stabilization of a class of linear parabolic partial integro differential equations p i des in one dimension is considered using the method of backstepping avoiding spatial discretization required in previous efforts the problem is formulated as a design of an integral operator whose kernel is required to satisfy a hyperbolic p i de the kernel p i de is then converted into an equivalent integral equation and by applying the method of successive approximations the equation s well posedness and the kernel s smoothness are established it is shown how to extend this approach to design optimally stabilizing controllers an adaptation mechanism is developed to reduce the conservativeness of the inverse optimal controller and the performance bounds are derived for a broad range of physically motivated special cases feedback laws are constructed explicitly and the closed loop solutions are found in closed form a numerical scheme for the kernel p i de is proposed its numerical effort compares favorably with that associated with operator riccati equations

uniqueness and observability of conceptual rainfall runoff model parameters the percolation process examined many researchers have expressed concerns regarding the uniqueness of parameter estimates for conceptual rainfall runoff r r models obtained through calibration recent studies sorooshian et al this issue sorooshian and gupta this issue have revealed that even though stochastic parameter estimation techniques can help the problems are not all due to inefficiencies in the calibration techniques used but are caused by the manner in which the model is structurally formulated thus even when calibrated under ideal conditions simulation studies it is often impossible to obtain unique estimates for the parameters it is possible to resolve this problem at least in part by appropriate reparameterizations of the pertinent model equations in this paper the percolation equation of the soil moisture accounting model of the national weather service river forecast system sma nwsrfs will be discussed it is shown that a logical reparameterization of this equation can result in conditions that improve the chances of obtaining unique parameter estimates it is believed that these results have implications for other conceptual r r models in which similar approaches are used in the representation of the percolation infiltration process

time varying input and state delay compensation for uncertain nonlinear systems a robust controller is developed for uncertain second order nonlinear systems subject to simultaneous unknown time varying state delays and known sufficiently small time varying input delays in addition to additive sufficiently smooth disturbances an integral term composed of previous control values facilitates a delay free open loop error system and the development of the feedback control structure a stability analysis based on lyapunov krasovskii lk functionals guarantees uniformly ultimately bounded tracking under the assumption that the delays are bounded and slowly varying numerical simulations illustrate robustness of the developed method to various combinations of simultaneous input and state delays

effective and efficient global optimization for conceptual rainfall runoff models the successful application of a conceptual rainfall runoff crr model depends on how well it is calibrated despite the popularity of crr models reports in the literature indicate that it is typically difficult if not impossible to obtain unique optimal values for their parameters using automatic calibration methods unless the best set of parameters associated with a given calibration data set can be found it is difficult to determine how sensitive the parameter estimates and hence the model forecasts are to factors such as input and output data error model error quantity and quality of data objective function used and so on results are presented that establish clearly the nature of the multiple optima problem for the research crr model sixpar these results suggest that the crr model optimization problem is more difficult than had been previously thought and that currently used local search procedures have a very low probability of successfully finding the optimal parameter sets next the performance of three existing global search procedures are evaluated on the model sixpar finally a powerful new global optimization procedure is presented entitled the shuffled complex evolution sce ua method which was able to consistently locate the global optimum of the sixpar model and appears to be capable of efficiently and effectively solving the crr model optimization problem

robustness and safe sampling of distributed delay control laws for unstable delayed systems in the control of delayed systems by a finite spectrum assignment fsa in the control law the integral over the time delay of a function of past control appears this assignment is in fact available for continuous delayed process independently of the stability of the latter which is very interesting since smith predictor is usually only used with stable processes nevertheless in case of fsa control implementation this integral control should be sampled so that spectrum assignment is not necessarily preserved and an unstable discrete closed loop can be obtained in this technical note fsa integral control robustness with respect to prediction time uncertainty is analyzed for an unstable continuous linear system a transformation approach is also proposed to understand the effects of different ways of sampling control laws in a last part a case study shows how simpson approximation of integral control law leads to an unstable digital closed loop

an lmi condition for the robustness of constant delay linear predictor feedback with respect to uncertain time varying input delays abstract this paper discusses the robustness of the constant delay predictor feedback in the case of an uncertain time varying input delay specifically we study the stability of the closed loop system when the predictor feedback is designed based on the knowledge of the nominal value of the time varying delay by resorting to an adequate lyapunov krasovskii functional we derive an lmi based sufficient condition ensuring the exponential stability of the closed loop system for small enough variations of the time varying delay around its nominal value these results are extended to the feedback stabilization of a class of diagonal infinite dimensional boundary control systems in the presence of a time varying delay in the boundary control input

output feedback boundary control of a heat pde sandwiched between two odes we present designs for exponential stabilization of an ordinary differential equation ode heat partial differential equation pde ode coupled system where the control actuation only acts in one ode the combination of pde backstepping and ode backstepping is employed in a state feedback control law and in an observer that estimates pde and two ode states using only one pde boundary measurement based on the state feedback control law and the observer the output feedback control law is then proposed the exponential stability of the closed loop system and the boundedness and exponential convergence of the control law are proved via lyapunov analysis finally numerical simulations validate the effectiveness of this method for the sandwiched system

finite spectrum assignment of unstable time delay systems with a safe implementation the instability mechanisms related to the implementation of distributed delay controllers in the context of finite spectrum assignment were studied in detail in the past few years in this note we introduce a distributed delay control law that assigns a finite closed loop spectrum and whose implementation with a sum of point wise delays is safe this property is obtained by implicitly including a low pass filter in the control loop this leads to a closed loop characteristic quasipolynomial of retarded type and not one of neutral type which was shown to be a cause of instability in previous schemes

compensating actuator and sensor dynamics governed by diffusion pdes for possibly unstable ode systems with actuator delay predictor based infinite dimensional feedback can compensate for actuator delay of arbitrary length and achieve stabilization we extend this concept to another class of pde ode cascades where the infinite dimensional part of the plant is of diffusive rather than convective type we derive predictor like feedback laws and observers with explicit gain kernels the gain kernels involve second order matrix exponentials of the system matrix of the ode plant which is the result of the second order in space character of the actuator sensor dynamics the construction of the kernel functions is performed using the continuum version of the backstepping method robustness to small perturbations in the diffusion coefficient is proved

input to state stability and inverse optimality of predictor feedback for multi input linear systems for the exact predictor feedback control design recently introduced by tsubakino krstic and oliveira for multi input linear systems with distinct input delays we establish input to state stability with respect to additive plant disturbances as well as robustness to constant multiplicative uncertainties affecting the inputs we also show that the exact predictor feedback controller is inverse optimal with respect to a meaningful differential game problem our proofs capitalize on the availability of a backstepping transformation which is formulated appropriately in a recursive manner an example computed numerically is provided to illustrate the validity of the developed results

predictor based control for an uncertain euler lagrange system with input delay controlling a nonlinear system with actuator delay is a challenging problem because of the need to develop some form of prediction of the nonlinear dynamics developing a predictor based controller for an uncertain system is especially challenging in this paper tracking controllers are developed for an euler lagrange system with time delayed actuation parametric uncertainty and additive bounded disturbances the developed controllers represent the first input delayed controllers developed for uncertain nonlinear systems that use a predictor to compensate for the delay the results are obtained through the development of a novel predictor like method to address the time delay in the control input lyapunov krasovskii functionals are used within a lyapunov based stability analysis to prove semi globally uniformly ultimately bounded tracking experimental results illustrate the performance and robustness of the developed control methods

nonlinear predictor feedback for input affine systems with distributed input delays prediction based transformation is applied to control affine systems with distributed input delays transformed system state is calculated as a prediction of the system s future response to the past input with future input set to zero stabilization of the new system leads to lyapunov krasovskii proven stabilization of the original one conditions on the original system are smooth linearly bounded open loop vector field and smooth uniformly bounded input vectors about the transformed system which turns out to be affine in the undelayed input but with input vectors dependent on the input history and system state we assume existence of a linearly bounded stabilizing feedback and quadratically bounded control lyapunov function if all assumptions hold globally then achieved exponential stability is global otherwise local analytical and numerical control design examples are provided

determining soil hydraulic functions from evaporation experiments by a parameter estimation approach experimental verifications and numerical studies a parameter estimation method is developed for the determination of unsaturated soil hydraulic properties from evaporation experiments under laboratory conditions variables used in the inversion procedure are soil water pressure heads at various positions and total soil weights both measured as a function of time during the experiment unknown parameters of different analytical expressions used to describe the soil hydraulic properties are estimated by coupling a finite difference solution of the richards equation with a nonlinear optimization problem this problem is formulated by minimizing the deviations between the numerical solution of the transient flow process and the real system response measured during the experiment minimization of the objective function is performed using a version of the levenberg marquardt s method the procedure also provides information about the uncertainty in parameter estimates the performance of the selected parametric relationships is evaluated and the applicability and accuracy of the proposed inverse method are shown by comparing estimated water retention and hydraulic conductivity functions with experimental results obtained via the instantaneous profile method parameter sensitivity analyses and stability of the inverse solutions are discussed with reference to the originally designed evaporation experiment and to an evaporation method that is developed with a view to reducing experimental efforts further insights into the properties of existence and uniqueness of inverse solutions are gained by examining contour plots of the objective functions under varying experimental conditions the results confirm the reliability and flexibility of the proposed method and suggest that the evaporation flux imposed at the upper soil surface may determine the well posedness of the optimization problem

global stabilisation of nonlinear delay systems with a compact absorbing set predictor based stabilization results are provided for nonlinear systems with input delays and a compact absorbing set the control scheme consists of an inter sample predictor a global observer an approximate predictor and a nominal controller for the delay free case the control scheme is applicable even to the case where the measurement is sampled and possibly delayed the closed loop system is shown to have the properties of global asymptotic stability and exponential convergence in the disturbance free case robustness with respect to perturbations of the sampling schedule and robustness with respect to measurement errors in contrast to existing predictor feedback laws the proposed control scheme utilizes an approximate predictor of a dynamic type which is expressed by a system described by integral delay equations additional results are provided for systems that can be transformed to systems with a compact absorbing set by means of a preliminary predictor feedback

brief paper lyapunov tools for predictor feedbacks for delay systems inverse optimality and robustness to delay mismatch we consider lti finite dimensional completely controllable but possibly open loop unstable plants with arbitrarily long actuator delay and the corresponding predictor based feedback for delay compensation we study the problem of inverse optimal re design of the predictor based feedback law we obtain a simple modification of the basic predictor based controller which employs a low pass filter and has been proposed previously by mondie and michiels for achieving robustness to discretization of the integral term in the predictor feedback law the key element in our work is the employment of an infinite dimensional backstepping transformation and the resulting lyapunov function for the infinite dimensional systems consisting of the state of the ode plant and the delay state the lyapunov function allows us to quantify the lyapunov stability properties under the modified feedback the inverse optimality of the feedback and its disturbance attenuation properties for the basic predictor feedback the availability of the lyapunov function also allows us to prove robustness to small delay mismatch in both positive and negative directions

not all feedback stabilized hyperbolic systems are robust with respect to small time delays in their feedbacks we present two examples of hyperbolic partial differential equations which are stabilized by boundary feedback controls and then destabilized by small delays in these controls we show that in a general case when the controls are distributed stabilized hyperbolic systems possess nontrivial periodic solutions if small time delays are introduced into their feedbacks we also indicate by means of an example that the general case of this phenomenon is harder to demonstrate for boundary control problems

extremum seeking for static maps with delays in this paper we address the design and analysis of multi variable extremum seeking for static maps subject to arbitrarily long time delays both gradient and newton based methods are considered multi input systems with different time delays in each individual input channel as well as output delays are dealt with the phase compensation of the dither signals and the inclusion of predictor feedback with a perturbation based averaging based estimate of the hessian allow to obtain local exponential convergence results to a small neighborhood of the optimal point even in the presence of delays the stability analysis is carried out using backstepping transformation and averaging in infinite dimensions capturing the infinite dimensional state due the time delay in particular a new backstepping like transformation is introduced to design the predictor for the gradient based extremum seeking scheme with multiple and distinct input delays the proposed newton based extremum seeking approach removes the dependence of the convergence rate on the unknown hessian of the nonlinear map to be optimized being user assignable as in the literature free of delays a source seeking example illustrates the performance of the proposed delay compensated extremum seeking schemes

delay dependent stabilization of linear systems with time varying state and input delays the integral inequality method is a new way of tackling the delay dependent stabilization problem for a linear system with time varying state and input delays email protected t ax t a 1x t h 1 t b 1u t b 2u t h 2 t in this paper a new integral inequality for quadratic terms is first established then it is used to obtain a new state and input delay dependent criterion that ensures the stability of the closed loop system with a memoryless state feedback controller finally some numerical examples are presented to demonstrate that control systems designed based on the criterion are effective even though neither a b 1 nor a a 1 b 1 is stabilizable

robust energy to peak filter design for stochastic time delay systems abstract this paper considers the robust energy to peak filtering problem for uncertain stochastic time delay systems the stochastic uncertainties appear in both the dynamic and the measurement equations and the state delay is assumed to be time varying attention is focused on the design of full order and reduced order filters guaranteeing a prescribed energy to peak performance for the filtering error system sufficient conditions are formulated in terms of linear matrix inequalities lmis and the corresponding filter design is cast into a convex optimization problem which can be efficiently handled by using standard numerical algorithms in addition the results obtained are further extended to more general cases where the system matrices also contain uncertain parameters the most frequently used ways of dealing with parameter uncertainties including polytopic and norm bounded characterizations have been taken into consideration with convex optimization problems obtained for the design of desired robust energy to peak filters

razumikhin type theorems for hybrid system with memory in this paper we address the stability problem of hybrid systems with memory which are newly developed to model hybrid dynamic systems affected by delays for such systems stability criteria are developed based on razumikhin type conditions which are usually applied in the delay systems we prove that the hybrid system with memory is uniformly globally pre asymptotically stable by small gain theorem besides a relaxed razumikhin type stability criterion is also proposed which does not require strict decrease of the lyapunov razumikhin function during jumps several examples are given to illustrate the effectiveness and generality of the proposed results

new predictive scheme for the control of lti systems with input delay and unknown disturbances a new predictive scheme is proposed for the control of linear time invariant lti systems with a constant and known delay in the input and unknown disturbances it has been achieved to include disturbances effect in the prediction even though there are completely unknown the artstein reduction is then revisited thanks to the computation of this new prediction an extensive comparison with the standard scheme is presented throughout the article it is proved that the new scheme leads to feedback controllers that are able to reject perfectly constant disturbances for time varying ones a better attenuation is achieved for a wide range of perturbations and for both linear and nonlinear controllers a criterion is given to characterize this class of perturbations finally some simulations illustrate the results

stability and l2 gain analysis for switched delay systems a delay dependent method in this paper we study stability and l 2 gain for a class of switched systems with time varying delays sufficient conditions for exponential stability and weighted l 2 gain are developed for a class of switching signals with average dwell time these conditions are delay dependent and are given in the form of linear matrix inequalities lmis as a special case of such switching signals we can obtain exponential stability and normal l 2 gain under arbitrary switching signals the state decay estimate is explicitly given two examples illustrate the effectiveness and applicability of the proposed method

on the identification of macroscopic root water uptake parameters from soil water content observations 1 in this paper we analyze the identification problem of macroscopic root water uptake parameters from soil water content observations for this study the macroscopic root water uptake is considered to be linearly decreasing with depth with a and b parameters conditioning respectively the maximum root water uptake at the surface and the decreasing rate with depth for identification of parameter a and b two different identification approaches are tested using a detailed soil moisture data set consisting of vertical profiles measured with time domain reflectometry tdr and neutron probe on 28 locations within a small maize cropped field during a dry period of 26 days the first approach is based on a simplified water balance while the second one uses an integrated soil vegetation atmosphere transfer svat model in an inverse mode results of the simplified water balance show first that the root water uptake measured within the field is quite variable with cv ranging from 22 to 34 for the root uptake parameters a and b respectively furthermore positive correlation between a and b suggests that low superficial root water uptake could be compensated by high deep root water uptake second numerical simulations used to test the validity of this simplified approach show that the method is quite robust at least for a certain range of a parameter values 0 008 a 0 013 for b and for all investigated differently textured soils except the coarse sand to investigate the feasibility and the robustness of the second approach we address the problems of insensitivity instability and nonuniqueness by means of numerical simulations results show for soils with different textures that the soil water content and to a lesser extent the time derivative of soil water content are quite insensitive to root water uptake parameters at least compared to soil hydraulic parameters furthermore instability analysis clearly illustrates that root water uptake parameters are quite and even very instable with respect to small uncertainties on the apparently known parameters e g soil parameters finally results show that if root water uptake plus additional other parameters e g soil parameters are simultaneously optimized nonuniqueness of parameter sets must be expected therefore a robust identification of root water uptake parameters by means of a full svat inversion is unlikely to be achieved during a dry period with soil water content observations at least when some other parameters driving the system like soil hydraulic properties are not error free in this context further in depth research is needed to investigate if the use of longer periods characterized by both drying and redistribution events may increase the success of a full svat inversion finally to extend the results of this study we recommend applying a similar analysis to other macroscopic conceptual root water uptake models

robustness of nonlinear predictor feedback laws to time and state dependent delay perturbations much recent progress has been achieved for stabilization of linear and nonlinear systems with input delays that are long and dependent on either time or the plant state provided the dependence is known in this paper we consider the delay variations as unknown and study robustness of nominal constant delay predictor feedbacks under delay variations that depend on time and the state we show that when the delay perturbation and its rate have sufficiently small magnitude the local asymptotic stability of the closed loop system under the nominal predictor based design is preserved for the special case of linear systems and under only time varying delay perturbations we prove robustness of global exponential stability of the predictor feedback when the delay perturbation and its rate are small in any one of four different metrics we present two examples one that is concerned with the control of a dc motor through a network and one of a teleoperation like system

a global multilevel coordinate search procedure for estimating the unsaturated soil hydraulic properties we present a new inverse modeling procedure to characterize the hydraulic properties of partially saturated soils from soil moisture measurements during a natural transient flow experiment the inversion of the governing one dimensional richards equation is carried out using the global multilevel coordinate search optimization algorithm in sequential combination with the local nelder mead simplex algorithm gmcs nms we introduce this optimization method in the area of unsaturated zone hydrology since it is adapted for solving accurately and efficiently complex nonlinear problems several numerical experiments have been conducted to evaluate the proposed inversion method using synthetic error free and error contaminated data for different textured soils inversion of the simulated error free data and examination of the related response surfaces demonstrated the uniqueness of the inverse solution and the suitability of the gmcs nms strategy when identifying four key parameters of the hydraulic functions described by the mualem van genuchten model inversion of the error contaminated data proved further the good stability of the inverse solution that is consistent with the needs required by real experiments

an adaptive smith controller for time delay systems with relative degree n 2 abstract this paper addresses the control of time delay systems whose relative degree does not exceed two an adaptive smith controller together with an adaptive law similar to the delay free case is proposed by using lyapunov krasovskii functionals for an appropriate model transformation of the original system semiglobal stability of the closed loop system and asymptotic convergence of the output error is established strict positive realness together with the low relative degree of the plant is exploited to establish the stability properties robustness properties of the adaptive controller are briefly discussed

brief paper observer based control of a class of time delay nonlinear systems having triangular structure time delay systems constitute a special class of dynamical systems that are frequently present in many fields of engineering it has been shown in the literature that the existence of a stabilizing observer based controller is related to delay dependent conditions that are generally satisfied for a small time delay motivating works towards reducing the conservatism of the results are among the on going research topics especially when partial state measurements are imposed this paper investigates the problem of observer based stabilization of a class of time delay nonlinear systems written in triangular form first we show that a delay nonlinear observer is globally convergent under the global lipschitz condition of the system nonlinearity then it is shown that a parameterized linear feedback that uses the observer states can stabilize the system whatever the size of the delay an illustrative example is provided to approve the theoretical results

rapid exponential stabilisation of linear kdv equation with long input delay on the left boundary in this paper we consider the one dimensional linear kdv korteweg de vries equation posed in bounded interval with delay boundary control acting on the left boundary by dirichlet condition where

the nilpotency of the radical in a finitely generated p i ring abstract let r x 1 x k be a p i ring satisfying a monic polynomial identity one of its coefficients is 1 where is a central noetherian subring it is proven that n r the nil radical of r is nilpotent as a corollary by taking f a field we settle affirmatively the open problem posed in c procesi rings with polynomial identities p 186 marcel dekker new york 1973 we prove the jacobson radical of a finitely generated p i algebra is nilpotent

compensating a string pde in the actuation or sensing path of an unstable ode how to control an unstable linear system with a long pure delay in the actuator path this question was resolved using predictor or finite spectrum assignment designs in the 1970s here we address a more challenging question how to control an unstable linear system with a wave partial differential equation pde in the actuation path physically one can think of this problem as having to stabilize a system to whose input one has access through a string the challenges of overcoming string wave dynamics in the actuation path include their infinite dimension finite propagation speed of the control signal and the fact that all of their infinitely many eigenvalues are on the imaginary axis in this technical note we provide an explicit feedback law that compensates the wave pde dynamics at the input of an linear time invariant ordinary differential equation and stabilizes the overall system in addition we prove robustness of the feedback to the error in a priori knowledge of the propagation speed in the wave pde finally we consider a dual problem where the wave pde is in the sensing path and design an exponentially convergent observer

input delay compensation of linear systems with both state and input delays by nested prediction abstract in this paper we consider the input delay compensation of linear systems with both state and input delays under the condition that the open loop time delay systems in the absence of input delay can be stabilized by delayed state feedback a nested predictor based approach is established to predict the future states so that the delays in the input are compensated it is shown that the compensated closed loop system in the presence of input delay possesses the same characteristic equation as the closed loop system in the absence of input delay the proposed approach can be generalized to general linear systems having multiple state delays and or multiple input delays to implement the nested predictor based controllers by applying numerical integration approaches an augmented nested predictor based approach by adding input filters is proposed two numerical examples are worked out to show the effectiveness of the proposed approach

on distributed delay in linear control laws part i discrete delay implementations this note proposes two approaches to approximate distributed delay in linear control laws and furthermore to implement it in the z domain and in the s domain the h sup spl infin norm of the approximation error converges to 0 when the number n of approximation steps approaches spl infin hence the instability problem due to the approximation error which has been widely studied in recent years does not exist provided that n is large enough moreover the static gain is guaranteed so that no extra efforts are needed to retain the steady state performance as by products two new formulas for the forward and backward rectangular rules are obtained these formulas are more accurate than the conventional ones when the integrand has an exponential term

one two and three dimensional root water uptake functions for transient modeling although solutions of multidimensional transient water flow can be obtained by numerical modeling their application may be limited as root water uptake is generally considered to be one or two dimensional only this is especially the case for trees the first objective of this paper is to test the suitability of a three dimensional root water uptake model for the simultaneous simulation of transient soil water flow around an almond tree the soil hydraulic and root water uptake parameters were optimized by minimizing the residuals between measured and simulated water content data water content was measured in a three dimensional grid around a sprinkler irrigated almond tree for a 16 day period following irrigation a second objective was to compare the performance and results of the three dimensional flow model with one and two dimensional root water uptake models for this purpose measured water contents were aggregated in the x and y direction in the one dimensional case and in the radial direction for the two dimensional uptake model for the estimation of root water uptake model parameters a genetic algorithm was used to estimate the approximate global minimum of the parameter space whereas final parameters were determined using the simplex optimization algorithm with the optimized root water uptake parameters simulated and measured water contents during the 16 day period were in excellent agreement for all root water uptake models most significantly the spatial variation in flux density below the rooting zone decreased when reducing multidimensional root water uptake to fewer dimensions thereby justifying the proposed multidimensional approach

input delay compensation of linear systems with both state and input delays by adding integrators abstract this paper studies stabilization of linear systems with both state and input delays a dynamic input delay compensator obtained by adding integrators is established to compensate the input delays that can be arbitrarily large with the input delay compensator the original stabilization problem reduces to the problem of stabilizing an augmented linear time delay system without input delay three methods are also proposed to design stabilizing controllers for the augmented linear time delay system the first method is based on linear matrix inequalities lmis and the second method is based on model reduction the third method is based on pole placement and is built for the particular case that the original time delay system has only a pure delayed state vector on its right hand side for this method the optimal gain such that the decay rate of the closed loop system is maximized is also proposed the effectiveness of the proposed approaches is illustrated by three linear time delay systems that are open loop unstable

analyses of infiltration events in relation to determining soil hydraulic properties by inverse problem methodology at the field scale because of the relatively large number of observation points required to estimate the spatial distributions of hydraulic properties application of inversion procedures must be based on a characteristic of the flow that for a given point in the field can be measured with relative ease and can be used as input for the inversion procedure suggesting the use of infiltration data for this purpose and recognizing the fact that a basic requirement for the design of a transient flow experiment is that the resulting inverse problem be sufficiently well posed to allow solution this paper addresses the question under which circumstances the resulting inverse problem is well posed utilizing the concepts of identifiability uniqueness and stability for this purpose three different models of the soil hydraulic properties were analyzed the main conclusion of this study is that when infiltration data measured at the darcy scale are used as input for the inversion procedure the inclusion of prior information on a single measurable parameter the saturated conductivity ks in the estimation criterion will enhance the likelihood of uniqueness and stability of the inverse solution provided that the structure of the hydraulic model is sufficiently simple however since for a particular situation it is impossible to determine a priori whether the resultant inverse problem is well posed or not this must be carried out only a posteriori by solving the problem several times with different initial parameter estimates accompanied by an analysis of the associated estimation errors

prediction based control for lti systems with uncertain time varying delays and partial state knowledge abstractthe stability of a prediction based controller for linear time invariant lti systems is studied in the presence of time varying input and output delays the uncertain delay case is treated as well as the partial state knowledge case the reduction method is used in order to prove the convergence of the closed loop system including the state observer the predictor and the plant explicit conditions that guarantee the closed loop stability are given thanks to a lyapunov razumikhin analysis simulations illustrate the theoretical results

linear systems with delayed controls a reduction linear systems with delayed control action are transformed into systems without delays under an absolute continuity condition the new system is an ordinary differential control equation in the general case the new system is a measure differential control system it is shown how the controllability stabilization and various optimization problems can be analyzed via the reduced systems

stabilization of nonlinear delay systems using approximate predictors and high gain observers we provide a solution to the heretofore open problem of stabilization of systems with arbitrarily long delays at the input and output of a nonlinear system using output feedback only the solution is global employs the predictor approach over the period that combines the input and output delays addresses nonlinear systems with sampled measurements and with control applied using a zero order hold and requires that the sampling holding periods be sufficiently short though not necessarily constant our approach considers a class of globally lipschitz strict feedback systems with disturbances and employs an appropriately constructed successive approximation of the predictor map a high gain sampled data observer and a linear stabilizing feedback for the delay free system the obtained results guarantee robustness to perturbations of the sampling schedule and different sampling and holding periods are considered the approach is specialized to linear systems where the predictor is available explicitly

stability theorems for delay differential inclusions this technical note addresses stability problems of delay differential inclusions a chain rule is proposed for a wide class of lyapunov krasovskii functionals which are not necessarily invariantly differentiable we also obtain an invariance like theorem where the derivative of the candidate functional is bounded above by a continuous negative semidefinite function several examples are given to show the effectiveness of the results

solving the estimation identification problem in two phase flow modeling in this paper a procedure is presented to solve the estimation identification problem in two phase flow modeling given discrete observations made on the system response an optimum parameter set is derived for an appropriate conceptual model by solving the inverse problem using standard optimization techniques subsequently a detailed error analysis is performed and nonlinearity effects are considered we discuss the iterative process of model identification and parameter estimation for a ventilation test performed at the grimsel rock laboratory switzerland a numerical model of the ventilation drift and the surrounding crystalline rock matrix is developed evaporation of moisture at the drift surface and the propagation of the unsaturated zone into the formation are simulated a sensitivity analysis is performed to identify the parameters to be estimated absolute permeability and two parameters of van genuchten s characteristic curves are subsequently determined based on measurements of negative water potentials evaporation rates and gas pressure data the performance of the minimization algorithm and the system behavior for the optimum parameter set are discussed the study shows that a field experiment conducted under two phase flow conditions can be successfully reproduced by taking into account a variety of physical processes and that it is possible to reliably determinemore the two phase hydraulic properties that are related to the given conceptual model 32 refs 8 figs 7 tabs less

delay robustness of linear predictor feedback without restriction on delay rate robustness is established for the predictor feedback for linear time invariant systems with respect to possibly time varying perturbations of the input delay with a constant nominal delay the prior results have addressed qualitatively constant delay perturbations robustness of stability in l 2 norm of actuator state and delay perturbations with restricted rate of change robustness of stability in h 1 norm of actuator state the present work provides simple formulas that allow direct and accurate computation of the least upper bound of the magnitude of the delay perturbation for which the exponential stability in supremum norm on the actuator state is preserved while the prior work has employed lyapunov krasovskii functionals constructed via backstepping the present work employs a particular form of small gain analysis two cases are considered the case of measurable possibly discontinuous time varying perturbations and the case of constant perturbations

control of transport pde nonlinear ode cascades with state dependent propagation speed in this paper we deal with the control of a transport partial differential equation nonlinear ordinary differential equation pde nonlinear ode cascade system in which the transport coefficient depends on the ode state we develop a pde based predictor feedback boundary control law which compensates the transport dynamics of the actuator and guarantees global asymptotic stability of the closed loop system the stability proof is based on an infinite dimensional backstepping transformation and a lyapunov like argument the relation of the pde ode cascade with a state dependent propagation speed to an ode system with a state dependent input delay which is defined implicitly via an integral of past values of the ode state is also highlighted and the corresponding equivalent predictor feedback design is presented together with an alternative proof of global asymptotic stability of the closed loop system based on the construction of a lyapunov functional the practical relevance of our control framework is illustrated in an example that is concerned with the control of a metal rolling process

the standard h sub spl infin problem in systems with a single input delay the standard h sub spl infin problem is solved for lti systems with a single pure input lag the solution is based on state space analysis mixing a finite dimensional and an abstract evolution model utilizing the relatively simple structure of these distributed systems the associated operator riccati equations are reduced to a combination of two algebraic riccati equations and one differential riccati equation over the delay interval the results easily extend to finite time and time varying problems where the algebraic riccati equations are substituted by differential riccati equations over the process time duration

stabilization of nonlinear systems with time varying input and state delays by approximate predictor in this paper the stabilization problem of nonlinear systems with time varying input and state delays is considered by an approximate predictor due to the introduction of state delays the nonlinear dynamic without state delays is used to predict the plant state and a new error term is introduced into the approximation error between the prediction value and the future state of the plant by lyapunov krasovskii functional and small gain argument the stability of the whole closed loop system is guaranteed provided that the sampling period the predictor accuracy and the upper bound of state delays satisfy an inequality constraint the effectiveness of the proposed results is illustrated by a numerical example

lie solvable enveloping algebras of characteristic two abstract lie solvable restricted enveloping algebras were characterized by riley and shalev except when the ground field is of characteristic 2 we resolve the characteristic 2 case here which completes the classification as an application of our result we obtain a characterization of ordinary lie algebras over any field whose enveloping algebra is lie solvable

pi algebras generated by nilpotent elements of bounded index abstract let r be an associative algebra over a field f of positive characteristic p we address the following problem if r is generated by nilpotent elements with bounded index under what conditions can we conclude that r itself is nil of bounded index we prove that whenever r satisfies the engel condition and p 0 or r is lie soluble and p 2 then the conclusion holds along the way we prove that if r satisfies the engel condition then there exists a positive integer n such that the map x x p n is additive the converse also holds when f is infinite or r is generated by nilpotent elements

lie identities on enveloping algebras of restricted lie superalgebras abstract let l be a restricted lie superalgebra with its restricted enveloping algebra u l over a field f of characteristic p 2 then u l can be viewed both as a lie algebra and a lie superalgebra we characterize l when u l is lie solvable lie nilpotent or lie super nilpotent

connections between razumikhin type theorems and the iss nonlinear small gain theorem a razumikhin type theorem that guarantees input to state stability for functional differential equations with disturbances is established using the nonlinear small gain theorem the result is used to show that input to state stabilizability for nonlinear finite dimensional control systems is robust in an appropriate sense to small time delays at the input also relaxed razumikhin type conditions guaranteeing global asymptotic stability for differential difference equations are given

when is a power of the frobenius map on a noncommutative ring a homomorphism abstract let x x p be the frobenius map on an associative unital ring r with prime characteristic p it is well known that whenever r is commutative n is a ring homomorphism for all positive integers n the converse however is not true in general indeed we prove that if r is m engel for some positive integer m then there exists a positive integer n 0 depending only on m such that for all n n 0 n is a ring homomorphism with central image conversely if any one of the following conditions holds n respects addition n respects multiplication n respects lie multiplication or the image of n is commutative then r is m engel for some m depending only on n consequently if is surjective and any one of the aforementioned conditions holds then r must be commutative

stabilization by means of approximate predictors for systems with delayed input sufficient conditions for global stabilization of nonlinear systems with delayed input by means of approximate predictors are presented an approximate predictor is a mapping which approximates the exact values of the stabilizing input for the corresponding system with no delay a systematic procedure for the construction of approximate predictors is provided for globally lipschitz systems the resulting stabilizing feedback can be implemented by means of a dynamic distributed delay feedback law illustrative examples show the efficiency of the proposed control strategy

pointwise stabilisation of a string with time delay in the observation abstractpointwise stabilisation is proposed in this paper for a string equation where the observation signal is subject to a time delay different from the boundary control the feedback stabiliser is acting at the middle joint of the string well posedness of the open loop system and solvability of the observer are shown first an observer system is then designed to estimate the state at the time interval when the observation is available and a predictor system is designed to predict the state at the time interval when the observation is not available pointwise output feedback controller is introduced to make the closed loop system asymptotically stable for the non smooth initial values and exponentially stable for the smooth initial values respectively simulation results demonstrate that the output feedback based on the observer and predictor effectively stabilises the pointwise control system with time delay