discrete time nonlinear h control with measurement feedback abstract this paper deals with the problem of h control via measurement feedback with internal stability for discrete time nonlinear systems using the theory of discrete time dissipative systems and differential game we first present a parameterization of a family of static state feedback h nonlinear controllers then we provide sufficient conditions for the existence of a dynamic output compensator which solves the problem of disturbance attenuation with internal stability for discrete time nonlinear systems the theory developed in this paper incorporates the well known results for discrete time linear systems and generalizes some recent advances in h control of continuous time nonlinear systems to their discrete time counterparts

dynamic contact problem for viscoelastic piezoelectric materials with slip dependent friction abstract in this paper we deal with a class of inequality problems for dynamic frictional contact between a piezoelectric body and a foundation the model consists of a system of the hemivariational inequality of hyperbolic type for the displacement the time dependent elliptic equation for the electric potential the friction condition is described to be the clarke subdifferential relations of nonmonotone and multivalued character in the tangential directions on the boundary the existence of a weak solution to the model is proved by embedding the problem into a class of second order evolution inclusions and by applying a surjectivity result for multivalued operators

synchronization and secure communication of uncertain chaotic systems based on full order and reduced order output affine observers this paper deals with the problems of chaos synchronization and secure communication for a class of uncertain chaotic systems the uncertain chaotic systems under consideration are subject to modeling uncertainties and depend affinely on a set of measurable system outputs two types of observer are proposed to achieve chaos synchronization and secure communication first a full order output affine observer is proposed to simultaneously estimate the system states and the message signals second a reduced order output affine observer is proposed to simultaneously estimate the unmeasured system states and the message signals a numerical example is given for a chaotic system to show the design procedure and the effectiveness of the proposed observers the simulation results indicate that the proposed observers work well

discrete time cal h _ infty control problem for nonlinear descriptor systems this note presents an explicit solution to the problem of disturbance attenuation with internal stability for discrete time nonlinear descriptor systems both the static state feedback and dynamic output feedback cases are considered in particular we characterize a family of hinfin controllers solving the problem locally around a neighborhood of the origin to do this we first derive two stability criteria for discrete time nonlinear descriptor systems and then a version of a bounded real lemma is also developed based on the concepts of dissipation inequality and differential game after that the results are used to derive the hinfin control theory for nonlinear discrete time descriptor systems the approach taken is mainly algebraic and hence is simple and clear

hemivariational inequalities modeling dynamic contact problems with adhesion abstract this paper deals with the mathematical modelling of viscoelastic frictional contact processes in mechanics which involve adhesion the model consists of a coupled system of the hemivariational inequality of hyperbolic type for the displacement and the ordinary differential equation for the bonding field the frictional forces are derived from nonconvex superpotentials through the generalized clarke subdifferential the properties of the body are described by a modified kelvin voigt constitutive law the existence of weak solution to the problem is proved by embedding it into a class of second order evolution inclusions and by applying a surjectivity result for multivalued pseudomonotone operators we also establish a result on the regularity of weak solution to the model finally examples of subdifferential boundary conditions which include the functions of d c type are provided

mixed h 2 h control via state feedback for nonlinear systems this paper studies a mixed h 2 h control problem with internal stability by means of memoryless state feedback for smooth nonlinear control systems the problem consists of combining the performance requirements of quadratic optimal controllers with the robustness properties of h controllers it is shown that under appropriate assumptions the problem is solvable if a pair of cross coupled hamilton jacobi isaacs equations allows smooth solutions our approach to the mixed h 2 h nonlinear control problem is drawn from the concepts of non zero sum differential game lasalle s invariance principle and completion of squares analogous results are also developed for discrete time nonlinear systems by using the taylor expansion argument finally all the results obtained in affine systems are generalized to non affine nonlinear systems

adaptive controller design for tracking and disturbance attenuation in parametric strict feedback nonlinear systems the authors develop a systematic procedure for obtaining robust adaptive controllers that achieve asymptotic tracking and disturbance attenuation for a class of nonlinear systems which are described in the parametric strict feedback form and are subject to additional exogenous disturbance inputs their approach to adaptive control is performance based where the objective for the controller design is not only to find an adaptive controller but also to construct an appropriate cost functional compatible with desired asymptotic tracking and disturbance attenuation specifications with respect to which the adaptive controller is worst case optimal three main issues of the paper are the backstepping methodology worst case identification schemes and singular perturbations analysis closed form expressions have been obtained for an adaptive controller and the corresponding value function a numerical example involving a third order system is given

h sup infinity control for nonlinear systems with output feedback the basic question of nonlinear h sup infinity control theory is to decide for a given two port system when feedback that makes the full system dissipative and internally stable exists this problem can also be viewed as a question about circuits and after translation also has a game theoretic statement several necessary conditions for solutions to exist are presented and sufficient conditions for a certain construction to lead to a solution are given

hemivariational inequality for viscoelastic contact problem with slip dependent friction abstract in this paper we consider a class of hyperbolic hemivariational inequalities modeling the frictional contact between a viscoelastic body and a rigid foundation the friction law is described by a multivalued subdifferential relation which includes the slip displacement dependent friction and the tresca models we establish the existence of weak solutions to the problem by using a surjectivity result for pseudomonotone mappings

h sub spl infin control for asymptotically stable nonlinear systems this paper deals with the problem of h sub spl infin control for a class of nonlinear systems the system under consideration is assumed to be globally asymptotically stable with a known lyapunov function based on this lyapunov function and using the notion of dissipativeness a state feedback controller is designed which renders the closed loop system globally asymptotically stable with a prescribed bound on the l sub 2 gain from the disturbance input to the controlled output the proposed controller design method is based on the explicit construction of a lyapunov function for the closed loop system which represents a significant advantage over existing methods

brief paper singular h suboptimal control for a class of nonlinear cascade systems in the present paper singular state feedback h suboptimal control for a class of nonlinear cascade systems is addressed under the assumption that a regular state feedback h suboptimal control problem is solvable for a particular subsystem of the cascade system an auxiliary nonlinear system is defined it is shown that a state feedback solution to the singular h suboptimal control problem for the auxiliary system also applies to the original problem the advantage of the auxiliary problem to the original problem is that the auxiliary penalty variable has lower dimension than the original penalty variable it is shown how this fact can simplify the problem considerably for the case when the auxiliary system can be strongly input output decoupled the theory is applied to a problem of a rigid spacecraft with actuator dynamics application to the special case when a subsystem of the nonlinear cascade system is passive is also considered

nonlinear h infinity control and related problems of homogeneous systems in this paper the problems of h infinity control and related l2 gain of nonlinear homo geneous systems are considered first of all l2 gains of homogeneous stable systems are estimated with a method in light of hamilton jacobi inequalities secondly by virtue of hamilton jacobi isaacs hji inequality the nonlinear h infinity induced l2 gain problem of a class of systems with homogeneous vector fields is discussed and global control law is given under an assumption similar to the one of stabilizability of linear systems then following the previous results homogeneous systems with higher degree perturbed terms are studied finally the analysis of finite test of homogeneous systems with perturbed parameter is presented

slip dependent friction in dynamic elasticity the dynamic evolution with frictional contact of an elastic body is considered in modeling the contact the tresca model and a slip dependent friction law are used the existence of a solution is proved in the two dimensional case the uniqueness is proved for the one dimensional shearing problem the convergence for a vanishing viscosity of the unique solution of the viscoelastic problem to a solution of the elastic problem is obtained

disturbance attenuation via state feedback for systems with a saturation nonlinearity in the control channel we study the problem of disturbance attenuation via state feedback for asymptotically stable systems with a saturation nonlinearity in the control channel the disturbance is assumed to be bounded with the bound known this amounts to adding a saturation nonlinearity in the disturbance channel a sufficient condition is derived in terms of algebraic matrix inequalities which are much simpler to solve than the general hamilton jacobi isaacs partial differential inequality a suboptimal control law is given based on the solution to the riccati inequalities the computational complexity of solving the optimal controller is similar to that of liner h controller design

disturbance attenuation and h sub infinity control via measurement feedback in nonlinear systems a solution to the problem of disturbance attenuation via measurement feedback with internal stability is presented for an affine nonlinear system it is shown that the concept of disturbance attenuation in the sense of truncated l sub 2 norms can be given an interpretation in terms of the response to periodic inputs in the sense of rms amplitude even in the nonlinear setup in the case of state feedback a family of controllers is also provided the proofs of all these results are simple and provide deeper insight even in the analysis of the corresponding linear control problem

l sub 2 gain analysis of nonlinear systems and nonlinear state feedback h sub infinity control previously obtained results on l2 gain analysis of smooth nonlinear systems are unified and extended using an approach based on hamilton jacobi equations and inequalities and their relation to invariant manifolds of an associated hamiltonian vector field on the basis of these results a nonlinear analog is obtained of the simplest part of a state space approach to linear h sub infinity control namely the state feedback h sub infinity optimal control problem furthermore the relation with h sub infinity control of the linearized system is dealt with

hemivariational inequality approach to the dynamic viscoelastic sliding contact problem with wear abstract the dynamic contact problem of sliding contact with wear between a viscoelastic body and a foundation is formulated as a hemivariational inequality the contact is modeled with a general normal damped response condition which is nonmonotone possibly multivalued and has the subdifferential form we establish the existence of weak solutions by using a surjectivity result for a class of pseudomonotone operators we also deliver conditions under which the solution of the evolution inclusion associated with the hemivariational inequality is unique

a system of evolution hemivariational inequalities modeling thermoviscoelastic frictional contact abstract in this paper we prove the existence and uniqueness of the weak solution for a dynamic thermoviscoelastic problem which describes frictional contact between a body and a foundation we employ the kelvin voigt viscoelastic law include the thermal effects and consider the general nonmonotone and multivalued subdifferential boundary conditions the model consists of the system of the hemivariational inequality of hyperbolic type for the displacement and the parabolic hemivariational inequality for the temperature the existence of solutions is proved by using a surjectivity result for operators of pseudomonotone type the uniqueness is obtained for a large class of operators of subdifferential type satisfying a relaxed monotonicity condition

inverse optimal design of input to state stabilizing nonlinear controllers we show that input to state stabilizability as defined by sontag 1989 1995 is both necessary and sufficient for the solvability of a hamilton jacobi isaacs equation associated with a meaningful differential game problem similar to but more general than the nonlinear h sub spl infin problem the significance of the result stems from the fact that constructive solutions to the input to state stabilization problem are available presented in the paper and that as shown here inverse optimal controllers possess margins on input to state stability against a certain class of input unmodeled dynamics rather than completion of squares the main tools in our analysis are legendre fenchel transformations and the general form of young s inequality

global h sub spl infin controllers for a class of nonlinear systems in this note the problem of state feedback h sub spl infin control for a class of nonlinear systems is considered the class under study is a generalization of the well known lur e systems the h sub spl infin problem is addressed via a class of storage functions of the lur e postnikov type whose integral term is parameterized by a nonlinear scalar function the related h sub spl infin controllers consist of a linear term which is designed for the underlying linearized system plus a nonlinear term which depends on the nonlinear function a simple geometrical criterion is provided for the characterization of the set of controllers which ensure a given level of l sub 2 performance globally some guidelines for an effective design of the controller within this set are discussed via two examples

lur e systems with multilayer perceptron and recurrent neural networks absolute stability and dissipativity sufficient conditions for absolute stability and dissipativity of continuous time recurrent neural networks with two hidden layers are presented in the autonomous case this is related to a lur e system with multilayer perceptron nonlinearity such models are obtained after parametrizing general nonlinear models and controllers by a multilayer perceptron with one hidden layer and representing the control scheme in standard plant form the conditions are expressed as matrix inequalities and can be employed for nonlinear h sub spl infin control and imposing closed loop stability in dynamic backpropagation

state feedback ℋ control for stochastic time delay nonlinear systems with state and disturbance dependent noise this article focuses on the state feedback control problem for the stochastic nonlinear systems with state and disturbance dependent noise and time varying state delays based on the maxmin optimisation approach both the delay independent and the delay dependent hamilton jacobi inequalities hjis are developed for synthesising the state feedback controller for a general type of stochastic nonlinear systems it is shown that the resulting control system achieves stochastic stability in probability and the prescribed disturbance attenuation level for a class of stochastic affine nonlinear systems the delay independent as well as delay dependent matrix valued inequalities are proposed the resulting control system satisfies global asymptotic stability in the mean square sense and the required disturbance attenuation level by modelling the nonlinearities as uncertainties in corresponding stochastic time delay systems the sufficient conditions in terms of a linear matrix inequality lmi and a bili

dynamic contact problem for viscoelastic piezoelectric materials with normal damped response and friction in this paper we deal with a class of inequality problems for dynamic frictional contact between a piezoelectric body and a foundation the model consists of a system of the hemivariational inequality of hyperbolic type for the displacement the time dependent elliptic equation for the electric potential the contact is modeled by a general normal damped response condition and a friction law which are nonmonotone possibly multivalued and have the subdifferential form the existence of a weak solution to the model is proved by embedding the problem into a class of second order evolution inclusions and by applying a surjectivity result for multivalued operators

neural network based online simultaneous policy update algorithm for solving the hji equation in nonlinear h_ infty control it is well known that the nonlinear h state feedback control problem relies on the solution of the hamilton jacobi isaacs hji equation which is a nonlinear partial differential equation that has proven to be impossible to solve analytically in this paper a neural network nn based online simultaneous policy update algorithm spua is developed to solve the hji equation in which knowledge of internal system dynamics is not required first we propose an online spua which can be viewed as a reinforcement learning technique for two players to learn their optimal actions in an unknown environment the proposed online spua updates control and disturbance policies simultaneously thus only one iterative loop is needed second the convergence of the online spua is established by proving that it is mathematically equivalent to newton s method for finding a fixed point in a banach space third we develop an actor critic structure for the implementation of the online spua in which only one critic nn is needed for approximating the cost function and a least square method is given for estimating the nn weight parameters finally simulation studies are provided to demonstrate the effectiveness of the proposed algorithm

nonlinear model validation using correlation tests new higher order correlation tests which use model residuals combined with system inputs and outputs are presented to check the validity of a general class of nonlinear models the new method is illustrated by testing both simple and complex nonlinear system models

approximated solutions to nonlinear discrete time h sub spl infin control it is shown that there exists an analytic solution to the discrete hamilton jacobi equation arising in the nonlinear discrete time h sub spl infin control problem if and only if the h sub spl infin control problem associated to the linear approximated system is solvable starting from the solution of the riccati equation associated to this linear problem we show that the nonlinear solution can be computed at any desired degree of approximation on this basis the control solution can be computed iteratively

global asymptotic stabilisation of non linear systems in this article the problem of global asymptotic stabilisation of non linear systems is considered first of all the global asymptotic stability of a class of non linear systems is considered it is proved that the class of non linear systems is globally asymptotically stable under certain appropriate conditions secondly based on the result obtained the global asymptotic stabilisation of a class of non linear systems is investigated and the feedback control laws which globally stabilise the class of systems are designed thirdly by the coordinate change and the results obtained the global stabilisation of the affine non linear systems are studied and then some sufficient conditions of stabilisation are presented finally the global asymptotic stabilisation of partially linear cascade non linear system is considered the sufficient conditions of global stabilisation are obtained and the corresponding feedback control laws which stabilise the non linear systems are designed in addition some

a computationally efficient lyapunov based scheduling procedure for control of nonlinear systems with stability guarantees we propose an alternative to gain scheduling for stabilization of nonlinear systems for a useful class of nonlinear systems the characterization of a region of stability based on a control lyapunov function is computationally tractable in the sense that computation times vary polynomially with the state dimension for a fixed number of scheduling variables using this fact we develop a procedure to expand the region of stability by constructing control lyapunov functions to various trim points of the system a lyapunov based control synthesis algorithm is used to construct a control law that guarantees closed loop stability for initial conditions in the expanded region of state space this control asymptotically recovers the optimal stability margin in the sense of a lyapunov derivative which in turn can be seen as a performance measure robustness to bounded disturbances and stabilization under bounded control are easily incorporated into this framework in the worst case the computational complexity of the analysis problem that develops in the new method is increased by an exponential in the disturbance dimension similarly we can handle control constraints with an increase in computational complexity of no more than an exponential in the control dimension we demonstrate the new control design procedure on an example

convergence analysis for reduced order adaptive controller design of uncertain siso linear systems with noisy output measurements we consider in this article a class of uncertain siso linear systems that are subject to system and measurement noises reduced order adaptive controller designs have been proposed before for such systems by the authors and stability analysis of the closed loop systems has been established here we analyse further the robustness properties for these reduced order adaptive control systems by providing detailed convergence analysis results for the key closed loop signals and parameter estimates we rigorously prove that whenever the exogenous disturbance input is of finite energy and bounded and the reference trajectory and its derivatives up to rth order are bounded r being the relative degree of the transfer function of the true system a set of signals including the tracking error the estimation error between the system output and its estimate the projection signal are of finite energy and converge to zero and the system states and their estimates exhibit asymptotic behaviours with certain form

on a state space approach to nonlinear h control we study the standard h optimal control problem using state feedback for smooth nonlinear control systems the main theorem obtained roughly states that the l2 induced norm from disturbances to inputs and outputs can be made smaller than a constant 0 if the corresponding h norm for the system linearized at the equilibrium can be made smaller than by linear state feedback necessary and sufficient conditions for the latter problem are by now well known e g from the state space approach to linear h optimal control our approach to the nonlinear h optimal control problem generalizes the state space approach to the linear h problem by replacing the hamiltonian matrix and corresponding riccati equation as used in the linear context by a hamiltonian vector field together with a hamiltonian jacobi equation corresponding to its stable invariant manifold

backstepping design with local optimality matching in nonlinear h sup spl infin optimal control design for strict feedback nonlinear systems our objective is to construct globally stabilizing control laws to match the optimal control law up to any desired order and to be inverse optimal with respect to some computable cost functional our recursive construction of a cost functional and the corresponding solution to the hamilton jacobi isaacs equation employs a new concept of nonlinear cholesky factorization when the value function for the system has a nonlinear cholesky factorization we show that the backstepping design procedure can be tuned to yield the optimal control law

evolution hemivariational inequality for a class of dynamic viscoelastic nonmonotone frictional contact problems in this paper we consider a class of hyperbolic hemivariational inequalities modeling the frictional contact between a viscoelastic body and a rigid foundation the friction condition is described by a multivalued subdifferential relation which includes both the slip displacement and the slip rate dependent friction and the tresca models the existence of weak solutions to the problem is proved by exploiting a surjectivity result for a class of pseudomonotone mappings

h sub spl infin control of discrete time nonlinear systems this paper presents an explicit solution to the problem of disturbance attenuation with internal stability via full information feedback state feedback and dynamic output feedback respectively for discrete time nonlinear systems the h sub spl infin control theory is first developed for affine systems and then extended to general nonlinear systems based on the concepts of dissipation inequality differential game and lasalle s invariance principle in discrete time a substantial difficulty that v a x b x u e x w respectively v f x u w is no longer quadratic in sub w sup u arising in the case of discrete time nonlinear systems has been surmounted in the paper in the case of a linear system we show how the results reduce to the well known ones recently proposed in the literature

input output parametric models for non linear systems part ii stochastic non linear systems recursive input output models for non linear multivariate discrete time systems are derived and sufficient conditions for their existence are defined the paper is divided into two parts the first part introduces and defines concepts such as nerode realization multistructural forms and results from differential geometry which are then used to derive a recursive input output model for multivariable deterministic non linear systems the second part introduces several examples compares the derived model with other representations and extends the results to create prediction error or innovation input output models for non linear stochastic systems these latter models are the generalization of the multivariable arm ax models for linear systems and are referred to as narmax or non linear autoregressive moving average models with exogenous inputs

parameterization of nonlinear h state feedback controllers state space formulas are derived for a family of controllers solving the nonlinear h state feedback control problem these controllers are obtained by interconnecting the central controller with an asymptotically stable free system that satisfies one additional cascade condition all proofs given are simple and clear and also provide a deeper insight into the synthesis of the corresponding linear h controllers

h sup spl infin control for more general nonlinear systems the authors consider the standard h sup spl infin control problem for more general nonlinear systems modeled by equations in which the penalty output and the measured output are in general functions of the state the exogenous input and the control input in particular we characterize a family of h sup spl infin controllers via output feedback as well as state feedback solving the problem the results obtained generalize some recent results in the literature

dynamic hemivariational inequalities in contact mechanics abstract this paper gives a review of results on the existence and uniqueness of solutions to some mechanical contact problems the second order evolution problems with a general normal compliance response condition and a normal damped response one in viscoelasticity are discussed finally a new result for a problem which includes the slip displacement dependent friction and the tresca model is provided

iterative adaptive dynamic programming for solving unknown nonlinear zero sum game based on online data h infty control is a powerful method to solve the disturbance attenuation problems that occur in some control systems the design of such controllers relies on solving the zero sum game zsg but in practical applications the exact dynamics is mostly unknown identification of dynamics also produces errors that are detrimental to the control performance to overcome this problem an iterative adaptive dynamic programming algorithm is proposed in this paper to solve the continuous time unknown nonlinear zsg with only online data a model free approach to the hamilton jacobi isaacs equation is developed based on the policy iteration method control and disturbance policies and value are approximated by neural networks nns under the critic actor disturber structure the nn weights are solved by the least squares method according to the theoretical analysis our algorithm is equivalent to a gauss newton method solving an optimization problem and it converges uniformly to the optimal solution the online data can also be used repeatedly which is highly efficient simulation results demonstrate its feasibility to solve the unknown nonlinear zsg when compared with other algorithms it saves a significant amount of online measurement time

brief paper robust h control of uncertain nonlinear systems this paper discusses the robust l 2 gain performance synthesis problem for a class of uncertain nonlinear systems it is shown that the hamilton jacobi equation approach to robust h performance synthesis can be extended to solve this problem based on a positive definite solution of a hamilton jacobi inequality a sufficient condition is given such that the uncertain nonlinear system is robust and stable and its l 2 gain is less than or equal to a prescribed value using this condition a state feedback law and an output feedback law which ensure robust l 2 gain performance of the closed loop system are derived finally an example is given

robust h sub spl infin control for linear discrete time systems with norm bounded nonlinear uncertainties this paper studies the problem of robust control of a class of uncertain discrete time systems the class of uncertain systems is described by a state space model with linear nominal parts and norm bounded nonlinear uncertainties in the state and output equations the authors address the problem of robust h sub spl infin control in which both robust stability and a prescribed h sub spl infin performance are required to be achieved irrespective of the uncertainties it has been shown that instead of the nonlinear uncertain system one may only consider a related linear uncertain system and thus a linear static state feedback control law is designed which is in terms of a riccati inequality

convex design control for practical nonlinear systems this paper describes a new control scheme for approximately optimal control aoc of nonlinear systems convex control design convcd the key idea of convcd is to transform the approximate optimal control problem into a convex semi definite programming sdp problem contrary to the majority of existing aoc designs where the problem that is addressed is to provide a control design which approximates the performance of the optimal controller by increasing the controller complexity the proposed approach addresses a different problem given a controller of fixed complexity it provides a control design that renders the controller as close to the optimal as possible and moreover the resulted closed loop system stable two numerical examples are used to show the effectiveness of the method

identification of mimo non linear systems using a forward regression orthogonal estimator abstract an orthogonal least squares estimator which was originally derived for single input single output systems is extended to multi input multi output non linear systems the estimator can provide information about the structure or which terms to include in the model and final parameter estimates in a very simple and efficient manner multivariable non linear model validity tests are also discussed and the results of applying the orthogonal estimator to both simulated and real data are included

h disturbance attenuation for state delayed systems in this note the differential game and dissipation inequality are applied to the disturbance attenuation or h control for linear systems with delayed state firstly a simple sufficient condition on the existence of a suboptimal h state feedback controller is given which is independent of delay and an observer based dynamic output feedback solution is presented in terms of riccati inequalities or riccati equations secondly a sufficient condition on the existence of a delay dependent state feedback is presented and the criterion is presented by a matrix inequality which can be solved by numerical methods

reduced complexity nonlinear h sup spl infin control of discrete time systems in this note we describe a reduced complexity solution to the nonlinear h sup spl infin control problem this reduction applies to systems where some of the states are perfectly known and is an intermediate problem between full state feedback and the standard measurement feedback problem the reduction of computational complexity is significant and of practical importance online implementation is feasible with 2003 computer technology for a range of practical engineering design problems

time dependent implicit evolution equations on presente des theoremes d existence et d unicite pour des problemes de cauchy correspondant aux equations abstraites de la forme d b t u t dt a t u t f t ou b t est une famille dependante du temps d operateurs lineaires

brief h controller reduction for nonlinear systems sufficient conditions are proposed for the existence of reduced order fixed order controllers solving the standard nonlinear h output feedback control problem state space formulas for such reduced order h controllers are also derived in terms of the solutions of two hamilton jacobi inequalities the development uses only elementary concepts of dissipativity and differential game thus the proofs given are simple and clear

fast orthogonal identification of nonlinear stochastic models and radial basis function neural networks a new fast orthogonal estimation algorithm is derived for a wide class of nonlinear stochastic models including training radial basis function neural networks the selection of significant regressors and the estimation of unknown parameters in the presence of nonlinear noise sources are considered and simulated examples are included to demonstrate the efficiency of the new procedure

improved parameter estimates for non linear dynamical models using a bootstrap method it is known that the least squares ls class of algorithms produce unbiased estimates providing certain assumptions are met there are many practical problems however where the required assumptions are violated typical examples include non linear dynamical system identification problems where the input and output observations are affected by measurement uncertainty and possibly correlated noise this will result in biased ls estimates and the identified model will exhibit poor generalisation properties model estimation for this type of error in variables problem is investigated in this study and a new identification scheme based on a bootstrap algorithm is proposed to improve the model estimates for non linear dynamical system identification

h sub spl infin control via measurement feedback for general nonlinear systems this paper shows how the problem of local disturbance attenuation via measurement feedback with internal stability can be solved for a nonlinear system of rather general structure the solution of the problem is shown to be related to the existence of solutions of a pair of hamilton jacobi inequalities in n independent variables which are associated with state feedback and respectively output injection design

hemivariational inequalities in thermoviscoelasticity abstract in this paper we present the existence and uniqueness of the weak solution for a dynamic thermoviscoelastic problem which describes frictional contact between a body and a foundation we employ the kelvin voigt viscoelastic law which includes the thermal effects and consider the general nonmonotone and multivalued subdifferential boundary conditions the model consists of the system of the hemivariational inequality of hyperbolic type for the displacement and the parabolic hemivariational inequality for the temperature the existence of solutions is obtained from a surjectivity result for operators of pseudomonotone type the uniqueness holds for a large class of operators of subdifferential type satisfying a relaxed monotonicity condition