model reference adaptive control of system having purely deterministic disturbances this note presents results relating to the adaptive control of linear time invariant systems having purely deterministic disturbances such as sine waves biases etc two key points are made first it is shown that the usual arma model used in adaptive control can also include a description of purely deterministic disturbances second it is shown that the existing convergence theory for adaptive control schemes can be extended in a very straightforward way to the case where disturbances are present

stabilized least squares type adaptive identifiers least squares type adaptive identifiers are proposed which are stabilized in the sense that the covariance equation has a positive definition asymptotically stable equilibrium this keeps the adaptive gain matrix bounded and the adaptive abilities of the algorithm always properly in operation the convergence speed of the stabilized adaptive identifiers is proportional to the signal level when the signal level is low and can be made to achieve almost arbitrarily fast convergence for high signal levels the algorithms require the inversion of positive definite matrices and or the solution of associated linear equations which is numerically well behaved as a result a slightly increased computational complexity as compared to known least squares type algorithms is to be paid for advanced stability and adaptive properties of the algorithms

arbitrary adaptive pole placement for linear multivariable systems this paper presents a methodology for adaptively assigning the closed loop poles of either continuous or discrete time linear mnltivariable systems the scheme is direct in nature in that no parametrized model of the unknown plant needs to be explicitely identified rather the control parameters and an equivalent plant parameterization are simultaneously estimated from input output data using linear parameter estimation procedures implementation of the scheme requires only knowledge of the system controllability indexes and an upper bound on the observabilily index

a new set of necessary and sufficient conditions for a system to be prime in this note we first generalize the notion of the interactor wolovich and falb 1 and modify the input output structure algorithm of silverman 2 in order to obtain simple relations between the dimension of supremal output nulling invariant subspace v and the degree of the determinant of the interactor partial t and the integers obtained from the structure algorithm then we show that these relations can be used to derive a new set of necessary and sufficient conditions for a linear multivariable system to be prime morse 3

the design of a precompensator for multivariable adaptive control a network theoretic approach a network theoretic approach to the design of a dynamic precompensator c s for a multiinput multioutput plant t s is considered the design is based on the relative degree of each element of t s specifically an efficient algorithm is presented for determining whether a given plant t s has a diagonal precompensator c s such that for almost all cases t s c s has a diagonal interactor the algorithm also finds any optimal precompensator in the sense that the total relative degree is minimal the algorithm can be easily modified to work even when a t s represented by a nonsquare matrix is given

exponential dichotomy roughness and structural stability for evolution families without bounded growth and decay abstract we show that if u t s is an exponentially dichotomic evolution operator then the unique solution of the volterra equation v t s u t s s t u t b v s d is also an exponentially dichotomic evolution operator for small b t as a consequence we prove that any exponentially dichotomic evolution family is structurally stable we improve the previous results showing that the condition of bounded growth and decay present everywhere in the existing literature can be completely removed

exponential trichotomy of differential systems on considere un systeme d equations differentielles on donne une caracterisation de la trichotomie exponentielle via une certaine fonction de lyapunov on presente plusieurs criteres pour l existence de la trichotomie exponentielle

infinite horizon nonstationary stochastic optimal control problem a planning horizon result we show the existence of a planning horizon for the infinite horizon nonstationary stochastic optimal control problem hence the original problem generally untractable reduces to solve a sequence of finite horizon problems which is computationally attractive

a topological classification of linear differential equations on banach spaces abstract in the present work we give necessary and sufficient conditions for linear differential non autonomous equations on a banach space that satisfy exponential dichotomy to be topologically equivalent we shall also prove that such equations are structurally stable

frequency domain conditions for parameter convergence in multivariable recursive identification abstract a multivariable adaptive identifier is designed on the basis of a canonical form leading to a unique set of parameters to identify frequency domain conditions for parameter convergence are derived the sufficient condition to guarantee convergence in all cases is that n v distinct frequency components be present in each input of the plant where v is the maximum of the observability indices and n the order of the plant on the other hand the necessary condition requires n mv distinct frequency components distributed over the inputs where m is the number of inputs and at least v frequency components are in each separate input through examples it is shown that convergence may or may not occur for intermediate numbers of frequency components depending on their location and on the plant parameters

multivariable adaptive control identifiable parameterizations and parameter convergence the paper presents a direct model reference adaptive control algorithm for multivariable systems that has guaranteed parameter convergence properties the algorithm requires fewer parameters than existing schemes and the parameters converge to their nominal values under persistency of excitation conditions simple frequency domain conditions on the external inputs are derived to satisfy these conditions the convergence of the controller parameters to their nominal values guarantees a certain degree of robustness of the algorithms and ensures that the model matching objective is satisfied asymptotically

error bounds for finite step approximations for solving infinite horizon controlled markov set chains this note considers finite step approximations for solving an infinite horizon controlled markov set chain problem with finite state and action spaces we develop a value iteration type algorithm based on the optimality equation developed by kurano et al and analyze an error bound relative to the optimal value that satisfies the optimality equation from the successive approximation we further analyze an error bound of the approximate control policy defined from a finite step approximate value by applying the value iteration type algorithm

output feedback model reference sliding mode control of uncertain multivariable systems this note considers the robust output tracking problem using a model reference sliding mode controller for linear multivariable systems of relative degree one it is shown that the closed loop system is globally exponentially stable and the performance is insensitive to bounded input disturbances and parameter uncertainties the strategy is based on output feedback unit vector control to generate sliding mode the only required a priori information about the plant high frequency gain matrix k sub p is the knowledge of a matrix s sub p such that k sub p s sub p is hurwitz which relaxes the positive definiteness requirement usually needed by other methods

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

characterizations of dichotomies of evolution equations on the half line abstract in this paper we investigate the characterization of dichotomies of an evolution family u u t s t s 0 of bounded linear operators on banach space x we introduce operators i0 and ix on subspaces of lp r x using the integral equation u t u t s u s ts u t f d the exponential and ordinary dichotomies of u are characterized by properties of i0 ix

nonuniform h k μ ν dichotomy with applications to nonautonomous dynamical systems the paper develops and studies a very general notion of dichotomy referred to as nonuniform h k dichotomy the new notion contains as special cases most versions of dichotomy existing in the literature the paper then provides corresponding new versions of robustness hartman grobman theorem and stable manifold theorem for nonautonomous dynamical systems in banach spaces in term of the nonuniform h k dichotomy

interactor and multivariable adaptive model matching the necessary minimal prior knowledge of a system in order to implement adaptive model matching and prove global stability is discussed some results concerning the degrees of interactor matrix entries are given it is shown that the bounds on the degrees of the interactor off diagonal terms given by m das j dynam sust measurement contr vol 108 p 151 153 1986 are the best possible ones

an algorithm for the calculation of a nilpotent interactor matrix for linear multivariable systems a new algorithm for the calculation of the delay structure for a linear multivariable system is presented the algorithm evaluates a nilpotent interactor matrix from the matrix of coefficients of the numerator of a right matrix fraction description of the system the resulting nilpotent interactor is a product of first degree nilpotent polynomial matrices

prior information in the design of multivariable adaptive controllers this note discusses the design of a dynamic precompensator w c s for an m times m mimo plant w p s such that for almost all cases w p s w c s has a diagonal hermite form

towards a link between the factorization approach and mimo robust adaptive control based on a doubly coprime factorization theorem nett et al 1984 an adaptive controller for discrete time mimo systems consisting of a not necessarily minimum phase modelled part and fraction type unmodelled dynamics which are not necessarily stable non linear and time varying is developed then by virtue of a stability result which is itself of interest it is shown that the adaptive closed loop system is bibo stable even in the presence of small but not necessarily stable unmodelled dynamics and arbitrarily bounded initial conditions consequently an initial but important step for applying the factorization approach to mimo robust adaptive control is completely established

robustness of nonuniform μ ν dichotomies in banach spaces abstract this paper focuses on the linear perturbation of dynamical systems in banach spaces which corresponds to a nonautonomous dynamical system admitting a nonuniform dichotomy we establish the robustness or roughness of nonuniform dichotomies in the sense that the linear dynamical system persists under a sufficiently small linear perturbation

stable adaptive control of non minimum phase systems abstract an adaptive pole placement design for not necessarily minimum phase systems is analyzed with respect to stability conditions are given for boundedness of closed loop signals when the process is subject to bounded disturbances the most restrictive one can be avoided in a local stability result

indirect adaptive pole placement control of mimo stochastic systems self tuning results in this paper we consider indirect adaptive pole placement control appc of linear multivariable stochastic systems instead of the canonical representation often used in the literature we propose using a non minimal but otherwise uniquely identifiable pseudo canonical parameterization that is more suitable for multivariable armax model identification to identify the plant we use the weighted extended least squares wels algorithm a least squares method with slowly decreasing weights which was introduced in bercu 1995 the pole placement controller parameters are then calculated by using a certain perturbation of the parameter estimates such that the linear models corresponding to the perturbed estimates are uniformly controllable and observable we prove that with a reasonable amount of prior information the resulting appc scheme is globally stabilizing and asymptotically self tuning regardless of the degree of persistency of external excitation these results represent the most complete study of stochastic multivariable appc systems to this date

on admissible perturbations for exponential dichotomy in this work we obtain an optimal upper bound for exponential dichotomy roughness in infinite dimensional banach spaces unlike some previous works we do not assume bounded growth we consider linear non autonomous ordinary differential equations with bounded and unbounded coefficients

existence and robustness of nonuniform h k μ ν dichotomies for nonautonomous impulsive differential equations abstract for the linear nonautonomous impulsive differential equation we propose a new notion called the nonuniform h k dichotomy which extends the notion of dichotomy of uniform and nonuniform types and is related to the theory of nonuniform hyperbolicity we establish a sufficient criterion for the existence of the nonuniform h k dichotomy in terms of appropriate lyapunov exponents for the linear perturbation we develop the robustness or roughness of nonuniform h k dichotomies in the sense that a nonuniform h k dichotomy persists under a sufficiently small linear perturbation

a parameter adaptive control structure for linear multivariable systems this paper presents an adaptive control structure which can be used to assign all poles and zeros of a continuous time linear multivariable system represented by an m times m strictly proper transfer matrix t s provided t s has no right half plane zeros the controller parameters can be directly estimated from input output data the paper also serves to point out the type of a priori information necessary for multivariable adaptive controller design this information is a natural extension of that required in the scalar case

multivariable adaptive control as a natural extension of siso adaptive control the concepts of a potentially structural non singularity and a structural non singularity are introduced in this paper using these concepts we derive the result that for almost all cases the plant to be controlled has a diagonal interactor by using an appropriate diagonal proper precompensator furthermore both the precom pensator and the interactor can be determined only from the structural information of t s the relative degrees of each element of t s without requiring any parametric information about t s therefore by assuming that the a priori knowledge of the plant consists of the relative degrees of each element of t s as well as the observability index of t s we can make mi mo adaptive control be quite a natural extension of siso adaptive control

prior knowledge in model reference adaptive control of multiinput multioutput systems this note shows how the prior knowledge necessary for model reference adaptive control of multiinput multioutput systems can be weakened in particular it is shown that the real variables appearing in the system interactor matrix can be estimated along with the other parameters appearing in the system model this represents a significant reduction in the amount of prior knowledge required relative to previous work which assumed that the full interactor matrix was available a theoretical convergence analysis of the resulting algorithm is presented together with simulation results

indirect adaptive periodic control a indirect adaptive control method is presented the method is based on a lifted representation of the plant that can be stabilized using a simple performant periodic control scheme the controller parameters computation involves the inverse of the controllability observability matrix potential singularities of this matrix are avoided by means of an appropriate estimates modification this estimates transformation is linked to the covariance matrix properties and hence it preserves the convergence properties of the original estimates this modification involves the singular value decomposition of the controllability observability matrix s estimate as compared with previous studies on the subject the controller proposed here does not require the frequent introduction of periodic n length sequences of zero inputs therefore the new controller is such that the system is almost always operating in closed loop which should lead to better performance characteristics

error bounds for rolling horizon policies in discrete time markov control processes error bounds are presented for rolling horizon rh policies in general stationary and nonstationary borel markov control problems with both discounted and average reward criteria in each of these cases conditions are given under which the reward of the rolling horizon policy converges geometrically to the optimal reward function uniformly in the initial state as the length of the rolling horizon increases a description of the control model and the general assumptions are given the approach is based on extending the results of j m alden and a r l smith 1988 on nonstationary processes with finite state and action spaces however the proofs presented are simpler this is because when stationary models are analyzed first the error bounds follow more or less directly from well known value iteration results the corresponding error bounds for nonstationary models are obtained by reducing these models to stationary ones

exponential dichotomy roughness on banach spaces in the present paper we extend existing results on exponential dichotomy roughness for linear ode systems to infinite dimensional banach space we give new conditions for the existence of exponential dichotomy roughness in infinite dimensional space and in the finite interval case we also improve previous results by indicating the exact values of the dichotomic constants of the perturbed equation

periodic tracking adaptive control for multivariable systems having more outputs than inputs this note presents an adaptive control algorithm for multivariable systems in which the number of outputs is greater than the number of inputs the algorithm can force the outputs to track arbitrary given reference signals periodically this is the best tracking performance for systems lacking output function controllability it has been shown that the tracking period is the upper bound on the controllability index of the controlled system the proposed algorithm is applicable to multivariable systems with arbitrary interactor matrix but no knowledge of the interactor matrix is required

markov decision processes with imprecise transition probabilities we present new numerical algorithms and bounds for the infinite horizon discrete stage finite state and action markov decision process with imprecise transition probabilities we assume that the transition probability mass vector for each state and action is described by a finite number of linear inequalities this model of imprecision appears to be well suited for describing statistically determined confidence limits and or natural language statements of likelihood the numerical procedures for calculating an optimal max min strategy are based on successive approximations reward revision and modified policy iteration the bounds that are determined are at least as tight as currently available bounds for the case where the transition probabilities are precise

singularity free multivariable model reference adaptive control in this paper we propose a way to solve the problem of singularities in model reference adaptive control of linear multi input multi output mimo systems using a parameter modification procedure based on the least squares covariance matrix inverse the scheme does not require any explicit prior knowledge about the leading coefficient matrix associated with the control input and secures a uniform lower bound for the determinant of the estimate of this matrix a global convergence analysis is presented

bounded parameter markov decision process in this paper we introduce the notion of a em bounded parameter markov decision process as a generalization of the traditional em exact mdp a bounded parameter mdp is a set of exact mdps specified by giving upper and lower bounds on transition probabilities and rewards all the mdps in the set share the same state and action space bounded parameter mdps can be used to represent variation or uncertainty concerning the parameters of sequential decision problems bounded parameter mdps can also be used in aggregation schemes to represent the variation in the transition probabilities for different base states aggregated together in the same aggregate state we introduce em interval value functions as a natural extension of traditional value functions an interval value function assigns a closed real interval to each state representing the assertion that the value of that state falls within that interval an interval value function can be used to bound the performance of a policy over the set of exact mdps associated with a given bounded parameter mdp we describe an iterative dynamic programming algorithm called em interval policy evaluation which computes an interval value function for a given bounded parameter mdp and specified policy interval policy evaluation on a policy policy computes the most restrictive interval value function that is sound i e that bounds the value function for policy in every exact mdp in the set defined by the bounded parameter mdp a simple modification of interval policy evaluation results in a variant of value iteration bellman57 that we call em interval value iteration which computes a policy for an bounded parameter mdp that is optimal in a well defined sense

parameter identification for uncertain linear systems with partial state measurements under an h sup spl infin criterion this paper addresses the worst case parameter identification problem for uncertain single input single output siso and multi input multi output mimo linear systems under partial state measurements and derives worst case identifiers using the cost to come function method in the siso case the worst case identifier obtained subsumes the kreisselmeier observer as part of its structure with parameters set at some optimal values its structure is different from the common least squares ls identifier however in the sense that there is additional dynamics for the state estimate coupled with the dynamics of the parameter estimate in a nontrivial way in the mimo case as well the worst case identifier has additional dynamics for the state estimate which do not appear in the conventional ls based schemes also for both siso and mimo problems approximate identifiers are obtained which are numerically much better conditioned when the disturbances in the measurement equations are small the theoretical results are then illustrated on an extensive numerical example to demonstrate the effectiveness of the identification schemes developed

solving controlled markov set chains with discounting via multipolicy improvement we consider markov decision processes mdps where the state transition probability distributions are not uniquely known but are known to belong to some intervals so called controlled markov set chains with infinite horizon discounted reward criteria we present formal methods to improve multiple policies for solving such controlled markov set chains our multipolicy improvement methods follow the spirit of parallel rollout and policy switching for solving mdps in particular these methods are useful for online control of markov set chains and for designing policy iteration pi type algorithms we develop a pi type algorithm and prove that it converges to an optimal policy

adaptive control of delay system the result of exact model matching for delay systems developed by the author is extended to the adaptive control of delay systems likewise using results from the adaptive control of systems without delay the principle of constructing adaptive systems for delay plants is also very simple and clear

finite step approximation error bounds for solving average reward controlled markov set chains this paper is a sequel to the analysis of finite step approximations in solving controlled markov set chains for infinite horizon discounted reward by the author for average reward controlled markov set chains with finite state and action spaces we develop a value iteration type algorithm and analyze an error bound relative to the optimal average reward that satisfies an optimality equation from the successive approximation under an ergodicity condition we further analyze an error bound of the rolling horizon control policy defined from a finite step approximate value by applying the value iteration type algorithm

parameter and structure identification of linear multivariable systems abstract in this paper a parameter and structure identification scheme which can be used for both continuous and discrete time systems is presented this scheme has an on line nature and it incorporates standard techniques such as state variable filters and adaptation laws developed through stability analysis the canonical form being used is based on the output injection which is constructed to assign all the poles of the system to an arbitrary chosen real number it is therefore named the canonical form

multivariable adaptive dynamic surface control based on norm estimation of unknown parameter matrices in this article a novel output feedback adaptive dynamic surface control scheme is proposed for linear time invariant multivariable plants based on the norm estimation of unknown parameter matrices besides avoiding the explosion of complexity problem in traditional multivariable backstepping design the proposed scheme has the following features 1 only one parameter needs to be updated on line regardless of the plant order and input output dimension 2 only the hurwitz condition is required for the high frequency gain matrix and 3 the performance of the tracking error can be guaranteed it is shown that all signals of the closed loop system are semi globally uniformly bounded simulation results are given to illustrate the effectiveness of the proposed scheme

a multivariable self tuning controller with integral action abstract in this paper a novel stochastic self tuning control algorithm for multivariable linear systems described by controlled autoregressive integrating moving average carima models is proposed in particular the presence of an integral action on each component of the error vector ensures the robust offset rejection for any constant load disturbance acting on the plant the leading assumption is made that the system interactor matrix is known a priori the algorithm is derived by resorting to the generalized minimum variance approach two simulation examples illustrate the main features of the method

on roughness of exponential dichotomy we present new perturbation theorems on the roughness of exponential dichotomy which improve previous results the proofs given here are also much simpler compared with previous ones the new results provide significant improvements of existing results in the case where the operator a t is unbounded for t j this is precisely the situation that is of interest from the point of view of the applications in lobe dynamics the results are also valid in banach spaces and useful for general purposes

necessary and sufficient conditions for parameter convergence in adaptive control a complete description of parameter convergence in model reference adaptive control may be given in terms of the spectrum of the exogenous reference input signal abstract using generalized harmonic analysis a complete description of parameter convergence in model reference adaptive control mrac is given in terms of the spectrum of the exogenous reference input signal roughly speaking if the reference signal contains enough frequencies then the parameter vector converges to its correct value if not it converges to an easily characterizable subspace in parameter space

multivariable model reference adaptive control without constraints on the high frequency gain matrix abstract a multivariable model reference adaptive control algorithm is presented for the case when the high frequency gain matrix is unknown only an upper bound on the norm of the matrix needs to be known a priori a transformation of the parameters with a sort of hysteresis is used to guarantee that a controller matrix which is normally the inverse of the estimate of the high frequency gain matrix remains nonsingular it is shown that all the signals in the adaptive system are bounded and that the tracking error and the regressor error converge to zero for all bounded reference inputs furthermore exponential convergence is achieved when the regressor vector is persistently exciting

simultaneous structure identification and parameter estimation of multivariable systems abstract a recursive identification algorithm for multivariable systems is developed by extending the siso augmented ud identification audi algorithm developed by niu fisher and xiao in 1992 this least squares type algorithm has a simple compact structure and provides simultaneous identification of model structure and parameters with excellent numerical properties a multivariable input output difference equation model is used as the model representation for identification and it is shown how the corresponding unique canonical state space representation can also be generated by a straightforward transformation the algorithm is easier to interpret and more straightforward to implement than the corresponding rls approaches

model reference adaptive control of multivariable plants with delays the design and complete stability analysis for the model reference adaptive control mrac of multivariable plants with input and or output delays are presented in this paper a modified estimation error which enables us to solve the non commutativity problem and the stability issue in the multivariable case is introduced in the adaptive law for updating the controller parameters a generalized controller structure which achieves stable model plant transfer matrix matching in the presence of delays is developed for the multivariable mrac scheme based on a unified framework it is shown that the proposed adaptive control scheme guarantees the global stability and asymptotic zero tracking error for the closed loop system

model reference adaptive control using the delta operator reference is made to a recent paper by g c goodwin r lozano leal d q mayne and r h middleton automatica vol 22 p 199 207 1986 where it is shown that a cancellation of nonminimum phase zeros appearing in discrete time model reference adaptive control mrac at a fast sampling rate can be easily avoided if the model to be identified is expressed in terms of the delta operator a new proof of stability of the mrac is given using the delta operator which in contrast to the proof given in the above paper does not require an assumption that a system consisting of a model determined by estimated parameters and a control law based on certainty equivalence principle is exponentially stable a simple parameterization is proposed for the discrete time mrac using the delta operator which allows application of the usual i e without dead zone estimation algorithms

research on system zeros a survey this report provides a review of notable publications regarding the topic of zeros of multivariable systems in the period from 1970 into 1989 particular attention is paid to relationships between definitions of such zeros and their theoretical development transmission invariant system module infinite and finite zeros are addressed the latter subdivided into a hierarchical structure with respect to information considered in the definition process