finite horizon ℋ 2 ℋ control for a class of nonlinear markovian jump systems with probabilistic sensor failures this article is concerned with the mixed 2 control problem over a finite horizon for a class of nonlinear markovian jump systems with both stochastic nonlinearities and probabilistic sensor failures the stochastic nonlinearities described by statistical means could cover several types of well studied nonlinearities and the failure probability for each sensor is governed by an individual random variable satisfying a certain probability distribution over a given interval the purpose of the addressed problem is to design state feedback controllers such that the closed loop system achieves the expected 2 performance requirement with a guaranteed disturbance attenuation level the solvability of the addressed control problem is expressed as the feasibility of certain coupled matrix equations the controller gain at each time instant k can be obtained by solving the corresponding set of matrix equations a numerical example is given to illustrate the effectiveness and applicability of the proposed al

brief paper bounded nash type controls for uncertain linear systems this paper deals with multicriteria controls for systems coping with polytopic uncertainties the proposed controls are inspired by a nash strategy for exactly known systems reformulated as a nonconvex coupling between semi definite programming problems the extension to the uncertain case duplicates the linear matrix inequalities for all vertices of the polytope a new iterative algorithm using semi definite programming is provided to design bounded nash type controls for uncertain systems a numerical example is given to illustrate the design method

h 2 h control for stochastic systems with delay this paper is concerned with the h2 h control problem for stochastic linear systems with delay in state control and external disturbance dependent noise a necessary and sufficient condition for the existence of a unique solution to the control problem is derived the resulting solution is characterised by a kind of complex generalised forward backward stochastic differential equations with stochastic delay equations as forward equations and anticipated backward stochastic differential equations as backward equations especially we present the equivalent feedback solution via a new type of riccati equations to explain the theoretical results we apply them to a population control problem

infinite horizon stochastic h2 h control for discrete time systems with state and disturbance dependent noise this paper studies the infinite horizon mixed h 2 h control for discrete time stochastic systems with state and disturbance dependent noise we shall first establish a version of stochastic bounded real lemma sbrl which by itself has theoretical importance based on the sbrl it is shown that under the condition of exact observability the existence of a static state feedback h 2 h controller is equivalent to the solvability of four coupled matrix valued equations a suboptimal h 2 h controller design is given based on a convex optimization approach and an iterative algorithm is proposed to solve the four coupled matrix valued equations

stochastic h2 h control with x u v dependent noise finite horizon case in this paper the finite horizon mixed h 2 h control problem is studied for the systems governed by ito type nonlinear stochastic differential equations with state control and external disturbance dependent noise it is shown that the mixed h 2 h control under consideration is associated with the four cross coupled hamilton jacobi equations a discrete approximation algorithm is presented for solving the coupled generalized differential riccati equations arising from linear stochastic h 2 h control a necessary condition and a sufficient condition for the existence of the finite horizon stochastic h 2 h control are derived in particular some previous results on deterministic and stochastic h 2 h control can be viewed as corollaries of our main theorems

a nash game approach to mixed h sub 2 h sub spl infin control the established theory of nonzero sum games is used to solve a mixed h sub 2 h sub spl infin control problem our idea is to use the two pay off functions associated with a two player nash game to represent the h sub 2 and h sub spl infin criteria separately we treat the state feedback problem and we find necessary and sufficient conditions for the existence of a solution both the finite and infinite time problems are considered in the infinite horizon case we present a full stability analysis the resulting controller is a constant state feedback law characterized by the solution to a pair of cross coupled riccati equations which may be solved using a standard numerical integration procedure we begin our development by considering strategy sets containing linear controllers only at the end of the paper we broaden the strategy sets to include a class of nonlinear controls it turns out that this extension has no effect on the necessary and sufficient conditions for the existence of a solution or on the nature of the controllers

lqg control with an h sup infinity performance bound a riccati equation approach an lqg linear quadratic gaussian control design problem involving a constraint on h sup infinity disturbance attenuation is considered the h sup infinity performance constraint is embedded within the optimization process by replacing the covariance lyapunov equation by a riccati equation whose solution leads to an upper bound on l sub 2 performance in contrast to the pair of separated riccati equations of standard lqg theory the h sup infinity constrained gains are given by a coupled system of three modified riccati equations the coupling illustrates the breakdown of the separation principle for the h sup infinity constrained problem both full and reduced order design problems are considered with an h sup infinity attenuation constraint involving both state and control variables an algorithm is developed for the full order design problem and illustrative numerical results are given

mixed h 2 h autopilot design of bank to turn missiles using fuzzy basis function networks this paper presents a novel mixed h2 h autopilot design for bank to turn missiles based on sliding control theory the proposed autopilot utilizes a fuzzy basis function network to approximate the unknown nonlinear functions of bank to turn missile dynamics enabling a mixed h2 h controller with weight updating laws to be applied to attenuate the effects of approximation errors and external disturbances moreover the mixed h2 h autopilot design can minimize h2 performance criteria under a desired h disturbance rejection constraint unlike general mixed h2 h control problems the proposed h2 h autopilot with self tuning fuzzy basis function network can avoid solving coupled riccati equations by adequately selecting diagonal weighting matrices in the h2 performance criterion and h constraint therefore the proposed h2 h control approach can be implemented efficiently computer simulation results are presented to illustrate the effectiveness of the proposed mixed h2 h autopilot for btt missiles

brief paper stochastic h2 h control for discrete time systems with state and disturbance dependent noise this paper is to study the discrete time stochastic h 2 h control with state and external disturbance dependent noise a necessary and sufficient condition for the existence of h 2 h control is presented which transforms the h 2 h controller design into solving four coupled matrix valued equations moreover a recursive algorithm for solving the four coupled matrix valued equations is also given

a numerical algorithm to find all feedback nash equilibria in scalar affine quadratic differential games this note deals with solving scalar coupled algebraic riccati equations these equations arise in finding linear feedback nash equilibria of the scalar n player affine quadratic differential game a numerical procedure is provided to compute all the stabilizing solutions the main idea is to reformulate the riccati equations into an extended eigenvalue eigenvector problem for a specific parametrized matrix u in i r 2 n times 2 n since the size of u increases exponentially on n the algorithm only applies for games where the number of players is not too large

some remarks on general nonlinear stochastic h_ infty control with state control and disturbance dependent noise this technical note studies the nonlinear stochastic h control of ito type differential systems with all the state control input and external disturbance dependent noise x u v dependent noise for short a sufficient condition is given for the finite infinite horizon h control of such a system by means of an hamilton jacobi inequality hji instead of three coupled hamilton jacobi equations hjes as in previous literature

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

necessary and sufficient conditions for mixed h sub 2 and h sub infinity optimal control it is shown that d s bernstein and w m hadad s ibid vol 34 no 3 p 293 1989 necessary condition for full order mixed h sub 2 and h sub infinity optimal control is also sufficient and that j c doyle et al s proc amer control conf p 2065 1989 sufficient condition for full order mixed h sub 2 and h sub infinity optimal control is also necessary they are duals of one another

a state space algorithm for the solution of the 2 block superoptimal distance problem a state space algorithm for computing the solution of the 2 block superoptimal distance problem sodp is presented given a rational and antistable matrix function r s r 11 s r 12 s find all stable approximations q s that lexicographically minimize the singular values of the error function e s r 11 s r 12 s q s conditions are given for which the superoptimal approximation is unique in addition an a priori upper bound on the macmillan degree of the approximation is given the algorithm may be stopped after minimizing a given number of singular values this premature termination of the algorithm carries with it an expected saving in the computational effort and a predictable reduction in the macmillan degree of the approximation the algorithm only requires standard linear algebraic computations and is therefore easily implemented

a maximum entropy principle for contractive interpolants abstract in this paper a maximum entropy principle is established for a class of continuous contractive m n matrix valued functions g with preassigned fourier coefficients gj j for j 0 1 the function g in this class which achieves the maximum entropy is characterized in a number of different ways and its entropy is computed in terms of a hankel operator based on the prescribed matrices 0 1 a pair of seemingly new szego type formulas are obtained enroute and some applications to nevanlinna pick interpolation are indicated

pareto optimal strategy for linear stochastic systems with h constraint in finite horizon abstract in this paper we derive conditions for the existence of pareto efficient strategy and pareto solution under h constraint for the linear quadratic lq finite horizon cooperative differential game of stochastic systems with state control and disturbance multiplicative noise firstly we present a stochastic bounded real lemma sbrl with any initial condition for the considered stochastic system next a necessary and sufficient condition for pareto optimal strategy under the h constraint is researched by two cross coupled generalized differential riccati equations gdres which is the key contribution of this paper another contribution is that the pareto solution for every controller is given under the pareto efficient strategy and worst case external disturbance finally a practical example is given to illustrate the effectiveness of our results

stochastic h sub 2 h sub spl infin control with state dependent noise this paper discusses the stochastic h sub 2 h sub spl infin control problem with state dependent noise by means of the stabilization exact observability and stochastic detectability of stochastic systems the infinite horizon stochastic h sub 2 h sub spl infin control design is developed for the finite horizon h sub 2 h sub spl infin control problem our results generalize the corresponding deterministic ones to the stochastic models finally the observer based suboptimal stochastic h sub 2 h sub spl infin control is discussed in which the state variables cannot be measured directly and a feasible design algorithm is proposed

on global existence of solutions to coupled matrix riccati equations in closed loop nash games presents comparison and global existence results for solutions of coupled matrix riccati differential equations appearing in closed loop nash games and in mixed h sub 2 h sub spl infin type problems convergence of solutions is established for the diagonal case solutions of the corresponding algebraic equations are discussed using numerical examples

reliable mixed l2 h fuzzy static output feedback control for nonlinear systems with sensor faults this paper is concerned with the design of reliable mixed l 2 h static output feedback sof fuzzy controllers for nonlinear continuous time systems with complete sensor faults the takagi and sugeno t s fuzzy model is employed to represent a nonlinear system a sufficient condition for the existence of reliable mixed l 2 h sof fuzzy controllers is presented in terms of a set of quadratic matrix inequalities qmis which not only guarantees that the closed loop fuzzy system satisfies a desired h disturbance attenuation constraint for all admissible operating regimes including the normal and sensor fault cases but also provides different upper bounds on the l 2 performance criterion for different operating regimes a suboptimal reliable fuzzy controller is obtained by the proposed iterative linear matrix inequality ilmi algorithm for minimizing the normal l 2 performance bound while maintaining acceptable lower levels of the bounds in the sensor fault cases finally a numerical example is given to illustrate the effectiveness of the proposed design method

relationship between nash equilibrium strategies and h_ 2 h_ infty control of stochastic markov jump systems with multiplicative noise this technical note is concerned with discussing the relationship between nash equilibrium strategies and the finite horizon h 2 h control of time varying stochastic systems subject to markov jump parameters and multiplicative noise it is revealed that the equivalence of these two problems depends on whether the disturbance enters into the diffusion term furthermore necessary and sufficient conditions for the finite horizon h 2 h control of stochastic markov jump systems are presented via coupled matrix valued equations

a state space approach to super optimal h sup infinity control problems a numerically stable algorithm is presented for solving the strengthened or super optimal model matching problem the steps of the algorithm follows closely those given by n j young 1986 except that for each step a reliable implementation using state space models is provided

stochastic h2 h control of nonlinear systems with time delay and state dependent noise this paper investigates the problem of h2 h control for nonlinear stochastic systems with time delay and state dependent noise firstly a sufficient condition for the existence of the nonlinear stochastic h2 h control with time delay is presented in terms of coupled hamilton jacobi equations hjes secondly by using the fuzzy approach the stochastic h2 h controller can be designed via solving a set of linear matrix inequalities instead of coupled hjes finally two numerical examples are employed to show the effectiveness of the results obtained

a model for the bus system in cuernavaca mexico the bus system in cuernavaca mexico and its connections to random matrix distributions have been the subject of an interesting recent study by m krbalek and p seba in 15 16 in this paper we introduce and analyse a microscopic model for the bus system we show that introducing a natural repulsion does produce random matrix distributions in natural double scaling regimes the techniques employed include non intersecting paths logarithmic potential theory determinantal point processes and asymptotic analysis of several orthogonal polynomial ensembles in addition we introduce a circular bus model and include various calculations of non crossing probabilities

state space algorithm for the computation of superoptimal matrix interpolating functions a state space algorithm is studied which generates the unique superoptimal nehari extension of a general rational matrix the procedure is to use a set of all pass transformations to sequentially minimize each frequency dependent singular value of the interpolating function in a dimension peeling algorithm these all pass transformations are determined by the maximal schmidt pairs of a sequence of hankel operators the process terminates when the original problem is reduced to one of rank one at this stage all the available degrees of freedom have been exhausted the work is an extension of that by young 1986 and gives a concrete state space implementation of his operator theoretic arguments in addition bounds are given on the minimum achievable values for s1 e sup ersi e j i 1 2 rank g0 and also the mcmillan degree of the final superoptimal extension here si denotes the ith singular value of a frequency dependent matrix and the numbering is taken to be in decrea

a game theoretic approach to h control for time varying systems a representation formula for all controllers that satisfy an mathcal l infty type constraint is derived for time varying systems it is now known that a formula based on two indefinite algebraic riccati equations may be found for time invariant systems over an infinite time support see j c doyle et al ieee trans automat control ac 34 1989 pp 831 847 k glover and j c doyle systems control lett 11 1988 pp 167 172 k glover et al siam j control optim 29 1991 pp 283 324 m green et al siam j control optim 28 1990 pp 1350 1371 d j n limebeer et al in proc ieee conf on decision and control austin tx 1988 g tadmor math control systems signal processing 3 1990 pp 301 324 in the time varying case two indefinite riccati differential equations are required a solution to the design problem exists if these equations have a solution on the optimization interval the derivation of the representation formula illustrated in this paper mak

multi player non zero sum games online adaptive learning solution of coupled hamilton jacobi equations in this paper we present an online adaptive control algorithm based on policy iteration reinforcement learning techniques to solve the continuous time ct multi player non zero sum nzs game with infinite horizon for linear and nonlinear systems nzs games allow for players to have a cooperative team component and an individual selfish component of strategy the adaptive algorithm learns online the solution of coupled riccati equations and coupled hamilton jacobi equations for linear and nonlinear systems respectively this adaptive control method finds in real time approximations of the optimal value and the nzs nash equilibrium while also guaranteeing closed loop stability the optimal adaptive algorithm is implemented as a separate actor critic parametric network approximator structure for every player and involves simultaneous continuous time adaptation of the actor critic networks a persistence of excitation condition is shown to guarantee convergence of every critic to the actual optimal value function for that player a detailed mathematical analysis is done for 2 player nzs games novel tuning algorithms are given for the actor critic networks the convergence to the nash equilibrium is proven and stability of the system is also guaranteed this provides optimal adaptive control solutions for both non zero sum games and their special case the zero sum games simulation examples show the effectiveness of the new algorithm

derivation of the maximum entropy h controller and a state space formula for its entropy the problem of maximizing the entropy of a stabilized closed loop system is solved the solution exploits the parametrization of all closed loop systems that meet an h norm bound the central solution of this set is shown to maximize the entropy at infinity and for this case a particularly simple formula is derived for the maximum value of the entropy

coordinate rings for the moduli stack of sl2 c quasi parabolic principal bundles on a curve and toric fiber products abstract we continue the program started in manon 2010 m1 to understand the combinatorial commutative algebra of the projective coordinate rings of the moduli stack m c p sl 2 c of quasi parabolic sl 2 c principal bundles on a generic marked projective curve we find general bounds on the degrees of polynomials needed to present these algebras by studying their toric degenerations in particular we show that the square of any effective line bundle on this moduli stack yields a koszul projective coordinate ring this leads us to formalize the properties of the polytopes used in proving our results by constructing a category of polytopes with term orders we show that many of results on the projective coordinate rings of m c p sl 2 c follow from closure properties of this category with respect to fiber products

mixed h sub 2 h sub infinity control a convex optimization approach the problem of finding an internally stabilizing controller that minimizes a mixed h sub 2 h sub infinity performance measure subject to an inequality constraint on the h sub infinity norm of another closed loop transfer function is considered this problem can be interpreted and motivated as a problem of optimal nominal performance subject to a robust stability constraint both the state feedback and output feedback problems are considered it is shown that in the state feedback case one can come arbitrarily close to the optimal even over full information controllers mixed h sub 2 h sub infinity performance measure using constant gain state feedback moreover the state feedback problem can be converted into a convex optimization problem over a bounded subset of n n and n q where n and q are respectively the state and input dimensions real matrices using the central h sub infinity estimator it is shown that the output feedback problem can be reduced to a state feedback problem in this case the dimension of the resulting controller does not exceed the dimension of the generalized plant

solutions to the h general distance problem which minimize an entropy integral abstract we pose and solve the problem of minimizing the entropy of an h norm bounded and stabilized closed loop solution proceeds via the equivalent error system distance problem the central member of the admissible class is shown to minimize the entropy at infinity and in that case an explicit state space formula is derived for the minimum value of the entropy links between entropy h 2 norms and h 2 optimal control are given

output feedback h2 h consensus control for stochastic time varying multi agent systems with x u v dependent noises abstract in this paper the output feedback h 2 h consensus control problem is investigated for discrete time varying stochastic multi agent systems with state control and disturbance dependent noises also called x u v dependent noises two new concepts for the h 2 and h consensus requirements are proposed to quantify the transient behavior of the consensus over a finite horizon for the addressed time varying multi agent systems we aim to design an output feedback consensus controller such that the closed loop multi agent systems achieve the prescribed h 2 and h consensus performances over a finite horizon by using the completing squares method and stochastic analysis techniques sufficient conditions are derived for the existence of the desired output feedback h 2 h consensus controller in terms of the solution to two coupled backward recursive riccati difference equations rdes moreover an iterative algorithm is proposed for solving the rdes by resorting to the moore penrose pseudo inverse a numerical example is utilized to illustrate the effectiveness of the proposed h 2 h consensus control strategy

a polynomial approach to minimax frequency domain optimization of multivariable feedback systems the properties of a feedback system where the plant has rational transfer matrix h and the compensator has transfer matrix g can be characterized through the system functions s i hg and t g i hg 1 good disturbance attenuation robustness limited bandwidth and compensator roll off may be obtained by minimizing a criterion of the form z where z v s t w1 wls t w2 w2t v with respect to the compensator transfer matrix g here v w1 and w2 are suitable rational weighting matrices the solution of the problem can be reduced to a pair of matrix polynomial equations since the optimal solution is highly non unique special solutions with additional optimality properties are considered as well the paper includes a discussion of the numerical solution of the polynomial equations and of the question how to choose the weighting matrices to ensure required feedback system properties an example illustrates the results

robust h filter design for neutral stochastic uncertain systems with time varying delay abstract in this paper the robust h filtering problem for a class of neutral stochastic systems is discussed the system under consideration contains parameter uncertainties ito type stochastic disturbances time varying delay the parameter uncertainties are assumed to be time varying norm bounded using the stochastic lyapunov stability theory and ito s differential rule a full order filter is designed for all admissible uncertainties and time varying delay which is expressed in the form of linear matrix inequality lmi the dynamics of the filtering error systems are guaranteed to be robust stochastically mean square asymptotically stable while achieving a prescribed stochastic robust h performance level at the end of this paper a numerical example is given to demonstrate the usefulness of the proposed method

state space solutions to standard h sub 2 and h sub infinity control problems simple state space formulas are derived for all controllers solving the following standard h sub infinity problem for a given number gamma 0 find all controllers such that the h sub infinity norm of the closed loop transfer function is strictly less than gamma it is known that a controller exists if and only if the unique stabilizing solutions to two algebraic riccati equations are positive definite and the spectral radius of their product is less than gamma sup 2 under these conditions a parameterization of all controllers solving the problem is given as a linear fractional transformation lft on a contractive stable free parameter the state dimension of the coefficient matrix for the lft constructed using the two riccati solutions equals that of the plant and has a separation structure reminiscent of classical lqg i e h sub 2 theory this paper is intended to be of tutorial value so a standard h sub 2 solution is developed in parallel

relations between maximum entropy h control and combined h lqg control abstract the maximum entropy h control problem and a combined h lqg control problem are presented in a unified way and shown to be equivalent in the case of a full order controller and equalized h lqg weights the result links two separate approaches which have distinctly different methods of solution only two decoupled algebraic riccati equations are needed to state the controller maximum value of the entropy and minimum value of the auxiliary cost

properties of feedback nash equilibria in scalar lq differential games in this paper we study the scalar linear quadratic differential game with state feedback information structure using a geometric approach we present a complete characterization when this game will have no one or multiple equilibria furthermore we investigate the effect on this solution structure of some characteristics of the game i e the number of players the entrance of new players the level of asymmetry and the impact entrance of an additional player has on the closed loop stability of the game for that purpose we distinguish three types of the game the economic game the regulator game and the mixed game the analysis is restricted to the case the involved cost depend only on the state and control variables

an analysis of the pole zero cancellations in h optimal control problems of the first kind the aim of this paper is to study the pole zero cancellations which occur in a class of h infty optimal control problems which may be embedded in the configuration of fig 1 h infty control problems are said to be of the first kind if both p 12 s and p 21 s are square but not necessarily of the same size it is primarily this class of problems which will concern us here a general bound on the mcmillan degree of all controllers which are stabilizing and lead to a closed loop which satisfies bf mathcal r s infty leqq rho rho need not be optimal in the l infty norm sense is derived as illustrated in fig 1 bf mathcal r s is the transfer function relating y 1 s to u 1 s if the mcmillan degree of p s in fig 1 is n we show that in the single loop siso case the corresponding unique h infty optimal controller never requires more than n 1 states in the multivariable case there is a continuum of optimal controllers whose mcmil