Topic
Riccati equation
About: Riccati equation is a research topic. Over the lifetime, 10428 publications have been published within this topic receiving 210015 citations. The topic is also known as: Riccati's differential equation.
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TL;DR: In this paper, the authors studied the stabilization and regulation of linear discrete-time systems whose coefficients depend on one or more parameters and derived closed-form expressions for a collection of stabilizing gains in terms of the reachability Gramian.
Abstract: The stabilization and regulation of linear discrete-time systems whose coefficients depend on one or more parameters is studied. For linear systems whose coefficients are continuous functions of real or complex parameters (respectively, analytic or rational functions of real parameters), it is shown that reachability of the system for all values of the parameters implies that the system can be stabilized using gains that are also continuous (analytic, rational) functions of the parameters. Closed-form expressions for a collection of stabilizing gains are given in terms of the reachability Gramian. For systems which are stabilizable for all values of the parameters, it is shown that continuous (analytic, rational) stabilizing gains can be computed from a finite-time solution to a Riccati difference equation whose coefficients are functions of the parameters. These results are then applied to the problem of tracking and disturbance rejection in the case when both the plant and the exogenous signals contain parameters.
97 citations
TL;DR: In this article, an approximation theory for the linear-quadratic-Gaussian optimal control problem for flexible structures whose distributed models have bounded input and output operators is presented, where the main purpose is to guide the design of finite-dimensional compensators that approximate closely the optimal compensator, which is infinite-dimensional.
Abstract: This paper presents approximation theory for the linear-quadratic-Gaussian optimal control problem for flexible structures whose distributed models have bounded input and output operators. The main purpose of the theory is to guide the design of finite-dimensional compensators that approximate closely the optimal compensator, which is infinite-dimensional. Design of the optimal compensator separates into an optimal linear-quadratic control problem and a dual optimal state estimation problem; the solution to each problem lies in the solution to an infinite-dimensional Riccati operator equation. The approximation scheme in the paper approximates the infinite-dimensional LQG problem with a sequence of finite-dimensional LQG problems defined for a sequence of finite-dimensional, usually finite-element or modal, approximations of the distributed model of the structure. Two Riccati matrix equations determine the solution to each approximating problem.The finite-dimensional equations for numerical approximation ...
97 citations
TL;DR: In this paper, it was shown that an appropriate solution of an algebraic Riccati type equation determines the value of the game but not necessarily any equilibrium strategies for a class of infinite time linear quadratic games.
Abstract: For a class of infinite time linear quadratic games it is shown that an appropriate solution of an algebraic Riccati type equation determines the value of the game but not necessarily any equilibrium strategies. In the case of nonexistence of equilibrium strategies, e-optimal strategies are constructed through the solutions of a differential Riccati equation.
97 citations
TL;DR: It is shown that the index of a 1-reducible subgroup of the differential Galois group of an ordinary homogeneous linear differential equation L(y) = 0 yields the best possible bound for the degree of the minimal polynomial of an algebraic solution of the Riccati equation.
97 citations
TL;DR: In this article, the global existence and uniqueness result for a general one-dimensional backward stochastic Riccati equation was obtained and applied to the mean-variance hedging problem.
97 citations