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.

Stability and the Infinite-Time Quadratic Cost Problem for Linear Hereditary Differential Systems

Abstract: This paper studies the infinite-time quadratic cost control problem for a general class of linear autonomous hereditary differential systems. It uses an approach which clarifies the system-theoretic relationship between stabilizability, stability and existence of a solution of an associated operator equation of Riccati type. For this purpose the stability problem is studied and an operator equation of the Lyapunov type is derived. In both cases we obtain equations which characterize the kernels of the Lyapunov and the Riccati equations.

Discrete Riccati Equations: Alternative Algorithms, Asymptotic Properties, and System Theory Interpretations

Abstract: Publisher Summary Algorithms have been developed that, while related to the Riccati algorithm, have important computational advantages. This chapter presents a self-contained exposition of the properties of the class of discrete-time Riccati equations that arise in the filtering problem. The point of view adopted is novel, which shows the relationship between various alternative algorithms and the Riccati equation while it connects up the asymptotic theory of such equations with the developments in linear systems theory. The chapter derives the Riccati equation and several related algorithms for the control problem by a novel approach that reveals its linear algebraic nature. It has been shown that the control problem could be reduced to a defined set of linear algebraic equations for which a solution could be found by employing orthogonal transformations. In the time-variable case, the square root version of the Riccati equation that emerges is related to similar algorithms developed in the filtering context.

Optimal quadratic guaranteed cost control of a class of uncertain time-delay systems

Abstract: The design of robust state feedback controllers for a class of uncertain linear time-delay systems with norm-bounded uncertainty is presented. The state feedback results extend previous results on quadratic guaranteed cost control to the case of uncertain time-delay systems. This is done by the authors' definition of quadratic stability for uncertain time-delay systems with norm bounded uncertainty. It is shown that the state feedback controller can be constructed via the solution of a parameter dependent Riccati equation.

Multiscale systems, Kalman filters, and Riccati equations

Abstract: An algorithm analogous to the Rauch-Tung-Striebel algorithm/spl minus/consisting of a fine-to-coarse Kalman filter-like sweep followed by a coarse-to-fine smoothing step/spl minus/was developed previously by the authors (ibid. vol.39, no.3, p.464-78 (1994)). In this paper they present a detailed system-theoretic analysis of this filter and of the new scale-recursive Riccati equation associated with it. While this analysis is similar in spirit to that for standard Kalman filters, the structure of the dyadic tree leads to several significant differences. In particular, the structure of the Kalman filter error dynamics leads to the formulation of an ML version of the filtering equation and to a corresponding smoothing algorithm based on triangularizing the Hamiltonian for the smoothing problem. In addition, the notion of stability for dynamics requires some care as do the concepts of reachability and observability. Using these system-theoretic constructs, the stability and steady-state behavior of the fine-to-coarse Kalman filter and its Riccati equation are analysed. >