In this paper we study the algebraic Riccati equation corresponding to the guaranteed cost control theory for an uncertain singularly perturbed system. The construction of the controller involves solving the full-order algebraic Riccati equation with small parameter ε. Under control-oriented assumptions, we first provide the sufficient conditions such that the full-order algebraic Riccati equat...

Abstract Two classes of recursive algorithms for computing the extreme solutions of the matrix equations X+AT X−1A = Q and X−AT X−1A = Q are presented. The Per Step Algorithms are based on the fixed point iteration method and its variations; the proposed Per Step Algorithm is an inversion free variant of the fixed point iteration method. The Doubling Algorithms are based on the cyclic reduction...

The purpose of this article is to present a brief exposition of the role of Riccati equations in the theory of reproducing kernel spaces. In particular, we shall exhibit a connection between positive semidefinite solutions of matrix Riccati equations and a class of finite dimensional reproducing kernel Hilbert spaces of rational vector valued functions, and an analogous (but more general) conne...

In this paper we examine the question when the LQR Riccati equation for matrices with components in a subalgebra A of L(H), where H is a Hilbert space, will have a unique nonnegative exponentially stabilizing solution with components in A. We give counterexamples to results claimed in the literature and some positive results for 2× 2 matrices. In addition, we pose a conjecture and an algebraic ...

In this paper, the optimal adaptive leader-follower consensus of linear continuous time multi-agent systems is considered. The error dynamics of each player depends on its neighbors’ information. Detailed analysis of online optimal leader-follower consensus under known and unknown dynamics is presented. The introduced reinforcement learning-based algorithms learn online the approximate solution...