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: This paper considers hybrid controls for a class of linear quadratic problems with white noise perturbation and Markov regime switching, where the regime switching is modeled by a continuous-time Markov chain with a large state space and the control weights are indefinite.
56 citations
01 Jul 1997
TL;DR: In this article, the authors focus on the problem of asymptotic stability of a class of linear neutral systems described by differential equations with delayed state, where the delay is assumed unknown, but constant.
Abstract: This note focuses on the problem of asymptotic stability of a class of linear neutral systems described by differential equations with delayed state. The delay is assumed unknown, but constant. Sufficient conditions for delay-independent asymptotic stability are given in terms of the existence of symmetric and positive definite solutions of a continuous Riccati algebraic matrix equation coupled with a discrete Lyapunov equation. The approach adopted here is based on a Lyapunov-Krasovskii functional technique.
56 citations
TL;DR: In this article, the relationship between the regulator problem for a singularly perturbed system and the analogous one for a descriptor system is investigated, and a decomposition approach is provided for solution of the linear quadratic regulator problem.
Abstract: The relationship between the regulator problem for a singularly perturbed system and the analogous one for a descriptor system is investigated. Meanwhile, a decomposition approach is provided for solution of the linear quadratic regulator problem for singularly perturbed systems. This approach is a significant advance over the two-stage method. >
56 citations
TL;DR: In this article, the authors established criteria for the existence and uniqueness of contractive solutions of the Riccati equation KBK + KA − DK − C = 0 under the assumption that the spectra of A and D are disjoint.
56 citations
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TL;DR: This paper derives the maximum principle for the leader's global Stackelberg solution under the adapted closed-loop memoryless information structure, where the term global signifies theLeader's domination over the entire game duration.
Abstract: This paper obtains the maximum principle for both stochastic (global) open-loop and stochastic (global) closed-loop Stackelberg differential games. For the closed-loop case, we use the theory of controlled forward-backward stochastic differential equations to derive the maximum principle for the leader's optimal strategy. In the special case of the open-loop linear quadratic Stackelberg game, we consider the follower's Hamiltonian system as the leader's state equation, derive the related stochastic Riccati equation, and show the existence and uniqueness of the solution to the Riccati equation under appropriate assumptions. However, for the closed-loop linear quadratic Stackelberg game, we can write the related Riccati equation consisting of forward-backward stochastic differential equations, while leaving the existence of its solution as an open problem.
56 citations