Well-posedness and attainability of indefinite stochastic linear quadratic control in infinite time horizon

DOI10.1016/S0167-6911(00)00046-3zbMath0985.93060WikidataQ127975923 ScholiaQ127975923MaRDI QIDQ1583219

John B. Moore, Xun Yu Zhou, Mustapha Ait Rami

Publication date: 26 October 2000

Published in: Systems \& Control Letters (Search for Journal in Brave)

zbMATH Keywords

semidefinite programminglinear matrix inequalitywell-posednessmaximal solutiongeneralized algebraic Riccati equationstabilizing solutionstochastic linear-quadratic controlindefinite cost weighting matrices

Mathematics Subject Classification ID

Stabilization of systems by feedback (93D15) Linear inequalities of matrices (15A39) Optimal stochastic control (93E20)

Related Items (23)

On the Matrix EquationX = Q − S∗X†S ⋮ An indefinite stochastic linear quadratic optimal control problem with delay and related forward-backward stochastic differential equations ⋮ On some iterations for optimal control of jump linear equations ⋮ Infinite horizon indefinite stochastic linear quadratic control for discrete-time systems ⋮ Partial stabilizability and hidden convexity of indefinite LQ problem ⋮ Indefinite LQ optimal control with equality constraint for discrete-time uncertain systems ⋮ Some remarks on infinite horizon stochastic \(H_2/H_\infty\) control with \((x,u,v)\)-dependent noise and Markov jumps ⋮ The LMI approach for stabilizing of linear stochastic systems ⋮ Stochastic linear quadratic optimal control problems in infinite horizon ⋮ Properties of Stein (Lyapunov) iterations for solving a general Riccati equation ⋮ Optimal regulators for a class of nonlinear stochastic systems ⋮ Optimal regulator for a class of nonlinear stochastic systems with random coefficients ⋮ An adaptive dynamic programming-based algorithm for infinite-horizon linear quadratic stochastic optimal control problems ⋮ Stabilization in probability and mean square of controlled stochastic dynamical system with state delay ⋮ Linear quadratic stochastic two-person zero-sum differential games in an infinite horizon ⋮ Iterations for solving a rational Riccati equation arising in stochastic control ⋮ Infinite horizon multiobjective optimal control of stochastic cooperative linear-quadratic dynamic difference games ⋮ Indefinite stochastic linear-quadratic optimal control problems with random jumps and related stochastic Riccati equations ⋮ Two iterative algorithms for stochastic algebraic Riccati matrix equations ⋮ Mean-field linear-quadratic stochastic differential games in an infinite horizon ⋮ Open-Loop and Closed-Loop Solvabilities for Stochastic Linear Quadratic Optimal Control Problems ⋮ Solvability and optimal stabilization controls of discrete-time mean-field stochastic system with infinite horizon ⋮ An equivalence result in linear-quadratic theory

Cites Work

• Discrete time LQG controls with control dependent noise
• Stochastic Linear Quadratic Regulators with Indefinite Control Weight Costs
• Linear Matrix Inequalities in System and Control Theory
• Linear matrix inequalities, Riccati equations, and indefinite stochastic linear quadratic controls
• Relationship Between Backward Stochastic Differential Equations and Stochastic Controls: A Linear-Quadratic Approach
• Semidefinite Programming
• On the Separation Theorem of Stochastic Control
• Extensions of quadratic minimization theory I. Finite time results
• Conditions for Positive and Nonnegative Definiteness in Terms of Pseudoinverses
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