Optimal bounded control with linear stochastic equations and quadratic cost

Solvability Conditions for Indefinite Linear Quadratic Optimal Stochastic Control Problems and Associated Stochastic Riccati Equations

A linear quadratic optimal stochastic control problem with random coefficients and indefinite state/control weight costs is usually linked to an indefinite stochastic Riccati equation (SRE), which is a matrix-valued quadratic backward stochastic differential equation along with an algebraic constraint involving the unknown. Either the optimal control problem or the SRE is solvable only if the g...

Haar Matrix Equations for Solving Time-Variant Linear-Quadratic Optimal Control Problems

‎In this paper‎, ‎Haar wavelets are performed for solving continuous time-variant linear-quadratic optimal control problems‎. ‎Firstly‎, ‎using necessary conditions for optimality‎, ‎the problem is changed into a two-boundary value problem (TBVP)‎. ‎Next‎, ‎Haar wavelets are applied for converting the TBVP‎, ‎as a system of differential equations‎, ‎in to a system of matrix algebraic equations‎...

Linear Optimal Control Problems and Quadratic Cost Functions Estimation

Inverse optimal control is a classical problem of control theory. It was first posed by Kalman in the early sixties. The problem, as addressed in literature, answers to the following two questions: (a) Given system matrices A,B and a gain matrix K, find necessary and sufficient conditions for K to be the optimal of an infinite time LQ problem. (b) Determine all weight matrices Q, R and S which ...

Solvability of indefinite stochastic Riccati equations and linear quadratic optimal control problems

A new approach to study the indefinite stochastic linear quadratic (LQ) optimal control problems, which we called the “equivalent cost functional method”, is introduced by Yu [15] in the setup of Hamiltonian system. On the other hand, another important issue along this research direction, is the possible state feedback representation of optimal control and the solvability of associated indefini...

Optimal Linear Quadratic Control