Stochastic linear-quadratic optimal control without time-consistency requirement

Time-Inconsistent Stochastic Linear-Quadratic Control

Abstract. In this paper, we formulate a general time-inconsistent stochastic linear–quadratic (LQ) control problem. The time-inconsistency arises from the presence of a quadratic term of the expected state as well as a state-dependent term in the objective functional. We define an equilibrium, instead of optimal, solution within the class of open-loop controls, and derive a sufficient condition...

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...

Time-Inconsistent Discrete-Time Stochastic Linear-Quadratic Optimal Control: Time-consistent Solutions

In this paper, the time-consistent solutions of a timeinconsistent discrete-time stochastic linear-quadratic optimal control are investigated. Different from the existing literature, the definiteness constraint is not posed on the state and the control weight matrices of the cost functional. Necessary and sufficient conditions are, respectively, obtained to the existence of the open-loop time-c...

Optimal Linear Quadratic Control

Linear Quadratic Optimal Control

In previous lectures, we discussed the design of state feedback controllers using using eigenvalue (pole) placement algorithms. For single input systems, given a set of desired eigenvalues, the feedback gain to achieve this is unique (as long as the system is controllable). For multi-input systems, the feedback gain is not unique, so there is additional design freedom. How does one utilize this...