Abstract:

Linear quadratic control of a class of continuous-time singular stochastic affine systems is investigated. After establishing some concepts of the stability for stochastic singular systems, the condition of the stability is presented by means of a linear matrix inequality. Then, by utilizing Riccati equation approach, the existent conditions of optimal feedback control in finite horizon and infinite horizon are respectively obtained by means of a generalized differential Riccati equation or a generalized algebraic Riccati equation. And explicit expressions of the optimal feedback controls and optimal cost function are given.

Key words: singular stochastic affine systems; linear quadratic control; linear matrix inequality; Riccati equation