Adaptive dynamic programming for optimal tracking control of stochastic linear continuous-time systems

This paper investigates optimal tracking control on stochastic continuous-time systems with multiplicative state-dependent and input-dependent noise. Preliminaries of stochastic systems and optimal tracking control are presented and an augmented stochastic differential equation of Ito's type has been constructed. To minimize the quadratic cost function, a model-dependent algorithm is shown to solve the stochastic algebraic Riccati equation. An adaptive dynamic programming (ADP) algorithm has been developed to scrap the reliance on the knowledge of system dynamics. The convergence and stability of the algorithm has been studied following. Finally, numerical simulations are performed to demonstate the effectiveness of the proposed ADP methodology on the tracking performance.