Adaptive Dynamic Programming for Stochastic Systems With State and Control Dependent Noise

In this technical note, the adaptive optimal control problem is investigated for a class of continuous-time stochastic systems subject to multiplicative noise. A novel non-model-based optimal control design methodology is employed to iteratively update the control policy on-line by using directly the data of the system state and input. Both adaptive dynamic programming (ADP) and robust ADP algorithms are developed, along with rigorous stability and convergence analysis. The effectiveness of the obtained methods is illustrated by an example arising from biological sensorimotor control.