A two-neural network approach to solving nonlinear optimal control problems is described in this study. This approach called the adaptive critic method consists of one neural network called the supervisor or the critic and a second network called an action network or a controller. The inputs to both these networks are the current states of the system to be controlled. Targets for each network updates are obtained with outputs of the other network, state propagation equations and the conditions for optimal control. When their outputs are mutually consistent, the controller network output is optimal. The optimality is however limited by the underlying system model. Hence, we develop a Lyapunov based theory for robust stability of these controllers when there is input uncertainty. This results in an expression for extra control. This extra control added with the base control effort keeps the system stable under input uncertainties. We illustrate this approach through a longitudinal autop...
Zhongwu Huang, S. N. Balakrishnan