Multilayer Neural Network-based Optimal Adaptive Tracking Control of Partially Uncertain Nonlinear Discrete-time Systems

In this paper, online optimal adaptive tracking control of nonlinear discrete-time systems in affine form with uncertain internal dynamics is presented. The augmented system and the cost function over infinite horizon for the augmented state are defined. Two-layer neural network (NN) -based actor-critic framework is introduced to estimate the optimal control input and value function. The temporal difference (TD) error is derived as a function of the difference between actual and estimated value function. The NN weights of critic and actor are tuned at every sampling instant as a function of the instantaneous temporal difference errors and control policy errors, respectively. The proposed scheme ensures the closed-loop stability in the form of boundedness. Simulation results are provided to illustrate the effectiveness of the proposed approach.