Neuro-optimal tracking control for a class of discrete-time nonlinear systems via generalized value iteration adaptive dynamic programming approach

In this paper, a novel value iteration adaptive dynamic programming (ADP) algorithm, called “generalized value iteration ADP” algorithm, is developed to solve infinite horizon optimal tracking control problems for a class of discrete-time nonlinear systems. The developed generalized value iteration ADP algorithm permits an arbitrary positive semi-definite function to initialize it, which overcomes the disadvantage of traditional value iteration algorithms. Convergence property is developed to guarantee that the iterative performance index function will converge to the optimum. Neural networks are used to approximate the iterative performance index function and compute the iterative control policy, respectively, to implement the iterative ADP algorithm. Finally, a simulation example is given to illustrate the performance of the developed algorithm.