Decentralized nearly optimal control of a class of interconnected nonlinear discrete-time systems by using online Hamilton-Bellman-Jacobi formulation

In this paper, the direct neural dynamic programming technique is utilized to solve the Hamilton Jacobi-Bellman (HJB) equation online and forward-in-time for the decentralized nearly optimal control of nonlinear interconnected discrete-time systems in affine form with unknown internal subsystem and interconnection dynamics. Only the state vector of the local subsystem is considered measurable. The decentralized optimal controller design for each subsystem consists of an action neural network (NN) that is aimed to provide a nearly optimal control signal, and a critic NN which approximates the cost function. The NN weights are tuned online for both the NNs. It is shown that all subsystems signals are uniformly ultimately bounded (UUB) and that the subsystem inputs approach their corresponding nearly optimal control inputs with bounded error.