Constrained Optimal Control for a Class of Nonlinear Systems with Uncertainties

Approximate dynamic programming formulation (ADP) implemented with an Adaptive Critic (AC) based neural network (NN) structure has evolved as a powerful technique for solving the Hamilton-Jacobi-Bellman (HJB) equations. As interest in the ADP and the AC solutions are escalating, there is a dire need to consider enabling factors for their possible implementations. A typical AC structure consists of two interacting NNs which is computationally expensive. In this paper, a new architecture, called the "Cost Function Based Single Network Adaptive Critic (J-SNAC)" is presented that eliminates one of the networks in a typical AC structure. This approach is applicable to a wide class of nonlinear systems in engineering. Many real-life problems have controller limits. In this paper, a non-quadratic cost function is used that incorporates the control constraints. Necessary equations for optimal control are derived and an algorithm to solve the constrained-control problem with J-SNAC is developed. A benchmark nonlinear system is used to illustrate the working of the proposed technique. Extensions to optimal control-constrained problems in the presence of uncertainties are also considered.