Constrained controller design for a class of nonlinear discrete-time uncertain systems

In this paper, constrained controller design is proposed for a class of nonlinear discrete-time uncertain system having matched type system uncertainties, using the solution of HJB (Hamilton-Jaccobi-Bellman) equation. The discrete-time HJB equation is formulated using a suitable non-quadratic term in the performance functional to tackle constraints on the control input. Based on the non-quadratic functional, a greedy HDP algorithm is used to obtain the constrained robust-optimal controller. The constrained robust controller requires knowledge of the upper bound of system uncertainties. For facilitating the implementation of the iterative algorithm, two neural networks are used to approximate the value function and to compute the optimal control policy, respectively. Their weights have been tuned using least squares method. Proposed algorithm has been applied on a nonlinear discrete-time system with matched uncertainties.