OStabilization of affine nonlinear systems with input constraints via generalized Hamilton-Jacobi-Bellman equation approach

This paper deals with the stabilization of affine nonlinear systems with input saturation. We formulate the Hamilton-Jacobi-Bellman (HJB) equation corresponding to constrained control. A recursive algorithm for sequential improvement of the control which converges to the nearly optimal law is proposed by solving for a sequence of cost functions satisfying a sequence of generalized Hamilton-Jacobi-Bellman (GHJB) equations, and may provide a procedure for selecting effective controls for nonlinear systems with input constraints. The approach has been applied to a simple example to show the effectiveness of the proposed controller with input constraints.