In this paper, we consider a class of nonlinear regulator optimal control problems with an infinite planning horizon. By assuming a specific feedback structure for the controller, the original problem is reduced to a constrained optimal parameter selection problem. Because the reduced problem is on an infinite planning horizon, we construct a sequence of finite time optimal parameter selection problems in which each is readily solvable using existing numerical software. The question concerning the asymptotical stability of the dynamical system under the obtained optimal feedback controller is then investigated. For illustration, two numerical examples are considered.
Teo, K. L., Fisher, M., & Moore, J. B. (1993). A suboptimal feedback stabilizing controller for a class of nonlinear regulator problems. Applied Mathematics and Computation, 59, 1-17. https://doi.org/10.1016/S0096-3003(93)90038-G