Optimal control designs for systems with input saturations and rate limiters

Most systems in practice have some input saturations due to physical restrictions. But taking input saturations into account directly is not easy in ordinary control design methods. In this report, we show that the method recently developed by one of the authors is useful to approximate the exact solutions of Hamilton-Jacobi equations for systems including input saturations. First, we propose a method to design nonlinear optimal controllers for systems with input saturations by solving Hamilton-Jacobi equations. Next, it will be extend to a design method of nonlinear optimal controllers for systems with rate limited actuators. Two numerical examples are illustrated for the input saturation and input rate limited problems.