Optimal controller designs satisfying state constraints

In this report, we consider the optimal control problems of the nonlinear system with state constraints in the design specifications. We design nonlinear feedback controllers to satisfy the state constraints without changing performance within the constraints by adding nonlinear weighting functions that take effect only when the state is out of the desirable bounds. We propose a method to design nonlinear optimal controllers to achieve the state constraints by solving Hamilton-Jacobi equations. We verify the effectiveness of the proposed method by a numerical example and a DC motor experiment.