Design of approximately optimal feedback controllers for systems with bounded states

Implementation is one of the most pronounced difficulties in designing optimal feedback controllers to prevent the state variables of the system from exceeding predetermined bounds. A method to obtain approximately optimal feedback controllers based on the geometric features of the optimal open-loop solution of the bounded state variable problem is presented in this paper. Easily instrumentable controllers are designed and successfully tested on various plants to furnish a value of the performance criterion close to the optimal. Typical examples illustrate the approach.