Optimization of continuous-time systems with constraints: controller design using the Hamilton-Jacobi-Bellman theory

We treat optimization issues for linear continuous-time systems whose states and control are bounded. The objective of this paper is to design a nonlinear full state feedback control algorithm that satisfies the constraints by minimizing nonquadratic costs. The fundamental ideas involve the application of nonquadratic functionals and approximation of the Hamilton-Jacobi-Bellman (HJB) equation using nonquadratic return functions. Utilizing necessary and sufficient conditions, a solution for the constrained optimization problem is found and an optimal control law in the closed form is designed