Optimal control of nonlinear continuous-time systems: design of bounded controllers via generalized nonquadratic functionals

By using the Hamilton-Jacobi framework and sufficiency theory, this paper presents a solution of the constrained optimization problem for nonlinear systems with soft and hard bounds imposed on control. The developed concept is based on the application of a generalized nonquadratic cost, and nonquadratic return functions are applied. Necessary and sufficient conditions have been used to synthesize the bounded controllers, and sufficient conditions are applied to verify the optimality. The constrained optimization problem is solved for nonlinear systems, and the offered results extend the application of the Hamilton-Jacobi theory by using a generalized nonquadratic cost. The design procedure is reviewed in the context of motion control applications. Analytical, numerical, and experimental results are presented for a servo-system actuated by a permanent-magnet DC motor. The designed nonlinear controller is experimentally verified.