Parallel Optimal Control for Weakly Coupled Nonlinear Systems Using Successive Galerkin Approximation

• Published in: IEEE transactions on automatic control Vol. 53; no. 6; pp. 1542 - 1547
• Main Authors: KIM, Young-Joong, LIM, Myo-Taeg
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.07.2008; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Applied sciences; Approximation; Computer science; control theory; systems; Concurrent computing; Control system synthesis; Control theory. Systems; Couplings; Design engineering; Dynamical systems; Exact sciences and technology; Feedback; Galerkin method; Galerkin methods; Integral equations; Law; Linear systems; Mathematical analysis; Modelling and identification; Nonlinear dynamics; Nonlinear equations; Nonlinear systems; Optimal control; Parallel processing; Riccati equations; weak coupling; Bellman equation; Control program; Non linear control; Computational complexity; Closed feedback; Galerkin-Petrov method; nonlinear systems; Successive approximation; Weak coupling; Optimal control; Parallel processing; Galerkin method; Reduced order systems
• ISSN: 0018-9286; 1558-2523
• DOI: 10.1109/TAC.2008.921047

This technical note presents a new algorithm for the closed-loop parallel optimal control of weakly coupled nonlinear systems with respect to performance criteria using the successive Galerkin approximation (SGA). By using the weak coupling theory, the optimal control law can be obtained from two reduced-order optimal control problems in parallel, but the resulting problem is difficult to solve for nonlinear systems. In order to overcome the difficulties inherent in the nonlinear optimal control problem, the parallel optimal control laws are constructed in terms of the approximated solutions to two independent Hamilton-Jacobi-Bellman equations using the SGA method. One of the purposes of this note is to design the closed-loop parallel optimal control law for the weakly coupled nonlinear systems using the SGA method. The second is to reduce the computational complexity when the SGA method is applied to the high-order weakly coupled systems.