A descriptor system approach to nonlinear singularly perturbed optimal control problem

This paper considers the infinite horizon nonlinear quadratic optimal control problem for a singularly perturbed system which is nonlinear in both, the slow and the fast variables. The relationship between this problem and the analogous one for a descriptor system is investigated. Parameter-independent controllers are constructed that solve the problem for the descriptor system and lead the full-order system to the near-optimal performance. Estimates on the closeness of the cost under near-optimal controllers to the optimal one are obtained.

[1]  Songjiao Shi,et al.  A descriptor-system approach to singular perturbation of linear regulators , 1988 .

[2]  Hiroaki Mukaidani,et al.  New method for composite optimal control of singularly perturbed systems , 1997, Int. J. Syst. Sci..

[3]  A. Isidori,et al.  Disturbance attenuation and H/sub infinity /-control via measurement feedback in nonlinear systems , 1992 .

[4]  P. Kokotovic,et al.  Singular perturbations and asymptotic analysis in control systems , 1986 .

[5]  A. Astolfi.  Disturbance Attenuation and H,-Control Via Measurement Feedback in , 1992 .

[6]  K. Mizukami,et al.  On the Isaacs equation of differential games for descriptor systems , 1994 .

[7]  Hassan K. Khalil,et al.  Singular perturbation methods in control : analysis and design , 1986 .

[8]  P. Kokotovic,et al.  A two stage Lyapunov-Bellman feedback design of a class of nonlinear systems , 1980, 1980 19th IEEE Conference on Decision and Control including the Symposium on Adaptive Processes.

[9]  H. Khalil,et al.  Stabilization and regulation of nonlinear singularly perturbed systems--Composite control , 1985 .

[10]  A. Kelley.  The stable, center-stable, center, center-unstable, unstable manifolds , 1967 .

[11]  A. Schaft.  On a state space approach to nonlinear H ∞ control , 1991 .

[12]  T. Başar,et al.  Time-scale separation and robust controller design for uncertain nonlinear singularly perturbed systems under perfect state measurements , 1996 .

[13]  Emilia Fridman,et al.  Exact slow{fast decomposition of the nonlinear singularly perturbed optimal control problem , 2000 .

[14]  C. Byrnes.  On the Riccati Partial Differential Equation for Nonlinear Bolza and Lagrange Problems , 2002 .

[15]  Singular Perturbations for Deterministic Control Problems , 1984 .

[16]  Joe H. Chow,et al.  Near-optimal feedback stabilization of a class of nonlinear singularly perturbed systems , 1978 .