Global Inverse Optimal Control With Guaranteed Convergence Rates of Input Affine Nonlinear Systems

• Published in: IEEE transactions on automatic control Vol. 56; no. 2; pp. 358 - 369
• Main Authors: Nakamura, N, Nakamura, H, Nishitani, H
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.02.2011; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Applied sciences; Asymptotic properties; Computer science; control theory; systems; Control Lyapunov function; Control system synthesis; Control systems; Control theory; Control theory. Systems; Controllers; Convergence; convergence rate; coordinate transformation; Design methodology; Dynamical systems; Exact sciences and technology; Invariants; Inverse; Linearity; Lyapunov method; Nonlinear control systems; Nonlinear dynamics; Nonlinear systems; Optimal control; Optimization; Stability; Invariant; Transformation of coordinates; Non linear control; Control synthesis; Non linear system; Affine transformation; Optimization; coordinate transformation; Asymptotic stability; nonlinear systems; Optimal control; Global stabilization; Homogeneity; Control Lyapunov function; convergence rate; Numerical convergence; Lyapunov function
• ISSN: 0018-9286; 1558-2523
• DOI: 10.1109/TAC.2010.2053731

In earlier works, global inverse optimal controllers were proposed for input affine nonlinear systems with given control Lyapunov functions. However, these controllers do not provide information about the convergence rates. If the systems have local homogeneous approximations, we can employ homogeneous controllers, which locally asymptotically stabilize the origin and specify the convergence rates. However, homogeneous controllers generally do not attain global stability for nonhomogeneous systems. In this paper, we design global inverse optimal controllers with guaranteed local convergence rates by utilizing local homogeneity of input affine nonlinear systems. If we do not consider inverse optimality, we can liberally adjust the sector margins. We also clarify that local convergence rates and sector margins are invariant under coordinate transformations.