Globally stabilizing adaptive control design for nonlinearly-parameterized systems

• Published in: 2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601) Vol. 1; pp. 195 - 200 Vol.1
• Main Authors: Zhihua Qu, Hull, R.A., Jing Wang
• Format: Conference Proceeding
• Language: English
• Published: Piscataway NJ IEEE 2004
• Subjects: Adaptative systems; Adaptive control; Adaptive estimation; Applied sciences; Asymptotic stability; Computer science; control theory; systems; Control system synthesis; Control systems; Control theory. Systems; Convergence; Estimation error; Exact sciences and technology; Modelling and identification; Nonlinear control systems; Nonlinear dynamical systems; Nonlinear systems; Parameter estimation; Estimation error; Parameter estimation; Error estimation; Information system; Adaptive system; Non linear control; Lyapunov method; Control synthesis; Adaptive estimation; Dynamical system; Non linear system; Affine transformation; Adaptive control; Modeling; Asymptotic stability; Global stabilization; Certainty equivalence principle; Non affine transform; System identification; Lyapunov function
• ISBN: 9780780386822; 0780386825
• ISSN: 0191-2216
• DOI: 10.1109/CDC.2004.1428629

In this paper, a new adaptive control design is proposed for nonlinear systems that are possibly non-affine and contain nonlinearly parameterized unknowns. The proposed control is not based on certainty equivalence principle, which forms the foundation of existing and standard adaptive control designs. Instead, a biasing vector function is introduced into parameter estimate, it links the system dynamics to estimation error dynamics, and its choice leads to a new Lyapunov-based design so that affine or non-affine systems with nonlinearly parameterized unknowns can be controlled by adaptive estimation. Explicit conditions are found for achieving global asymptotic stability of the state, and the convergence condition for parameter estimation is also found. The conditions are illustrated by several examples and classes of systems. Besides global stability, the proposed adaptive control has the unique feature that it does not contains no robust control part which typically overpowers unknown dynamics, is conservative, and also interferes with parameter estimation.