Adaptive Dynamic Inversion via Time-Scale Separation

• Published in: IEEE transactions on neural networks Vol. 19; no. 10; pp. 1702 - 1711
• Main Authors: Hovakimyan, Naira, Lavretsky, Eugene, Cao, Chengyu
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.10.2008; Institute of Electrical and Electronics Engineers
• Subjects: Adaptative systems; Adaptive control; Adaptive control systems; Algorithms; Applied sciences; Computer science; control theory; systems; Computer Simulation; Control nonlinearities; Control system synthesis; Control systems; Control theory. Systems; Dynamic inversion; Dynamical systems; Errors; Exact sciences and technology; Feedback; Mathematical models; Modelling and identification; Models, Theoretical; nonaffine systems; Nonlinear control systems; Nonlinear dynamical systems; Nonlinear dynamics; Nonlinear equations; Nonlinear systems; Nonlinearity; Numerical Analysis, Computer-Assisted; Programmable control; State feedback; time-scale separation; ultimate boundedness; Uncertain systems; State feedback; dynamic control; Bounded error; Non linear control; Lyapunov method; Control synthesis; Error bound; Time scale; Inversion; ultimate boundedness; time-scale separation; Dynamical system; Adaptive control; Modeling; Adaptive method; nonaffine systems; Dynamic method; Reference model; Uncertain system; Input to state stability; Predictive control; Lyapunov function
• ISSN: 1045-9227; 1941-0093
• DOI: 10.1109/TNN.2008.2001221

This paper presents a full state feedback adaptive dynamic inversion method for uncertain systems that depend nonlinearly upon the control input. Using a specialized set of basis functions that respect the monotonic property of the system nonlinearities with respect to control input, a state predictor is defined for derivation of the adaptive laws. The adaptive dynamic inversion controller is defined as a solution of a fast dynamical equation, which achieves time-scale separation between the state predictor and the controller dynamics. Lyapunov-based adaptive laws ensure that the predictor tracks the state of the nonlinear system with bounded errors. As a result, the system state tracks the desired reference model with bounded errors. Benefits of the proposed design method are demonstrated using Van der Pol dynamics with nonlinear control input.