Trust-region reflective adaptive controller for time varying systems

• Published in: IET control theory & applications Vol. 9; no. 2; pp. 240 - 247
• Main Author: Moubarak, Paul M
• Format: Journal Article
• Language: English
• Published: The Institution of Engineering and Technology 19.01.2015
• Subjects: Adaptive control; Algorithms; approximation theory; closed loop systems; closed‐loop system; Controllers; damping; Disturbances; heuristic approximation; linear systems; linearisable system; Mathematical models; natural frequencies; online adaptive control; optimisation; parametric disturbance; Poles; Real time; search problems; search space restriction; Searching; time varying linear system; time‐varying systems; TRAC; trust‐region optimisation; trust‐region reflective adaptive controller; trust‐region search; time-varying systems; approximation theory; trust-region search; natural frequencies; search space restriction; heuristic approximation; TRAC; adaptive control; linear systems; damping; trust-region optimisation; closed loop systems; parametric disturbance; time varying linear system; optimisation; linearisable system; trust-region reflective adaptive controller; online adaptive control; search problems; closed-loop system
• ISSN: 1751-8644; 1751-8652
• DOI: 10.1049/iet-cta.2014.0380

The new algorithm presented in this study, called TRAC (trust-region reflective adaptive controller), performs online adaptive control of time-varying linear or linearisable systems subject to parametric disturbances. The process of accomplishing such adaptive control consists of feeding the measured output signal back to TRAC – which occupies the outer loop of a control scheme – as well as the reference signal. Knowing the order of the closed-loop system in the inner loop, a parametric model of the time-varying output is derived as a function of the system's variables, such as damping and natural frequencies. Using trust-region optimisation, these parameters are estimated in real-time by recursively fitting the actual output into the parametric model. This allows for the location of the actual poles to be estimated in the s-domain after the poles have been shifted by the disturbance. Accordingly, the gains are re-tuned in order to return the actual poles to their desired location and absorb the disturbance. The primary advantage of TRAC relative to the state-of-the-art is its computational simplicity which is owed to search space restriction and heuristic approximations with trust-region search. A video of a sample application describing real-time TRAC-based control can be found on the IET's Digital Library.