Trust-region reflective adaptive controller for time varying systems

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.