Adaptive variable structure control of a class of non-linear systems

The problem of tuning the parameters of a controller operating in the presence of noise, time-varying parameters, non-linearities, and uncertainties in practice requires the process of continuous adjustment of the parameters influencing the performance. When the diversity of the challenges in the domain of real-time applications is taken into consideration, it becomes apparent that the adopted controller structure must be sufficiently flexible, and its operating principles must be well explained, particularly in accounting for the stability issues. In this paper, a method is proposed for tuning the parameters of controllers whose outputs are linear in the adjustable parameters, utilizing variable structure systems theory. The method discussed constructs the best error measure at the controller output, and uses this quantity with a suitably designed tuning law, which drives the system under control to a predefined sliding regime and maintains the sliding mode. It is shown analytically that the parametric evolution takes place in a finite volume space, indicating that the controller parameters evolve bounded. In the simulation studies, the approach presented has been tested on the control of a double pendulum system and the superior performance of the strategy has been shown under the existence of noisy observations and large non-zero initial errors.