| Uncertainties in control systems are characterized and studied in some uniform framework. An effective strategy for improving performance of robust control systems is to decrease system uncertainty. Constructive design approaches are proposed to introduce learning in robust control systems, for three classes of systems. Several general issues in learning uncertainties in control systems have been studied. Using Gaussian networks as the leaning identifier, a convergent algorithm for learning uncertainties in the three classes of systems is developed with identification error bound analyses. Further, constructive design approaches are proposed for a robust adaptive on-line control strategy applicable to two of the three classes of systems with unknown bounded nonlinearities. These methods are robust under certain assumptions. The adaptive pan of the control strategy is based on a proposed construction method for strictly positive real (SPR) function so that convergence and system stability are guaranteed. The construction of the SPR function is simple and systematic. The robust part of the method is based on techniques for modeled and unmodeled dynamics that, again, guarantee stability. The proposed constructive design approaches for learning and control for systems with uncertainties have been validated using three example case hardware experimental setups: (I) A DC-motor driven disk load (LTI system) and stick-slip friction and other parasitic effects (uncertainty); (II) A DC-motor driven 4-bar linkage load (nonlinear system) and friction, parameters perturbation, and other parasitic effects (uncertainty); and (III) DC motor driven flexible beam load (LTI non-minimum phase) and friction, truncated higher modes, and other parasitic effects (uncertainty). Both theoretical investigations and experimental results show that the proposed constructive design approaches for incorporating learning stably in control systems improves control performance by decreasing the size of uncertainties, for the classes of systems considered. |
