A robust nonlinear adaptive control algorithm

The focus of this dissertation is the control of a class of nonlinear systems which can be transformed to a linear equivalent form. This is accomplished by representing the process model in a new coordinate system, and applying linearizing feedback. In principle, this requires that a perfect model of the process is available. Making this assumption is unrealistic, since model uncertainty is always present in practice. Additional steps must be taken to compensate for uncertainty in the model of the process. Recently, several control algorithms have been proposed which rely on parameter adaptation to compensate for model uncertainty which has a specific well defined structure. These adaptive control laws attempt to provide an assurance that the closed-loop system will be asymptotically stable. However, if unstructured sources of model uncertainty are also present, it may not be possible to make this guarantee. Since this usually is the case, the stability properties of these algorithms are questionable when applied to realistic problems. Unless restrictive assumptions are made about the uncertainty, achieving asymptotic stability is not a relistic objective. A relaxed form of stability, known as practical stability, is a reasonable alternative. Practical stability requires the system response to be uniformly bounded, uniformly ultimately bounded, and uniformly stable. This dissertation examines the use of parameter adaptation within a control strategy which guarantees the closed-loop system has practical stability. This adaptive algorithm is developed in detail, and then applied to a realistic nonlinear control problem. The results of a simulation study indicate this algorithm performs better than its non-adaptive counterpart, despite the presence of significant amounts of structured and unstructured model uncertainty. Since practical stability can be guaranteed for a broad spectrum of uncertainty, this algorithm can be applied to nonlinear control problems found in practice.