| Real-time control of nonlinear systems remains a very challenging area of research. While theoretical aspects of nonlinear control have progressed, there is a large gap between the theory and practice of controlling physical systems. There are two drawbacks that limit the utility of the existing theoretical developments in practical control. Firstly, the system may not satisfy standard assumptions such as well-defined relative degree, and minimum phase behavior. Secondly, it is difficult to obtain a model for the system that would characterize the system behavior under all operating conditions.;In this thesis, a framework for the control of nonlinear systems that guarantees system performance under approximate control is developed. The framework provides rigorous mathematical formulation that results in tractable control strategies. It is shown that the framework results in a multi-level control strategy, wherein the primary controller is a conventional PID controller tracking loop and control loops of increasing sophistication can be added depending on system complexity. Controllers based on this framework are easy to implement and fill a void that exists in the lack of repeatable design techniques for nonlinear systems.;The problem of non-minimum phase behavior is tackled by utilizing different time-scales in the system and designing a control that not only guarantees tracking performance but also stabilizes the internal dynamics. The problem of stabilizing systems with ill-defined relative degree is attempted by designing an approximate control. Both these methods make sense intuitively and give the controls designer an insight into tradeoffs between stabilization and tracking performance of nonlinear systems.;The control of systems with unknown dynamics is confronted using Neural Networks and Fuzzy logic controllers. The approximation properties of these networks are studied and novel update algorithms developed. The on-line tracking performance, stability and robustness properties are rigorously proven and the continuous-time and discrete-time performance verified through numerical examples. The passivity properties of the controllers developed are also studied and a unifying framework is developed that can be used to control unknown systems whose dynamics satisfy some mild structural conditions. |
