Nonlinear feedback designs offer the potential to take advantage of genuinely nonlinear effects, for instance, to induce large effects using small controls. The objective of this proposal is to develop theoretically- sound, practically-useful passivity-based low-gain and low-and-high gain control methods for designing feedback controllers that achieve global asymptotic stability, performance robustness against modeling uncertainty, and disturbance attenuation, for a large class of nonlinear systems which cannot be adequately controlled by existing methods. A unique thread in our theoretical development would be the systematic use of small controls and feedback passivation, which focus on ways to exploit the inherently dominant nonlinearities of the dynamic system in the feedback design, rather than to design controllers by canceling the nonlinearities via feedback linearization. The purpose of a feedback control is to stabilize or regulate the system globally and do so in a robust fashion, that is, in a manner that is not sensitive to various perturbations and structural uncertainties in the system. A unified, passivity-based theory of robust nonlinear control would contribute to our ability to design high performance nonlinear controllers capable of attenuating disturbances and tracking desired trajectories, without relying as much on an accurate description of the system model or model parameters and on explicit descriptions of the disturbance signals as does conventional modern control theory.
Many dynamic systems of practical importance (e.g. robotics, electrically stimulated muscles, rotating machines, induction motors, power systems, aerospace vehicles, aircraft, missiles and so on) have essentially inherent nonlinear characteristics that cannot be ignored in feedback design. More importantly, control systems that exploit their genuine nonlinearities are likely to achieve better performance than those that do not. Because most engineering systems involve highly nonlinear actuators, sensors and process elements, a goal of active research is to transform a nonlinear system into a linear system for which well-defined linear control techniques are readily applicable. This approach has serious limitations, e.g. the requirement of high energy actuators and the lack of robustness of such schemes to parameter variations and disturbances. Consequently, these techniques have had relatively little successful in solving real-world problems. The research plan in this proposal addresses the needs called for in feedback design, and it proposes approaches to tackle some of the most important issues that we believe are critical to the advancement and application of nonlinear control theory. The main outcome of the proposed research will be new, systematic design methodologies for the control of nonlinear dynamic systems, which are not available in the existing literature. The significance of this proposal is that it identifies the main barriers that hamper the advance and application of nonlinear control theory, but also delineates concrete problems for the control of inherently nonlinear systems, and suggests theoretically innovative and practically feasible methods to resolve them. A number of important and challenging open problems will be solved. In the long term, it will provide insight and thrust for future investigations into several theoretical and practical issues. It is believed that the benefits to a systematic approach towards using low energy control will be becoming more widely appreciated, particularly in industries (e.g. manufacturing, aerospace, power and biomedical engineering) where many applications of nonlinear control with actuator saturation can be found. It is also expected that the nonlinear control schemes to be developed in this program will find much broader applications in other branches of engineering than traditional control theory, due to their significant features and the inclusion of realistic assumptions.
