PYIA: Nonlinear Control Systems

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The main objective of this research program is to develop methodologies for the design of nonlinear digital controllers for nonlinear dynamic systems. Since the choice of a controller structure is highly dependent upon the structural properties of the underlying system, the first step will be to determine how the geometric properties of a continuous-time system are deformed by the introduction of the usual sample-and-hold devices. Recent work of the author and his students has clarified the linear case, but for nonlinear systems, much work remains to be done. However, preliminary results show that the additional flexibility gained by allowing multi-rate sampling is crucial to achieving such design goals as feedback linearization; this second avenue of investigation will be further pursued. A third goal will be to develop a notion of "transmission dynamics" of a discrete-time nonlinear system; this will play the role of the transmission zeros of a linear system and will lead to conditions for the existence of controllers which simultaneously decouple and stabilize a nonlinear discrete-time system. Finally, joint work will be done with Dr. C. Moog, of France, and Dr. M. di Benedetto, of Italy, on differential algebraic tools for the analysis of nonlinear systems. The main objective of this research is to develop methodologies for the design of nonlinear digital controllers for nonlinear dynamic systems. This research will be valuable in controlling high performance nonlinear systems such as those encountered in advanced aircraft and process control.