Mathematical Sciences: Quadratic Functionals, Stability and Optimal Control for Delay - Differential Systems

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Louisell DMS-9500565 Louisell will continue his investigations in the area of delay-differential equations, and in systems theory and control, particularly in topics where the two areas overlap. One of these involves the links between the Lyapunov method used for analyzing eigenvalue abscissas and the Newton-Raphson method of quadratic optimal control. Because of the direct linear algebra approach of Louisell's method, it is well suited for a Newton-Raphson approach to constructing LQ-optimal controllers for delay systems. Through this method he can link such areas as LQ-optimal control, H-infinity optimization, and risk sensitive control. This direction will be further developed. The proposed research involves delayed feedback in the control of linear systems. One might expect that delays destroys stability, but in fact, stability may be obtained by increasing delays. This research will lead to a better understanding of this phenomenon.