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

Louisell DMS-9500565 Louisell将继续他在时滞微分方程式、系统理论和控制领域的研究，特别是在这两个领域重叠的主题中。其中之一涉及用于分析特征值横坐标的Lyapunov方法和二次最优控制的牛顿-拉夫森方法之间的联系。由于Louisell方法的直接线性代数方法，它非常适合于构造时滞系统的LQ-最优控制器的牛顿-拉夫森方法。通过这种方法，他可以将LQ-最优控制、H-无穷优化和风险敏感控制等领域联系起来。这一方向将得到进一步发展。所提出的研究涉及线性系统控制中的延迟反馈。人们可能会认为拖延会破坏稳定，但实际上，稳定可能是通过增加拖延来获得的。这项研究将有助于更好地理解这一现象。

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.