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OPTIMUM CONTROL OF LINEAR SYSTEMS WITH TIME LAGS,
ILLINOIS UNIV URBANA COORDINATED SCIENCE LAB
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The problem of optimal control of a system governed by linear differential-difference equations with constant coefficients is studied. The performance index is the integrated square error plus weighted control and the final time is infinite. An important question that arises in the study of the optimization problem is the existence of the optimal solution. In the case of dynamic systems governed by ordinary linear differential equations it is known that the existence of the optimal solution is related to the concept of controllability. The controllability conditions for such systems are also known. In this thesis the necessary and sufficient conditions for complete controllability of a system of linear differential-difference equations with constant coefficients are established. For single input systems, with the help of these conditions, the optimal control problem is related to classical frequency domain problem of improving the sensitivity of the overall system with respect to parameter variations. In order to extend the relation between the optimization problem and the sensitivity improvement for multiple input systems, a sensitivity matrix is defined and its relationship with optimization is established. Author
APPROVED FOR PUBLIC RELEASE