| Abstract: | A spline approach to certain practical and important constrained optimal control problems is studied in this thesis. Three types of constraints, namely: interpolatory, convex, and smoothing constraints, will be investigated in detail. Under very mild conditions, we will develop some new spline-based techniques to give fairly complete solutions to these three different types of constrained optimal control problems subject to linear dynamic systems and quadratic form of the cost functionals. The existence, uniqueness, and characterization theorems will be obtained, and explicit constructive methods and algorithms for obtaining optimal solutions to some important specific problems will also be given. Our approach is in some sense a unified method which completes, extends, and/or generalizes many of the existing results from the spline approach to the optimal control problems in the literature. |
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