THE APPLICATION OF AN ALGORITHM FOR SEQUENTIAL OPTIMIZATION OF CONTROL SYSTEMS.
CALIFORNIA UNIV LOS ANGELES DEPT OF ENGINEERING
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The subject of this thesis is the application of an algorithm for optimization of nonlinear control problems. The method used is the development of a digital computer program which applies the algorithm to study problems for verification of the technique. Possible extension of the theoretical developments studied is also investigated. The basic problem involves linearization of the results of a nonlinear solution about a nonoptimal control for the problem. Sequentially iterating on the improvements to the control derived by application of a linear optimization technique produces a nonlinear optimal system. The linearity of the improvement is controlled by limiting the size of the steps in the sequential optimization. The linear solution is derived by application of Pontryagins Maximum Principle for an optimal system. A geometric approach to the solution results in a gradient technique for arriving at the optimal control for this phase of the problem. The solution of the gradient technique is accomplished by use of an acceleration scheme to provide rapid convergence to the control improvement. The final nonlinear solution is accomplished by applying the linear optimization technique in the controlled manner to the nonlinear problem.