Optimal design for dynamics and control using a sequential quadratic programming algorithm

This dissertation describes numerical analyses and detailed procedures for evaluation of the performance of various variations of an optimization algorithm, and applications of the method to dynamic response problems. A recently developed optimization method called Sequential Quadratic Programming (SQP) that has shown considerable promise for practical applications is selected for further analyses and improvements. The method uses potential constraint strategy and second order information about the Lagrange function for the problem. Thousands of numerical experiments among a variety of test problems are performed with the method. As a result, the algorithmic parameters and conditions can be quantitatively specified to obtain better performance with respect to robustness and efficiency for general applications.; A major difficulty in solving dynamic response and control optimization problems is that the continuum dynamic constraints must be satisfied over the entire time interval. Evaluation of the dynamic response and the constraints can require enormous computational effort. Also, design sensitivity analysis of dynamic constraints must be performed. The mathematical programming methods, the design sensitivity analysis procedures and several other numerical procedures need to be evaluated for solving general dynamic response optimization problems. Several example problems from mechanical system dynamics and optimal control literature are used to thoroughly investigate these numerical procedures. Three procedures for verification of design sensitivity analysis of time dependent functions are also described. Role of designer interaction in optimal design for dynamics is investigated. It is shown that the software system for dynamic response optimization must be flexible and interactive, allowing designer to control the iterative process. This allows designer to start with a rough model for the problem and interactively refine if after the preliminary model has been verified. Optimal control problems with/without state and/or control variable constraints are also solved to examine efficiency of the proposed methods. Numerical experience with the solution procedures is described and conclusions that can be useful to users of optimization and other researchers are drawn from the study.