New Approach for the Solution of Optimal Control Problems on Parallel Machines.

摘要

This thesis develops a highly parallel solution method for nonlinear optimal control problems. Balakrishnan's epsilon method is used in conjunction with the Rayleigh-Ritz method to convert the dynamic optimization of the optimal control problem into a static optimization problem. Walsh functions and orthogonal polynomials are used as basis functions to implement the Rayleigh-Ritz method. The resulting static optimization problem is solved using matrix operations which have well defined massively parallel solution methods. To demonstrate the method, a variety of nonlinear optimal control problems are solved. The nonlinear Raleigh problem with quadratic cost and nonlinear van der Pol problem with quadratic cost and terminal constraints on the states are solved in both serial and parallel on an eight processor Intel Hypercube. The solutions using both Walsh functions and Legendre polynomials as basis functions are given. In addition to these problems which are solved in parallel, a more complex nonlinear minimum time optimal control problem and nonlinear optimal control problem with an inequality constraint on the control are solved. Results show the method converges quickly, even from relatively poor initial guesses for the nominal trajectories.