Nonlocal Optimization Methods for Quadratic Control Systems with Terminal Constraints

Abstract

A new approach to optimization of state-quadratic optimal control problems with terminal constraints based on the sequential solution of control improvement problems in the form of special boundary value problems is considered. The developed approach for improving the admissible controls is based on the formulas for the functional increment without the remainder of the expansions. Such formulas make it possible to avoid the laborious operation of parametric variation to improve control, which ultimately leads to increased efficiency of the developed optimization procedures. The nonlocality of improving control is achieved by solving a special boundary value problem, which is much simpler than the boundary value problem of the maximum principle. To solve the boundary-value improvement problem, an iterative algorithm is constructed with the fulfillment of all terminal constraints at each iteration, based on the known perturbation principle. The proposed approach allows the formulation of new necessary optimality conditions that strengthen the known maximum principle in the class of problems under consideration and makes it possible to strictly improve non-optimal controls that satisfy the maximum principle. The comparative efficiency of the considered nonlocal methods with the known methods is illustrated by numerical calculations of model examples.KeywordsQuadratic control systemTerminal constraintsControl improvement problemOptimality conditionsIterative algorithm