Generalized Programming Solution of Continuous-Time Linear-System Optimal Control Problems

摘要

An algorithm for solving Dantzig's generalized programming formulation of continuous-time linear-system optimal control problems is developed. Dantzig's work is extended to include continuous-time versions of quadratic loss criteria and minimum fuel problems. New results in parametric linear and quadratic programming problems, where the parameter dependence is nonlinear, are derived with internal schemes to avoid cycling due to degeneracy. Finite switching results in the completely linear system, including the minimum fuel and minimal time problems, are presented without assuming Pontryagin's general position principal or uniqueness properties. The procedure initially finds a feasible and admissible solution to the continuous-time problem without using discrete approximations. The algorithm continues to converge monotonically to the optimal solution while remaining feasible and, at each stage, provides a bound on the value of the loss function for termination purposes. This procedure is well suited for systems with a relatively high number of state variables and control inputs for which discrete time linear or quadratic programming models become too large. (Author)