论文信息 - An explicit procedure for discretizing continuous, optimal control problems

An explicit procedure for discretizing continuous, optimal control problems

An explicit procedure for obtaining discrete approximations to general, nonlinear, fixed-time, continuous, optimal control problems with no intermediate trajectory constraints is presented. It is proved that, if the associated system of differential equations is linear in the control variable, then the optimal solutions of these approximationsconverge to extremals of the original continuous problem.

J. Cullum

[1] M. Evans Munroe,et al. Introduction to Measure and Integration , 1953 .

[2] E. Coddington,et al. Theory of Ordinary Differential Equations , 1955 .

[3] L. A. Li︠u︡sternik,et al. Elements of Functional Analysis , 1962 .

[4] P. Henrici. Discrete Variable Methods in Ordinary Differential Equations , 1962 .

[5] L. S. Pontryagin,et al. Mathematical Theory of Optimal Processes , 1962 .

[6] J. Warga. Relaxed variational problems , 1962 .

[7] E. Roxin. The existence of optimal controls. , 1962 .

[8] E. Lee. A Sufficient Condition in the Theory of Optimal Control , 1963 .

[9] J. Cullum. Perturbations of Optimal Control Problems , 1966 .

[10] E. Polak,et al. Constrained Minimization Problems in Finite-Dimensional Spaces , 1966 .

[11] H. Halkin,et al. Discretional Convexity and the Maximum Principle for Discrete Systems , 1966 .

[12] Arthur Stoddart,et al. Existence of optimal controls , 1967 .

[13] J. Cullum. Discrete Approximations to Continuous Optimal Control Problems , 1969 .

[14] J. Daniel. On the convergence of a numerical method for optimal control problems , 1969 .

[15] E. Polak,et al. Theory of optimal control and mathematical programming , 1969 .