On the Relation Between the Minimum Principle and Dynamic Programming for Classical and Hybrid Control Systems

被引：33
作者：
Pakniyat, Ali [1 ,2 ]
Caines, Peter E. [1 ,2 ]
机构：
[1] McGill Univ, Ctr Intelligent Machines, Montreal, PQ H3A 0G4, Canada
[2] McGill Univ, Dept Elect & Comp Engn, Montreal, PQ H3A 0G4, Canada
来源：
IEEE TRANSACTIONS ON AUTOMATIC CONTROL | 2017年 / 62卷 / 09期
基金：
加拿大自然科学与工程研究理事会;
关键词：
Dynamic programming (DP); Hamilton-Jacobi-Bellman equation; hybrid systems; nonlinear control system; optimal control; Pontryagin minimum principle (MP); MAXIMUM PRINCIPLE; CONNECTION; CONTINUITY;
D O I：
10.1109/TAC.2017.2667043
中图分类号：
TP [自动化技术、计算机技术];
学科分类号：
0812 ;
摘要：
Hybrid optimal control problems are studied for a general class of hybrid systems, where autonomous and controlled state jumps are allowed at the switching instants, and in addition to terminal and running costs, switching between discrete states incurs costs. The statements of the Hybrid Minimum Principle and Hybrid Dynamic Programming are presented in this framework, and it is shown that under certain assumptions, the adjoint process in the Hybrid Minimum Principle and the gradient of the value function in Hybrid Dynamic Programming are governed by the same set of differential equations and have the same boundary conditions and hence are almost everywhere identical to each other along optimal trajectories. Analytic examples are provided to illustrate the results.
引用
收藏
页码：4347 / 4362
页数：16
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