A unified theory of maximum principle for continuous and discrete time optimal control problems
Zaidong Zhan Shuping Chen Wei Wei
Mathematical Control & Related Fields 2012, 2(2): 195-215 doi: 10.3934/mcrf.2012.2.195
Traditionally, the time domains that are widely used in mathematical descriptions are limited to real numbers for the case of continuous-time optimal control problems or to integers for the case of discrete-time optimal control problems. In this paper, based on a family of "needle variations", we derive maximum principle for optimal control problem on time scales. The results not only unify the theory of continuous and discrete optimal control problems but also conclude problems involving time domains in partly continuous and partly discrete ingredients. A simple optimal control problem on time scales is discussed in detail. Meanwhile, the results also unify the theory of some hybrid systems, for example, impulsive systems.
keywords: maximum principle Ekeland's variational principle optimal control Time scales impulsive control.

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