The stochastic maximum principle for optimal control problems of delay systems involving continuous and impulse controls

Automatica ◽  
2012 ◽  
Vol 48 (10) ◽  
pp. 2420-2432 ◽  
Author(s):  
Zhiyong Yu
Keyword(s):  
Optimal Control ◽  
Maximum Principle ◽  
Optimal Control Problems ◽  
Stochastic Maximum Principle ◽  
Delay Systems ◽  
Control Problems ◽  
Impulse Controls

scholarly journals Maximum Principle for Optimal Control Problems of Forward-Backward Regime-Switching Systems Involving Impulse Controls

2015 ◽  
Vol 2015 ◽  
pp. 1-13 ◽  
Author(s):  
Shujun Wang ◽  
Zhen Wu
Keyword(s):  
Optimal Control ◽  
Maximum Principle ◽  
Markov Chains ◽  
Regime Switching ◽  
Optimal Control Problems ◽  
Sufficient Conditions ◽  
Control Problems ◽  
Optimal Controls ◽  
Switching Systems ◽  
Impulse Controls

This paper is concerned with optimal control problems of forward-backward Markovian regime-switching systems involving impulse controls. Here the Markov chains are continuous-time and finite-state. We derive the stochastic maximum principle for this kind of systems. Besides the Markov chains, the most distinguishing features of our problem are that the control variables consist of regular and impulsive controls, and that the domain of regular control is not necessarily convex. We obtain the necessary and sufficient conditions for optimal controls. Thereafter, we apply the theoretical results to a financial problem and get the optimal consumption strategies.

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