This paper studies a linear-quadratic control problem for discretetime switched systems with subsystems perturbed by uncertainty. Analytical expressions are derived for both the optimal objective function and the optimal switching strategy. A two-step pruning scheme is developed to efficiently solve such problem. The performance of this method is shown by two examples.
Along with the development of the modern science and technology, people face a lot of data in different areas of production and life. In dealing with these data which include many indeterminant factors, we can use the multifactor uncertain system to describe a dynamical system with uncertain noises. Optimal control problem is an important research topic which aims at finding the optimal strategy in a dynamical system. In this paper, we consider the optimal control problem for the multifactor uncertain system with two evaluation criterions. Then a two person zero sum differential game model in a multifactor uncertain system is discussed. Finally, as an application, our result is used to solve an uncertain portfolio game model.
The saddle point equilibrium problem is of great importance in differential game theory. In this paper, an optimistic value model for the saddle point equilibrium problem under uncertain environment is investigated. The equilibrium equation for the proposed model is presented. Then a linear quadratic model is discussed. Finally, a counter terror problem is analyzed by the results obtained in the paper.
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