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Controllability of Nash Equilibrium in Game-Based Control Systems
Zhang, Ren-Ren; Guo, Lei
AbstractControlling complex systems to desired states is of primary importance in science and engineering. In the classical control framework, the plants to be controlled usually do not have their own payoff or objective functions; however, this is not the case in many practical situations in, for examples, social, economic, and "intelligent" engineering systems. This motivates our introduction of the game-based control system (GBCS), which has a hierarchical decision-making structure: one regulator and multiple agents. The regulator is regarded as the global controller that makes decision first, and then, the agents try to optimize their respective objective functions to reach a possible Nash equilibrium as a result of noncooperative dynamic game. A fundamental issue in the GBCS is: Is it possible for the regulator to change the macrostates by regulating the Nash equilibrium formed by the agents at the lower level? This leads to the investigation of controllability of the Nash equilibrium of the GBCS. In this paper, we will first formulate this new problem in a general nonlinear framework and then focus on linear systems. Some explicit necessary and sufficient algebraic conditions on the controllability of the Nash equilibrium are given for a linear GBCS, by solving the controllability problem of the associated forward and backward dynamic equations, which is a key technical issue and has rarely been explored in the literature.
KeywordControllability hierarchical structure maximum principle Nash equilibrium noncooperative differential games
Funding ProjectNational Natural Science Foundation of China[11688101] ; National Natural Science Foundation of China[91634203] ; National Natural Science Foundation of China[61227902]
WOS Research AreaAutomation & Control Systems ; Engineering
WOS SubjectAutomation & Control Systems ; Engineering, Electrical & Electronic
WOS IDWOS:000490772500017
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Document Type期刊论文
Corresponding AuthorGuo, Lei
AffiliationChinese Acad Sci, Acad Math & Syst Sci, Inst Syst Sci, Beijing 100190, Peoples R China
Recommended Citation
GB/T 7714
Zhang, Ren-Ren,Guo, Lei. Controllability of Nash Equilibrium in Game-Based Control Systems[J]. IEEE TRANSACTIONS ON AUTOMATIC CONTROL,2019,64(10):4180-4187.
APA Zhang, Ren-Ren,&Guo, Lei.(2019).Controllability of Nash Equilibrium in Game-Based Control Systems.IEEE TRANSACTIONS ON AUTOMATIC CONTROL,64(10),4180-4187.
MLA Zhang, Ren-Ren,et al."Controllability of Nash Equilibrium in Game-Based Control Systems".IEEE TRANSACTIONS ON AUTOMATIC CONTROL 64.10(2019):4180-4187.
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