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RISS 인기검색어
- 검색키워드
- 저자 : Tamer Basar (검색결과 2 건)
- 무료
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Risk-sensitive Control of Markov Jump Linear Systems: Caveats and Difficulties
문준,Tamer Basar 제어·로봇·시스템학회 2017 International Journal of Control, Automation, and Vol.15 No.1
In this technical note, we revisit the risk-sensitive optimal control problem for Markov jump linearsystems (MJLSs). We first demonstrate the inherent difficulty in solving the risk-sensitive optimal control problemeven if the system is linear and the cost function is quadratic. This is due to the nonlinear nature of the coupledset of Hamilton-Jacobi-Bellman (HJB) equations, stemming from the presence of the jump process. It thus followsthat the standard quadratic form of the value function with a set of coupled Riccati differential equations cannot bea candidate solution to the coupled HJB equations. We subsequently show that there is no equivalence relationshipbetween the problems of risk-sensitive control and H¥ control of MJLSs, which are shown to be equivalent in theabsence of any jumps. Finally, we show that there does not exist a large deviation limit as well as a risk-neutral limitof the risk-sensitive optimal control problem due to the presence of a nonlinear coupling term in the HJB equations.
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Linear Quadratic Risk-Sensitive and Robust Mean Field Games
Moon, Jun,Basar, Tamer IEEE 2017 IEEE transactions on automatic control Vol.62 No.3
<P>This paper considers two classes of large population stochastic differential games connected to optimal and robust decentralized control of large-scale multiagent systems. The first problem (P1) is one where each agent minimizes an exponentiated cost function, capturing risk-sensitive behavior, whereas in the second problem (P2) each agent minimizes a worst-case risk-neutral cost function, where the 'worst case' stems from the presence of an adversary entering each agent's dynamics characterized by a stochastic differential equation. In both problems, the individual agents are coupled through the mean field term included in each agent's cost function, which captures the average or mass behavior of the agents. We solve both P1 and P2 via mean field game theory. Specifically, we first solve a generic risk-sensitive optimal control problem and a generic stochastic zero-sum differential game, where the corresponding optimal controllers are applied by each agent to construct the mean field systems of P1 and P2. We then characterize an approximated mass behavior effect on an individual agent via a fixed-point analysis of the mean field system. For each problem, P1 and P2, we show that the approximated mass behavior is in fact the best estimate of the actual mass behavior in various senses as the population size, N, goes to infinity. Moreover, we show that for finite N, there exist is an element of-Nash equilibria for both P1 and P2, where the corresponding individual Nash strategies are decentralized in terms of local state information and the approximated mass behavior. We also show that is an element of can be taken to be arbitrarily small whenN is sufficiently large. We show that the is an element of-Nashequilibria of P1 and P2 are partially equivalent in the sense that the individual Nash strategies share identical control laws, but the approximated mass behaviors for P1 and P2 are different, since in P2, the mass behavior is also affected by the associated worst-case disturbance. Finally, we prove that the Nash equilibria for P1 and P2 both feature robustness, and as the parameter characterizing this robustness becomes infinite, the two Nash equilibria become identical and equivalent to that of the risk-neutral case, as in the one-agent risk-sensitive and robust control theory.</P>
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