35,609 research outputs found

    Partial Information Differential Games for Mean-Field SDEs

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    This paper is concerned with non-zero sum differential games of mean-field stochastic differential equations with partial information and convex control domain. First, applying the classical convex variations, we obtain stochastic maximum principle for Nash equilibrium points. Subsequently, under additional assumptions, verification theorem for Nash equilibrium points is also derived. Finally, as an application, a linear quadratic example is discussed. The unique Nash equilibrium point is represented in a feedback form of not only the optimal filtering but also expected value of the system state, throughout the solutions of the Riccati equations.Comment: 7 page

    Distributed Linear Quadratic Control and Filtering:a suboptimality approach

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    Design of distributed protocols for multi-agent systems has received extensive attention in the past two decades. A challenging problem in this context is to develop distributed synchronizing protocols that minimize given cost criteria. Recent years have also witnessed an increasing interest in problems of distributed state estimation for large-scale systems. Two challenging problems in this context are the problems of distributed H-2 and H-infinity optimal filtering.In this dissertation, we study both distributed linear quadratic optimal control problems and distributed filtering problems. In the framework of distributed linear quadratic control, both for leaderless and leader-follower multi-agent systems we provide design methods for computing state-feedback-based distributed suboptimal synchronizing protocols. In the framework of distributed H-2 suboptimal control, both for homogeneous and heterogeneous multi-agent systems we establish design methods for computing state-feedback-based and output-feedback-based distributed suboptimal synchronizing protocols.The distributed H-2 and H-infinity optimal filtering problem are the problems of designing local filter gains such that the H-2 or H-infinity norm of the transfer matrix from the disturbance input to the output estimation error is minimized, while all local filters reconstruct the full system state asymptotically. Due to their non-convex nature, it is not clear whether optimal solutions exist. Instead of studying these optimal filtering problems, in this dissertation we therefore address suboptimality versions of these problems and provide conceptual algorithms for obtaining H-2 and H-infinity suboptimal distributed filters, respectively

    Bellman equations for optimal feedback control of qubit states

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    Using results from quantum filtering theory and methods from classical control theory, we derive an optimal control strategy for an open two-level system (a qubit in interaction with the electromagnetic field) controlled by a laser. The aim is to optimally choose the laser's amplitude and phase in order to drive the system into a desired state. The Bellman equations are obtained for the case of diffusive and counting measurements for vacuum field states. A full exact solution of the optimal control problem is given for a system with simpler, linear, dynamics. These linear dynamics can be obtained physically by considering a two-level atom in a strongly driven, heavily damped, optical cavity.Comment: 10 pages, no figures, replaced the simpler model in section
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