Conference Paper

Optimal Performance of Feedback Control Systems with Limited Communication over Noisy Channels

Dept. of Electr. Eng. & Comput. Sci., Michigan Univ., Ann Arbor, MI
DOI: 10.1109/CDC.2006.377735 In proceeding of: Decision and Control, 2006 45th IEEE Conference on
Source: IEEE Xplore

ABSTRACT A discrete time stochastic feedback control system with a noisy communication channel between the sensor and the controller is considered. The sensor has limited memory. At each time, the sensor transmits encoded symbol over the channel and updates its memory. The controller receives a noisy version of the transmitted symbol, and generates a control action based on all its past observations and actions. This control action is fed back into the system. At each stage the system incurs an instantaneous cost depending on the state of the plant and the control action. The objective is to choose encoding, memory updating and control strategies to minimize the expected total costs over a finite horizon, or the expected discounted cost over an infinite horizon, or the expected average cost per unit time over an infinite horizon. For each case we obtain a sequential decomposition of the optimization problem. The results are extended to the case when the sensor makes an imperfect observation of the state of the system

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    ABSTRACT: A real-time communication system with noisy feedback is considered. The system consists of a Markov source, forward and backward discrete memoryless channels, and a receiver with limited memory. The receiver can send messages to the encoder over the backward noisy channel. The encoding at the encoder and the decoding, the feedback, and the memory update at the receiver must be done in real-time. A distortion metric that does not tolerate delays is given. The objective is to design an optimal real-time communication strategy, i.e., design optimal real-time encoding, decoding, feedback, and memory update strategies to minimize a total expected distortion over a finite horizon. This problem is formulated as a decentralized stochastic optimization problem and a methodology for its sequential decomposition is presented. This results in a set of nested optimality equations that can be used to sequentially determine optimal communication strategies. The methodology exponentially simplifies the search for determining an optimal real-time communication strategy.
    IEEE Journal on Selected Areas in Communications 06/2008; · 3.12 Impact Factor
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    [Show abstract] [Hide abstract]
    ABSTRACT: A discrete time stochastic feedback control system with a noisy communication channel between the sensor and the controller is considered. The sensor has limited memory. At each time, the sensor transmits encoded symbol over the channel and updates its memory. The controller receives a noisy version of the transmitted symbol, and generates a control action based on all its past observations and actions. This control action is fed back into the system. At each stage the system incurs an instantaneous cost depending on the state of the plant and the control action. The objective is to choose encoding, memory updating and control strategies to minimize the expected total costs over a finite horizon, or the expected discounted cost over an infinite horizon, or the expected average cost per unit time over an infinite horizon. For each case we obtain a sequential decomposition of the optimization problem. The results are extended to the case when the sensor makes an imperfect observation of the state of the system
    Decision and Control, 2006 45th IEEE Conference on; 01/2007

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