Channel modeling and LQG control in the presence of random delays and packet drops

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We study the modeling and control for discrete-time networked control systems (NCSs) over the random delay and packet drop channel. By analyzing the relation between delays and data packets, the notion of channel states is proposed and conditional probability distributions are employed to model the channel. The channel states are characterized by the finite Markov states, enabling the computation of the corresponding transition probability matrix. As the number of Markov states increases exponentially with respect to the delay bound, the reduced channel states are proposed and studied to ease the complexity issue in the controller design. The linear quadratic Gaussian control problem is then studied for the NCS in which random delays and packet drops exist at both the plant input and output. The controller design problem is converted into state feedback control and state estimation for the augmented system of the plant and channel models. Under the framework of Markovian jump linear systems, the optimal control laws, which are non-causal, are obtained, implemented by transmitting multiple control data in a single packet. An optimal jump linear estimator that has a recursive form is also derived. Finally, comparative simulations are provided to demonstrate the effectiveness of the proposed modeling and design methods.

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