Abstract
This article considers the transmission power scheduling in the control of a linear plant when the plant state is transmitted from a sensor to the controller over a wireless fading channel. The power allocated to these transmissions determines the probability of successful packet reception. This article focuses on investigating how much power should be assigned to transmit the data packet at each time. A new framework of optimal power allocation is established by introducing a cost function, which weighs the control performance and energy cost. First, a necessary and sufficient condition for the existence of the solution to finding an admissible schedule is given. Then, by combining an adaptive dynamic programming technique with fuzzy approximation theory, a new state-dependent scheduling algorithm is proposed to find the optimal power allocation policy. The convergence analysis shows that the proposed power scheduling algorithm can approximate the optimal solution on a compact set with a desired precision. Simulation results are presented to illustrate the effectiveness of the proposed algorithm.
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