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LQ-power Consistent Control: Leveraging Transmission Power Selection in Control Systems

We consider a linear control system, where the sensors communicate to the controller via a wireless network in which the probability of successful data transmissions is an increasing function of the selected radio signal power. We tackle the problem of jointly selecting the transmission power at every transmission time as a function of the state, much like in event-triggered control systems, and of designing a controller in order to minimize an average quadratic cost. Our proposed power scheduler and corresponding control policy are shown to outperform the optimal control policy when the radio signal power is constant at all times, while using at most the same average transmission power. For this result to hold, the function relating the transmission power to the probability of successful transmission must be convex in the region of interest. We call such a policy LQ-power consistent.