Stochastic stabilisation and power control for nonlinear feedback loops communicating over lossy wireless networks

Abstract

We study emulation-based stabilisation of nonlinear networked control systems communicating over multiple wireless channels subject to packet loss. Specifically, we establish sufficient conditions on the rate of transmission that guarantee Lp stability-in-expectation of the overall closed-loop system. These conditions depend on the cumulative dropout probability of the network nodes for static protocols. We use the obtained stability results to study power control, where we show there are interesting trade-offs between the transmission rate, transmit power, and stability. Lastly, numerical examples are presented to illustrate our results.

Optimal quantised bits for estimation over a capacity and power limited, lossy channel

“…Figure 2 plots the variations of EEV as b c increases for a fixed SNR per bit of 25 dB for square QAM. Observe from the figure that the EEV first decreases and then saturates at a low value, EEV L (b c ) as given by Equations ( 10) and ( 11) before sharply increasing and then saturating at a higher value, as given by Equation (12). Clearly, there is a range of b c 's for which EEV is minimised.…”

“…For remote linear estimation, the optimal linear encoder for uniform quantiser was devised in [8], and simultaneous design of the encoder and the quantiser was presented in [9]. KF with transmit power constraint have been addressed in [10][11][12][13][14][15]. However, these works consider the quantisation noise and packet loss rate as independent.…”

Transmission Power Policies for Energy-Efficient Wireless Control of Nonlinear Systems

“…Hence, when communication instants depend on time, instead of the state, results on communication energy minimization have been developed in [15], assuming packets are always successfully transmitted but with varying costs, and in [16], in which the average transmission power is minimized while ensuring the desired control performance for stochastic communication. Even though recent works like [17] and [18] explore power control for interference management in nonlinear WNCS over static channels, results for nonlinear systems are crucially lacking and the design of transmission policies over a time-varying channel are missing even for linear systems.…”

Time-based transmission power policies for energy-efficient wireless control of nonlinear systems

“…When communication instants depend on time, instead of the state, which may be easier to realize in practice, results on communication energy minimization have been developed in [15], assuming packets are always successfully transmitted but with varying costs, and in [16], in which the average transmission power is minimized while ensuring the desired control performance for stochastic communication. Even though recent works like [17] and [18] explore power control for interference management in nonlinear WNCS over static channels, results for nonlinear systems are crucially lacking and the design of transmission policies over a timevarying channel are missing even for linear systems.…”