Sparse Packetized Predictive Control of Disturbed Plants Over Channels with Data Loss

TL;DR

This paper analyzes the stability of disturbed linear plants controlled via packetized predictive control over lossy channels, proposing sparse control strategies based on optimization that guarantee practical stability under bounded disturbances.

Contribution

It introduces two sparse PPC methods using l0 and l1-l2 optimization, providing stability guarantees and bounds in the presence of packet dropouts and disturbances.

Findings

Both strategies guarantee practical stability with bounded system states.

Performance degrades with larger disturbances, but stability is maintained.

Simulation confirms effectiveness of the proposed sparse PPC methods.

Abstract

This paper investigates closed-loop stability of a linear discrete-time plant subject to bounded disturbances when controlled according to packetized predictive control (PPC) policies. In the considered feedback loop, the controller is connected to the actuator via a digital communication channel imposing bounded dropouts. Two PPC strategies are taken into account. In both cases, the control packets are generated by solving sparsity-promoting optimization problems. One is based upon an l2-constrained l0 optimization problem. Such problem is relaxed by an l1-l2 optimization problem in the other sparse PPC setting. We utilize effective solving methods for the latter optimization problems. Moreover, we show that in the presence of plant disturbances, the l2-constrained l0 sparse PPC and unconstrained l1-l2 sparse PPC guarantee practical stability for the system if certain conditions are met. More precisely, in each case, we can derive an upper bound on system state if the design parameters satisfy certain conditions. The bounds we derive are increasing with respect to the disturbance magnitude. We show via simulation that in both cases of proposed sparse PPC strategies, larger disturbances bring about performance degradation with no effect on system practical stability.