Sparsity Promoting Observer Design for Wireless Sensor-Estimator Networks

In this article, we consider the design of structured Luenberger observers to generate sparse sensor-estimator communication networks. We first illustrate the relationship between the topology of communication channels and the structure of the observer gain matrix. To balance the estimation error and the communication cost, we formulate the design of the sparsity-promoting observer as a regularized $\ell _{1}$-optimization problem. Then, we characterize its first-order optimality condition using gradient information and propose a linear programming method to verify stationary solutions. We further develop a multiblock alternating direction method of multipliers algorithm with linear matrix inequality-based warm start for computation. We prove that the solution returned by our algorithm is at least a stationary solution. Numerical simulations are provided to verify the proposed theoretical results and show that the communication burden of networked control systems can be greatly relieved by using the designed observers.