Joint Optimization of Wireless Communication and Networked Control Systems

L. Xiao, M. Johansson, H. Hindi, S. Boyd, and A. Goldsmith

Chapter in Switching and Learning, Springer Lecture Notes in Computer Science 3355, R. Murray-Smith and R. Shorten, editors, pages 248–272, 2005.

We consider a linear system, such as an estimator or a con- troller, in which several signals are transmitted over wireless commu- nication channels. With the coding and medium access schemes of the communication system fixed, the achievable bit rates are determined by the allocation of communications resources such as transmit powers and bandwidths, to different channels. Assuming conventional uniform quan- tization and a standard white-noise model for quantization errors, we consider two specific problems. In the first, we assume that the linear system is fixed and address the problem of allocating communication re- sources to optimize system performance. We observe that this problem is often convex (at least, when we ignore the constraint that individual quantizers have an integral number of bits), hence readily solved. We describe a dual decomposition method for solving these problems that exploits the problem structure. We briefly describe how the integer bit constraints can be handled, and give a bound on how suboptimal these heuristics can be. The second problem we consider is that of jointly allo- cating communication resources and designing the linear system in order to optimize system performance. This problem is in general not convex. We present an iterative heuristic method based on alternating convex optimization over subsets of variables, which appears to work well in practice.