Abstract

Animal sensorimotor control systems have a particularly interesting tradeoff between speeds versus accuracy in nervous system communications, motivating a minimal model to explore its resulting impact system performance. We derived an analytical solution of system performance when robust control is done using communication with lower bounds on delay and quantisation error. This yields surprisingly different results from the insight gained from information theory, which has dominated theoretical neuroscience. We then extend the same technique to design the controller and channel for a sampled data system with a distributed controller, time-varying delay, quantisation, saturation, and external disturbances. We show how to construct an invariant set of the state dynamics by a linear program without constructing a Lyapunov function. The use of l infinity signal (and is corresponding induced matrix defined in the talk) appears essential to capture the communication error and facilitate scalable computation. We finish with the analysis of its sub-optimality gap and the feasibility condition of the proposed linear program.

Nakahira, Y., Doyle, J.C., and Matni, N. (2015). Hard limits on robust control over delayed and quantized communications. 54th Conference on Decision and Control.

Nakahira, Y., Seungil Y. (2015) A linear programming framework for networked control system design. 5th IFAC Workshop on Distributed Estimation and Control in Networked Systems.