Robust Feedback Control vs Uncertainty Model Complexity: from Information Theory to Networked Control
Authors :
Conference : 2007 Workshop on Control over Communication Channels (ConCom 07) part of WiOpt ’07
Date: April 01 - April 01, 2007
We develop a framework for designing controllers for general, partially observed nonlinear systems which are robust with respect to uncertainties. Most significantly we include both parametric as well as structural model uncertainties. A general deterministic model for uncertainties is introduced, leading to a dynamic game formulation of the robust control problem. This problem is solved using an appropriate information state. We then develop a stochastic framework for decision making under such uncertainties, by employing maximum entropy stochastic models for the nonlinear system. This leads naturally to a risk-sensitive stochastic control problem, which we formulate and solve. The most significant contribution of the paper is the subsequent linkage of the two approaches to designing controllers under model uncertainty via the Lagrange multipliers involved in the maximum entropy model construction. On the one hand they provide for the first time a rigorous justification for the ‘randomization’ involved. On the other hand, and again for the first time, they provide sensitivities of controller performance vs modeling uncertainty bounds (or the cost of uncertainty) – that is what is the relative value of a model for a particular control objective. This relationship is further established via duality theory. The result is a unified treatment of system performance robustness against uncertainty models of various complexities. We show how this framework captures several essential results from classical information theory, to modem robust control. We then proceed to develop a similar framework in the multi-agent case, which leads us to a new framework for understanding the fundamental tradeoffs in any networked system – between the benefits from collaboration vs the cost for collaboration. These constrained coalitional games are shown to capture the essentials in network design, network optimization and network control. They also capture the fundamentals of network formation in many areas including economics, sociology, biology and engineering. We describe how network architecture and connectivity pattern can emerge as a result from this framework – in particular we explain small world architectures from this perspective. We close with a result on networked control systems, which attempts to quantify the duality between information pattern and multi-agent control performance.
Download Full Paper