Some Results on Optimal Estimation and Control for Lossy Networked Control

Professor Chris Byrnes, Washington University, St Louis, USA

Abstract: A long term goal in the theory of systems and control is to develop a systematic methodology for the design of feedback control schemes capable of shaping the response of complex dynamical systems, in both an equilibrium and a nonequilibrium setting. The most classical example of a nonequilibrium attractor for a nonlinear dynamical system is a periodic orbit. In this talk, we present sufficient  conditions for the existence of oscillations in a nonlinear dynamical system, e.g. a closed-loop control system. Just as in Liapunov theory, these conditions can be checked point-wise and therefore do not require the knowledge of the trajectories of the system, in marked contrast with existing criteria requiring the existence of cross-sections for the dynamics. Moreover, using the recent solution of the Poincaré Conjecture in all dimensions, we show that these same conditions are necessary for the existence of an asymptotically stable periodic orbit. These results are illustrated by showing the existence of an asymptotically stable oscillation in a three dimensional, nonholonomic mathematical model of an AC controlled rotor, controlled to turn at a constant angular velocity. We also apply these results to show the existence of a periodic response of a dissipative nonlinear control system, when forced with
a periodic input.

In this talk I will describe some problems related the effect of packets loss and random delay on the design and performance of networked control systems. In particular, I will try to show that communication and control are tightly coupled and they cannot be addressed independently.  For example, where should we place my controller? near the sensors, near the actuators or somewhere in the middle? What is the impact of packet loss on the closed loop performance? Which features should communication protocols have to reduce performance degradation due to packet loss? If sensors and actuators are provided with computational resources, can we use them to improve performance? From a closed-loop performance perspective, is it better to have a protocols with small packet delay and high packet loss or protocols with low packet loss and longer delay? If actuators have no computational resources what should we do when a control packet is loss: use the previous control values (hold-input) or do nothing (zero-input)? These are some of the questions addressed in the presentation. I will propose some possible solutions and comment on their implications on the design ofgeneral networked control systems.