Control of continuous plants by symbolic output feedback

Abstract

This contribution addresses the following hybrid control problem: A continuous plant is to be controlled via symbolic, or quantized, measurement and control signals. Quantization levels may be arbitrarily coarse (e.g. “temperature is too high”, “ok” or “too low”, “valve open” or “closed”). Sensor quantization is assumed to partition the plant output space into a finite number of rectilinear cells, each of which is associated with a unique measurement symbol. Measurement symbols are processed by a control algorithm, which generates a control signal with finite range, i.e. a symbolic signal. The latter determines the evolution of the plant state in time. Interaction between plant and controller is modeled by an interrupt structure, where information exchange is represented by sequences of timed (measurement and control) events. It is shown that, if certain observability conditions hold, the continuous plant state can be reconstructed from a sequence of measurement events. Likewise, if certain controllability/reachability conditions hold, the plant state can be transferred to any desired point in IRⁿ by applying a suitable sequence of control events. These results are used in a heuristic Certainty Equivalence feedback scheme reminiscent of “receding horizon” strategies.

The author wishes to acknowledge support by “Deutsche Forschungsgemeinschaft” through Grant Ra 516-1. Part of this work was done while the author was visiting the Department of Electrical and Computer Engineering at the University of Toronto.