Symbolic sub-systems and symbolic control of linear systems

This paper presents an approach to the control of continuous systems through the use of symbolic models describing the system behavior only at a finite number of points in the state space. These symbolic models can be seen as abstract representations of the continuous dynamics enabling the use of algorithmic controller design methods. We identify a class of linear control systems for which the loss of information incurred by working with symbolic sub-systems can be compensated by feedback. We also show how to transform symbolic controllers designed for a symbolic sub-system into controllers for the original system. The resulting controllers combine symbolic controller dynamics with continuous feedback control laws and can thus be seen as hybrid systems. Furthermore, if the symbolic controller already accounts for software/hardware requirements, the hybrid controller is guaranteed to enforce the desired specifications by construction thereby reducing the need for formal verification.