Symbolic Control of Linear Systems Based on
Symbolic Subsystems, Paulo Tabuada · 2006
This paper describes 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 representa- tions 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 subsystems can be compensated by feedback. We also show how to transform symbolic controllers designed for a symbolic subsystem 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. model can be used in another model. Analysis/design could then be performed on simpler models thereby reducing the complexity of these tasks. In this paper, we take important steps along this direction by focusing on the control of continuous time systems based on symbolic models. In particular, we are interested in finite state models capturing the essential properties of linear control sys- tems. The finite state nature of these models is important for two main reasons. First, finite state models are especially well suited for automated analysis and design which is becoming in- creasingly important given the size of nowadays complex con- trol systems. The use of such models thus opens new algorithmic perspectives for analysis and design. Second, finite state models offer a common language to describe an abstract view of con- tinuous dynamics as well as the software implementation of control algorithms. It is, therefore, possible to formally reason about the behavior of the interconnection between continuous dynamics and software which has been one of the main thrusts behind the research area of hybrid systems. With the objective of strengthening this connection between continuous models of dynamics and finite state models of software we will focus, in this paper, on a particular symbolic model for control systems: symbolic subsystems. B. Contributions