An invariant‐based approach to the design of hybrid control systems

2007

Acta Informatica

Abstract. In this paper we provide a bridge between the infinite state models used in control theory to describe the evolution of continuous physical processes and the finite state models used in computer science to describe software. We identify classes of control systems for which it is possible to construct equivalent (bisimilar) finite state models. These constructions are based on finite, but otherwise arbitrary, partitions of the set of inputs or outputs of a control system.

Section: R a F Tmentioning

confidence: 99%

Symbolic models for control systems

2007

Acta Informatica

“…Synthesis for hybrid systems using logic has already been considered in [22], however the logic is not used to model the specifications but rather to motivate the development of the synthesis procedures as well as to prove several facts regarding the proposed algorithms. Other synthesis techniques include supervisory control based on approximate finite abstractions [9], invariants for the continuous dynamics [28], convexity properties of affine systems [12] and mixed integer linear programming [5].…”

Section: Introductionmentioning

confidence: 99%

Model Checking LTL over Controllable Linear Systems Is Decidable

Lecture Notes in Computer Science

Pappas

2003

Abstract. The use of algorithmic verification and synthesis tools for hybrid systems is currently limited to systems exhibiting simple continuous dynamics such as timed automata or rectangular hybrid systems. In this paper we enlarge the class of systems amenable to algorithmic analysis and synthesis by showing decidability of model checking Linear Temporal Logic (LTL) formulas over discrete time, controllable, linear systems. This result follows from the construction of a language equivalent, finite abstraction of a control system based on a set of finite observations which correspond to the atomic propositions appearing in a given LTL formula. Furthermore, the size of this abstraction is shown to be polynomial in the dimension of the control system and the number of observations. These results open the doors for verification and synthesis of continuous and hybrid control systems from LTL specifications.

“…This different perspective justifies why this paper focuses on control systems rather than on dynamical systems. Initial approaches to the development of symbolic models of control systems seem to have been based on the use of integrals of motion [8], [41]. Integrals or constants of motion are a quite natural way of defining state space partitions compatible with the continuous dynamics.…”

Section: Related Workmentioning

confidence: 99%

Symbolic Control of Linear Systems Based on Symbolic Subsystems

IEEE Trans. Automat. Contr.

2006

Abstract-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 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 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.