Model Checking LTL over Controllable Linear Systems Is Decidable

Abstract

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.

Hybridization methods for the analysis of nonlinear systems

“…Temporal logic model-checking problems are not decidable for most general hybrid systems. However, decidability results have been proven for some particular classes of hybrid systems (see [4,54] for a survey). These classes must be restricted either in continuous dynamics (e.g.…”

Hybrid Control and Verification of a Pulsed Welding Process

“…In order to rewrite the dynamics of the system into shift register form it first needs to be put on Brunovsky normal form [7], for which a controllable linearized form of the system is needed.…”

“…A discrete state space Z 2 of R 2 is now introduced, as described in [7], which is used to form the space in which the shift-register form system will operate. The 3 domains in which the system operates is, with reference to figure 4, the Arc Length Control (q 1 ), the Metal Transfer Control (q 2 ) and the Short Circuit Control (q 3 ).…”

“…This deficiency is however remedied by relaxing the arc length constraint, which again makes the spaces of interest squares. As described in [7] the partitioning needs to be equidistant, which would seem rather cumbersome for these domains due to the large ratio between z 1 and z 2 , thus a scaling transformation is introduced, S i , which transform each domains into a sufficiently equiproportional domain. In this case it is only desirable to divided the spaces into 3 by 3 grid to prove the concept, thus a transformation that scales the 3 domains into squares are used.…”

“…One of the main objective in [7] was to enlarge this class of systems to all linear controllable systems, which is continued in this paper by showing how this theory apply in practice to the Gas Metal Arc Welding (GMAW) process. By restricting the observations for the system to a finite set of partitions, enables a bisimulation of the system to be modeled using simple timed automata.…”