Abstraction, discretization, and robustness in temporal logic control of dynamical systems

Abstract

Abstraction-based, hierarchical approaches to control synthesis from temporal logic specifications for dynamical systems have gained increased popularity over the last decade. Yet various issues commonly encountered and extensively dealt with in control systems have not been adequately discussed in the context of temporal logic control of dynamical systems, such as inter-sample behaviors of a sampled-data system, effects of imperfect state measurements and unmodeled dynamics, and the use of time-discretized models to design controllers for continuous-time dynamical systems. We discuss these issues in this paper. The main motivation is to demonstrate the possibility of accounting for the mismatches between a continuous-time control system and its various types of abstract models used for control synthesis. We do this by incorporating additional robustness measures in the abstract models. Such robustness measures are gained at the price of either increased nondeterminism in the abstracted models or relaxed versions of the specification being realized. Under a unified notion of abstraction, we provide concrete means of incorporating these robustness measures and establish results that demonstrate their effectiveness in dealing with the above mentioned issues.

CASP solutions for planning in hybrid domains

“…Some examples include (Cimatti et al 2015;Cavada et al 2014;Tabuada et al 2002;Maly et al 2013;Bae et al 2016;Liu and Ozay 2014;Henzinger and Otop 2014), sampling-based planners (Karaman et al 2011;Lahijanian et al 2014). Similarly, falsification of hybrid systems tries to guide the search towards the error states, that can be easily cast as a planning problem, (Plaku et al 2013;Cimatti et al 1997).…”

Controller synthesis with inductive proofs for piecewise linear systems: An SMT-based algorithm

“…There is a large body of results on automata theoretic approaches for controller synthesis [1], [16], [18], [23], [25]. The approach here is to construct a finite abstraction of the dynamical system and then invoke the LTL synthesis algorithms such as the one in [5].…”

Variable elimination for scalable receding horizon temporal logic planning

“…The state of the environment and system at any time step is described by a truth assignment tuple (x, y) ∈ X × Y where X = 2 X and Y = 2 Y . These states can be the result of discretization, as described in [8], [11], where the variables in X and Y abstract a continuous state space.…”