Hierarchical Decomposition of LTL Synthesis Problem for Nonlinear Control Systems

Abstract

This paper deals with the control synthesis problem for a continuous nonlinear dynamical system under a Linear Temporal Logic (LTL) formula. The proposed solution is a topdown hierarchical decomposition of the control problem involving three abstraction layers of the problem, iteratively solved from the coarsest to the finest. The LTL planning is first solved on a small transition system only describing the regions of interest involved in the LTL formula. For each pair of consecutive regions of interest in the resulting accepting path satisfying the LTL formula, a discrete plan is then constructed in the partitioned workspace to connect these two regions while avoiding unsafe regions. Finally, an abstraction refinement approach is applied to synthesize a controller for the dynamical system to follow each discrete plan. The second main contribution, used in the third abstraction layer, is a new monotonicity-based method to overapproximate the finite-time reachable set of any continuously differentiable system. The proposed framework is demonstrated in simulation for a motion planning problem of a mobile robot modeled as a disturbed unicycle.

On the distributed backward reachability problem for large scale systems

“…In particular, reachability has been studied and exploited as a fundamental tool for evaluating or enforcing state space invariance of control systems [8,27,9,41,28] or reach-avoid set control and differential games [34,18,30,10,20]. A renewed interest in the (both forward and backward) reachability problem is witnessed by more recent literature too, where this tool is exploited in the derivation of dynamical systems abstraction techniques and symbolic control approaches for the verification of fundamental properties such as safety or for the enforcement of formal logics specifications [44,39,46,47,49,48,37,45,16,11,31,32]. This fact, indeed, comes from its inherent peculiarity of addressing how two regions of the state space (a starting and an ending region) are mapped through the dynamics of a (in general nonlinear) system under selected inputs.…”

A particle swarm optimization approach using adaptive entropy-based fitness quantification of expert knowledge for high-level, real-time cognitive robotic control

“…However, synthesizing high-level controllers in a, dynamic environment remains a challenge. Meyer and Dimarogonas [22] introduces a framework to increase the adaptability of the synthesis process, by using a 3-layer top-down hierarchical decomposition of the control problem. A three step-approach is used to firstly, solve the LTL problem on a FSA, secondly, find the best policy for transitioning and thirdly, synthesize a controller.…”

Reachability-based Control Synthesis under Signal Temporal Logic Specifications

“…For instance, linear temporal logic (LTL) has been widely used in formal verification [2]. Toward temporal logic specifications, a general approach is to construct a symbolic abstraction for the considered system such that formal methods like automata-theoretic and graph-searching methods can be applied to design a discrete controller to ensure the satisfaction of LTL specifications [3]- [6]. However, the abstraction-based control design may have huge computational complexity [7], which increases with system dimension and specification complexity, and is based on backward search techniques [8], which may be not available when time constraints are involved, e.g., in Signal Temporal Logic (STL).…”