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This paper studies the controller synthesis problem for Linear Temporal Logic (LTL) specifications using (constrained) zonotope techniques. To begin with, we implement (constrained) zonotope techniques to partition the state space and further to verify whether the LTL specification can be satisfied. Once the LTL specification can be satisfied, the next step is to design a controller to guarantee the satisfaction of the LTL specification for dynamic systems. Based on the verification of the LTL specification, an abstraction-based control design approach is proposed in this paper: a novel abstraction construction is developed first, then finite local abstract controllers are designed to achieve the LTL specification, and finally the designed abstract controllers are combined and refined as the controller for the original system. The proposed control design strategy is illustrated via a numerical example from autonomous robots.
Given a Markov decision process (MDP) and a linear-time ($omega$-regular or LTL) specification, the controller synthesis problem aims to compute the optimal policy that satisfies the specification. More recently, problems that reason over the asympto
We show that given a desired closed-loop response for a system, there exists an affine subspace of controllers that achieve this response. By leveraging the existence of this subspace, we are able to separate controller design from closed-loop design
Reactive synthesis is a key technique for the design of correct-by-construction systems and has been thoroughly investigated in the last decades. It consists in the synthesis of a controller that reacts to environments inputs satisfying a given tempo
This paper studies the robust satisfiability check and online control synthesis problems for uncertain discrete-time systems subject to signal temporal logic (STL) specifications. Different from existing techniques, this work proposes an approach bas
This paper investigates the online motion coordination problem for a group of mobile robots moving in a shared workspace, each of which is assigned a linear temporal logic specification. Based on the realistic assumptions that each robot is subject t