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. 1

Abstract: In this chapter, a class of discrete time uncertain linear hybrid systems, affected by both parameter variations and exterior disturbances, is considered. The main question is whether there exists a controller such that the closed loop system exhibits desired behavior under dynamic uncertainty and exterior disturbances. The notion of attainability is introduced to refer to the specified behavior that can be forced to the plant by a control mechanism. We give a method for attainability checking that employs the predecessor operator and backward reachability analysis, and a procedure for controller design that uses finite automata and linear programming techniques. Finally, Networked Control Systems (NCS) are proposed as a promising application area of the results and tools developed here, and the ultimate boundedness control problem for the NCS with uncertain delay, package dropout and quantization effects is formulated as a regulation problem for an uncertain hybrid system.

Abstract. Abstraction is a natural way to hierarchically decompose the analysis and design of hybrid systems. Given a hybrid control system and some desired properties, one extracts an abstracted system while preserving the properties of interest. Abstractions of purely discrete systems is a mature area, whereas abstractions of continuous systems is a recent activity. In this paper we present a framework for abstraction that applies to discrete, continuous, and hybrid systems. We introduce a composition operator that allows to build complex hybrid systems from simpler ones and show compatibility between abstractions and this compositional operator. Besides unifying the existing methodologies we also propose constructions to obtain abstractions of hybrid control systems.

Abstract. In this paper, the problem of synthesizing a hybrid controller for a specification expressed as a temporal logic formula φ is considered. We propose a hierarchical approach which consists of three steps. First, the plant to be controlled is abstracted to a fully actuated system. Using the notion of approximate simulation relation, we design a continuous interface allowing the plant to track the trajectories of its abstraction with a guaranteed precision δ. The second step, which is also the main contribution of this paper, consists in deriving a more robust specification φ ′ from the temporal logic formula φ such that given a trajectory satisfying φ ′ , any other trajectory remaining within distance δ satisfies φ. Third, we design a hybrid controller for the abstraction such that all its trajectories satisfy the robust specification φ ′. Then, the trajectories of the plant satisfy the original specification. An application to the control of a second order model of a planar robot in a polygonal environment is considered. 1

Abstract — The problem of designing hybrid controllers in order to satisfy safety or liveness specifications has received much attention in the past decade. Much more recently, there is an increased interest in designing hybrid controllers in order to achieve more sophisticated discrete specifications, such as those expressible in temporal logics. A great challenge is how to compose safety and liveness controllers in order to achieve more complex specifications. Existing approaches are predominantly bottom-up, in the sense that the overall control and composition (or switching) logic requires verification of the integrated closed-loop hybrid system. In this paper, we advocate and develop a top-down approach for this problem by synthesizing controllers which satisfy the specification by construction. Given a flat linear temporal logic specification as an input, we develop an algorithm that translates the temporal logic specification into a hybrid automaton where in each discrete mode we impose controller specifications for the continuous dynamics. In addition to achieving the desired specification by construction, our methodology provides a very natural interface between high level logic design and low level control design. I.

Abstract—This paper provides a framework to automatically generate a hybrid controller that guarantees that the robot can achieve its task when a robot model, a class of admissible environments, and a high-level task or behavior for the robot are provided. The desired task specifications, which are expressed in a fragment of linear temporal logic (LTL), can capture complex robot behaviors such as search and rescue, coverage, and collision avoidance. In addition, our framework explicitly captures sensor specifications that depend on the environment with which the robot is interacting, which results in a novel paradigm for sensor-based temporal-logicmotion planning. As one robot is part of the environment of another robot, our sensor-based framework very naturally captures multirobot specifications in a decentralized manner. Our computational approach is based on first creating discrete controllers satisfying specific LTL formulas. If feasible, the discrete controller is then used to guide the sensor-based composition of continuous controllers, which results in a hybrid controller satisfying the highlevel specification but only if the environment is admissible. Index Terms—Controller synthesis, hybrid control, motion planning, sensor-based planning, temporal logic. I.

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A great challenge for modern systems theory is the design of controllers for continuous systems but with logical specifications. In this paper, we are interested in developing algorithmic methods which given a discretetime controllable linear system and a discrete specification (in the form of a finite transition system or a temporal logic formula), automatically design controllers resulting in desired, closed-loop behavior. This can be achieved using a natural approach involving three steps. In the first step, given a controllable linear system and discrete specification, we extract a finite transition system model which is equivalent (bisimilar) to the continuous system. The second step solves the controller synthesis problem for finite transition systems using well known and well developed algorithms. The third step, which is the focus of this paper, refines the discrete controller of the finite transition system, to a (necessarily) hybrid controller for the original continuous system. The hybrid controller composed with the continuous plant results in a closed-loop hybrid system that, by construction, satisfies the desired, discrete specification.

We re-examine the basic hybrid control set-up of a continuous plant in a closed feedback loop with a finite state control automaton and an interface consisting of an A/D map and a D/A map. We address the question of how dynamic specifications can be formulated independently of a particular A/D map, and of the e#ect of refining an A/D map. The main contribution of this paper is that it extends the framework of supervisory controller synthesis for hybrid systems to include more general dynamic specifications, and demonstrates how to employ known results to solve these synthesis problems.

Abstract. We introduce a notion of bisimulation equivalence between general flow systems, which include discrete, continuous and hybrid systems, and compare it with similar notions in the literature. The interest in the proposed notion is based on our main result, that the temporal logic GFL ⋆ – an extension to general flows of the well-known computation tree logic CTL ⋆ – is semantically preserved by this equivalence. 1