E. Asarin, O. Bournez, T. Dang, O. Maler, and A. Pneuli. Effective synthesis of switching controllers for linear systems. Proc. IEEE, 88(7):1011--1025, July 2000.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....synthesis of hybrid control systems. The first investigations of piecewise linear hybrid systems can be found in [39, 40, 41] The main problems studied in this framework were stability, controllability, and input output regulation. Piecewise linear dynamical systems have been considered also in [9, 4, 5]. Amethodology for approximating the reachable states is developed and a supervisory control framework is used for controller design. A class of hybrid systems which is similar to piecewise linear hybrid systems is considered in [6, 7, 8] These systems are described by linear dynamic equations ....

E. Asarin, O. Bournez, T. Dang, O. Maler, and A. Pnueli. Effective synthesis of switching controllers for linear systems. Proceedings of IEEE, 88(7):1011--1025, July 2000.

....and continuous reachability solvers and the types of initial conditions, inputs, invariants and guards that they admit. Most are described as running forwards in time from a set of safe initial conditions, in which case G is computed as the smallest controllable invariant set. For exam ple, in [7, 8] reachability is run with as the controlled inputs and E as the disturbance inputs with the resulting safe set as G. The CheckMate tool [9] deals with threshold event driven hybrid systems meaning that switches are both enabled and forced only at hyperplanes in the continuous state space so ....

E. Asarin, O. Bournez, T. Dang, O. Maler, and A. Pnueli, "Effective synthesis of switching controllers for linear systems," Proceedings of the IEEE, vol. 88, no. 7, pp. 1011-1025, July 2000.

....like avoiding an unsafe region of the state space. The process of formal design consists of synthesizing controllers for hybrid systems in order to meet a given specification. Both directions have received large attention in the hybrid systems community, and the reader is referred to [3] [11], 23] 25] 33] 42] 55] and [73] for expositions to much of the research in the field. In this paper, we are interested in the formal analysis of hybrid systems. The formal analysis of large scale, hybrid systems is typically a very difficult process due to the complexity and scale of the ....

E. Asarin, O. Bournez, T. Dang, O. Maler, and A. Pnueli, "Effective synthesis of switching controllers for linear systems," , vol. 88, pp. 1011--1025, July 2000.

....B. Overview: Mathematical Models As our basic mathematical model, we take a class of systems known as hybrid automata, which have gained wide acceptance since their introduction in [18] and [19] The same model or generalizations of it are used in several other papers in this special issue [31] [41] [43] and the switched systems considered in [44] are close relatives. A (basic) hybrid automaton is a closed system with a built in control structure determining when and how the system switches between its various discrete modes, where the continuous behavior in each discrete mode is ....

....THE IEEE, VOL. 88, NO. 7, JULY 2000 system consists of a finite control automaton operating in a closed feedback loop with a continuous plant, with communication via AD and DA interface maps. This quintessentially hybrid configuration is closely related to the switching controller architecture in [41] and is the focus of earlier work by the second author [46] among many others. In Section II, we show how the resulting closed loop system gives rise to a basic hybrid automaton, and is thus amenable to logic based formal specification and analysis. As an illustrative example, to which we return ....

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E. Asarin, O. Bournez, T. Dang, O. Maler, and A. Pnueli, "Effective synthesis of switching controllers for linear systems," Proc. IEEE, vol. 88, pp. 1011--1025, July 2000.

....synthesis of hybrid control systems. The first investigations of piecewise linear hybrid systems can be found in [35, 36, 37] The main problems studied in this framework are stability, controllability, and input output regulation. Piecewise linear dynamical systems have been considered also in [10, 5, 6]. A methodology for approximating the reachable states is developed and a supervisory control framework is used for controller design. A class of hybrid systems which is similar to piecewise linear hybrid systems is considered in [7, 8, 9] These systems are described by linear dynamic equations ....

E. Asarin, O. Bournez, T. Dang, O. Maler, and A. Pnueli. Effective synthesis of switching controllers for linear systems. Proceedings of IEEE, 88(7):1011--1025, July 2000.

....is implemented by an exact (accurate) computational algorithm that terminates. Initialised rectangular automata therefore are, together with timed automata, classes of hybrid automata for which the controller synthesis procedure terminates. Beyond that approximating schemes are needed, see [7]. If the hybrid automaton can be partitioned into finitely bisimulation classes (see [3, 2.1.18] for a definition and discussion of this term) like a timed automaton (see [1] then the supervisory control problem is decidable and the supervisor computable, see also [3, 2.1.36] However for the ....

E Asarin, O Bournez, T Dang, O Maler, A Pnueli, Effective Synthesis of Switching Controllers for Linear Systems, Proceeding of the IEEE. To appear.

....sufficient for performing a reachability, or more general, task. In this paper, we focus on Problem 1, while setting up the framework for considering these more general questions in the future. In its full generality, Problem 1 can be tackled using controller synthesis methods for hybrid systems [1, 7, 11]. However, termination conditions for such synthesis procedures are limited [6] and the computational complexity of such procedures could be prohibitive due to nested reachability computations. It is therefore evident that in order to scale our methods to real life examples, structure must be ....

....generally, one can envision more complicated tasks that can be specified in temporal logic, but in this paper we restrict our attention to reachability specifications. 3 A Mode Switching Condition In its full generality, Problem 2 can be posed as a controller synthesis problem for hybrid systems [7, 11]. Such synthesis methods involve nested, and possibly cyclic reachability computations, where each reachability computation involves computing the capture set of a differential game. Furthermore, termination guarantees for controller synthesis methods are rather limited [6] In our mode ....

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E. Asarin, O. Bournez, T. Dang, O. Maler, and A. Pnueli, Effective Synthesis of Switching Controllers for Linear Systems, Proceedings of the IEEE, 88(2):10111025.

....simulation. When we have a closed form solution, e.g. t] x 0 e At for linear systems, we can claim to have solved the problem because F = fx 0 e At : t 0g is a representation of all reachable states. But then, how can we check 11 A longer answer can be found in the introduction to Asarin et al. 2000b) P x 0 0 Fig. 16. A continuous behavior that intersects P while its numerical approximation 0 does not. whether F P is empty where P is some simple subset of R n defined by, say, combination of linear equalities From the point of view of effective computation, such closed form ....

....technique, inspired by Greenstreet (1996) is called face lifting and is based on maximizing normal derivatives of f on the faces of the polyhedron, see Dang and Maler (1998) It applies to arbitrary non linear systems. The other, more efficient technique is specialized for linear systems, see Asarin et al. 2000a) and uses some optimal control ideas, proposed by Varaiya (1998) A similar technique was developed independently by Chutinan and Krogh (1998, 1999) Other approaches to solve reachability problems use ellipsoids instead of polyhedra, e.g. Kurzhanski and Valyi (1997) Botchkarev and Tripakis ....

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Asarin, E., O. Bournez, T. Dang, O. Maler and A. Pnueli (2000b). Effective synthesis of switching controllers for linear systems. Proceedings of the IEEE 88, 1011--1025.

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E. Asarin, O. Bournez, T. Dang, O. Maler and A. Pnueli, Effective Synthesis of Switching Controllers for Linear Systems, Proceedings of the IEEE 88, 1011-1025, 2000.

....faces of the polyhedron inside and finding an orthogonal under approximation. Backward reachability, that is, finding all the points from which a set F is reachable can be performed by computing ffi for the reversed system x = GammaAx. For the purpose of controller synthesis for hybrid systems [ABDPM00] we need an under approximation of the F Until G operator, which returns the points from which you can stay within the set F either forever or until you reach a set G (which is typically the guard of a transition to another state) A similar operator is needed for analyzing hybrid systems with ....

E. Asarin, O. Bournez, T. Dang, A. Pnueli and O. Maler, Effective Synthesis of Switching Controllers for Linear Systems, submitted for publication, 2000.

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E. Asarin, O. Bournez, T. Dang, O. Maler, and A. Pneuli. Effective synthesis of switching controllers for linear systems. Proc. IEEE, 88(7):1011--1025, July 2000.

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E. Asarin, O. Bournier, T. Dang, O. Maler, and A. Pnueli. Effective synthesis of switching controllers for linear systems. In Proc. IEEE, 88:1011--1025, 2000. 14

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E Asarin, O Bournez, T Dang, O Maler, A Pnueli, Effective Synthesis of Switching Controllers for Linear Systems, Proceeding of the IEEE, October 2000.

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E. Asarin, O. Bournez, T. Dang, O. Maler, A. Pnueli. Effective synthesis of switching controllers for linear systems. Proceedings of the IEEE, vol. 88:7, pp. 1011--1025, 2000.

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E. Asarin, O. Bournez, T. Dang, O. Maler, A. Pnueli. Effective synthesis of switching controllers for linear systems. Proceedings of the IEEE, vol. 88:7, pp. 1011--1025, 2000.

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