R. Grossman, A. Nerode, A. Ravn, and H. Reischel, editors. Hybrid Systems, Lecture Notes in Computer Science 736. Springer Verlag, 1993.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....transient analysis, digital control I. INTRODUCTION Recent advances in sensor and information technology alleviate the development of control engineering applications for changing operating environments. The majority of the resulting solutions can be considered as hybrid dynamical systems [1], which combine continuous state and discrete event dynamics. Such systems can be characterized by a number of distinct operational modes [2] 3] If there is an energy content mismatch between the subsequent modes of the dynamical system, then reconfiguration transients are unavoidable [4] ....

Grossman, R.L., A. Nerode, A.P. Ravn, and H. Rischel, Eds., Hybrid Systems, Lecture Notes in Computer Science, no. 736, New York: Springer Verlag, 1993.

....case, one may obtain a discrete event model of the plant together with the interface using automata or Petri nets; the controller is then designed using DES supervisor methodologies. Approaches analogous to the former also exist. Further information on hybrid systems may be found in references [GRO 93] PNU 95] ANT 95] ALU 96] ANT 97] ANT 98a, b, c] MAL 97] MOR 97] HEN 98a] ZAY 98] 2.1. Modelling Approaches Several different mathematical paradigms have been used for modeling hybrid systems revealing the diversity of the researches. Tavernini [TAV 87] used differential ....

GROSSMAN R.L., NERODE A., RAVN A.P., RISCHEL H., Eds., Hybrid Systems. Lecture Notes in Computer Science, Vol. 736. Springer-Verlag, 1993.

.... sinusoid generator random generator random MuxMux S HS H demo2 Help Window Palettes Context Move Copy Replace Align Link Delete Flip Save Undo Replot View Calc Back There have been a number of models proposed in the literature for hybrid dynamical systems (see for example [3, 4]) A simple, yet powerful model is the following: x = f(x) 1) if h i (x) 0; then x : g(i; x) i = 1; 2; m; 2) where x 2 R n is the state of the system, f is a vector field on R n , g is a mapping fromN ThetaR n R n and h i s are continuous functions. 2) should be ....

.... [ A;B;C;D] c , f f] list( symbolic parameters dlg= strcat(sci2exp(A) strcat(sci2exp(B) strcat(sci2exp(C) strcat(sci2exp(D) strcat(sci2exp(x0) initial icon definition gr i= txt= Jump ; A,B,C,D) xstringb(orig(1) orig(2) txt,sz(1) sz(2) fill ) sz=[3 2] initial block size x=standard define(sz,model,dlg,gr i) end INRIA SCICOS A Dynamic System Builder and Simulator User s Guide Version 1.0 31 The only hard part of defining an Interfacing function is the set case which handles user dialogue and determines system parameters. For example, in ....

Grossman, R. L., Nerode A., Ravn, A. P. and Rischel H. (Eds.), Hybrid Systems, Lecture Notes in Computer Science 736, Springer Verlag, Berlin Heidelberg, 1993.

....invariance of state space sets with respect to the actions of dynamical systems. The focus is on dynamical systems given by differential equations, building up to hybrid systems. 1 Introduction We are interested in the formal verification of safety and performance properties of hybrid systems [1, 8, 17]. In computer science, there is large formal verification literature (e.g. 2, 5, 9, 11, 12, 16, 19] of discrete dynamic systems, such as automata. Usually, the proofs that verify safety and performance involve the search for certain formulas which are (proven to be) invariant over the actions ....

R. L. Grossman et al., editors. Hybrid Systems, vol. 736 of Lecture Notes in Computer Science. Springer, New York, 1993. .

....discrete digital and continuous electrical models of chips, and the coupling of digital and biological systems. Outside the algebraic approach, there are questions concerning the relationship between our models and the various theories of hybrid control systems (see the various approaches in [GNRR93], for example) This field of applications is blessed with a landscape of models and logics for reasoning about the behaviour and control of timed state systems, timed automata, and abstract machines. Furthermore, work is needed on questions concerning the hierarchy, including the refinement, ....

R L Grossman, A Nerode, A P Ravn, and H Rischel, editors. Hybrid systems. Lecture Notes in Computer Science 736. Springer-Verlag, 1993.

....systems, well posedness, lexicographic inequalities. 1 Introduction Various approaches to modeling, analysis, and control synthesis of hybrid systems have been developed within the computer science community and the systems and control community, from di#erent points of view (see, e.g. [1] [6] In the computer science community, as an extension of finite automata, several models of hybrid systems such as timed automata [7] and hybrid automata [8] have been proposed and some results on verification of their models have been obtained. In the control community, from the dynamical ....

....field is necessarily continuous in the state x. Now, how about the case of discontinuous vector fields Let us consider the following example shown in Figure 1. The equations of motion of this system are given by 8 : mode 1 : x 1 x 2 = 01 00 x 1 x 2 , if y =[1 0] x 1 x 2 # 0 mode 2 : x 1 x 2 = 01 k d x 1 x 2 , if y = 1 0] x 1 x 2 # 0. 3) 3 [ N G # # Figure 1: Collision to an elastic wall By simple calculations, we see that this system is well posed (without jumps and sliding modes) although the vector ....

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R.L Grossman, A. Nerode, A.P. Ravn, and H. Rischel (Eds.). Hybrid systems. Lecture Notes in Computer Science 736, New York, Springer-Verlag, 1993.

....is described with a different set of equations. These regions can be viewed as discrete states; within each discrete state, the differential equations describe the evolution of the continuous state. Systems with discrete and continuous state form a subset of the class of so called hybrid systems [11, 12]. 3.1 Mathematical formulation Let the continuous state space X of the dynamical system with n states be given by: X = p [ j=1 D j ; 11) where D j are pairwise disjoint, connected subsets of IR n . On each subset D j , the system is described with system equations: x = F j (x; u) 12) ....

R. L. Grossman, A. Nerode, A. P. Ravn, and H. R. (Eds.), Hybrid systems, vol. 736 of Lecture notes in computer science. New York: Springer-Verlag, 1993.

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R. Grossman, A. Nerode, A. Ravn, and H. Reischel, editors. Hybrid Systems, Lecture Notes in Computer Science 736. Springer Verlag, 1993.

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R. L. Grossman, A. Nerode, A. P. Ravn, and H. Rischel, editors, Hybrid Systems, Lecture Notes in Computer Science, Volume 736, SpringerVerlag, New York, 1993.

....level of con dence, that a system adheres to its requirements, models describing in great detail the essence of the system are made. These models often are subject to analysis, validation and veri cation. Formalisms that allow for modelling hybrid systems have been proposed in the past (e.g. [9], 2] 1] some of which have become quite popular. On the one hand, theory in these formalisms is investigated and on the other hand, the theory is applied on case studies. In this paper, a process algebraic approach is investigated. Process algebras come in several variants (e.g. CSP [10] CCS ....

R.L. Grossman, A. Nerode, A. Ravn, and H. Rischel, editors. Hybrid Systems, Lecture Notes in Computer Science 736. Springer-Verlag, 1993.

....the existence of bisimulations for certain classes of planar hybrid systems. 1 Introduction Hybrid systems consist of finite state machines interacting with di#erential equations. Various modeling formalisms, analysis, design and control methodologies, as well as applications, can be found in [3,4,5,10,17]. Formal verification is the main computational approach for analyzing properties of hybrid systems. One of the most important verification problems for hybrid systems is the reachability problem which asks whether trajectories of the hybrid system can reach certain undesirable regions of the ....

R. L. Grossman, A. Nerode, A. P. Ravn, and H. Rischel (eds.), Hybrid systems, Lecture Notes in Computer Science, vol. 736, Springer-Verlag, 1993.

....is with Portland State University, Portland, OR 97207 USA (e mail: gerardo mth.pdx.edu) Publisher Item Identifier S 0018 9219(00)06460 4. 53] Their wide applicability has inspired a great deal of research from both control theory and theoretical computer science [1] 2] 7] 9] 10] [29], 31] 52] 75] Many of the above motivating applications are safety critical and require guarantees of safe operation. Consequently, much research focuses on formal analysis and design of hybrid systems. Formal analysis of hybrid systems is concerned with verifying whether a hybrid system ....

R. L. Grossman, A. Nerode, A. P. Ravn, and H. Rischel, Eds., Hybrid Systems. New York: Springer-Verlag, 1993, vol. 736, Lecture Notes in Computer Science.

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R. L. Grossman, A. Nerode, A. P. Ravn, and H. Rischel, Eds. Hybrid Systems, Lecture Notes in Computer Science, vol. 736. New York: Springer, 1993.

.... earliest hybrid system models were those of Witsenhausen [63] and Tavernini [64] However, in the last decade or so, hybrid system modeling has evolved dramatically beginning with Peleties and DeCarlo [50] 65] 68] and continuing with Stiver et al. 69] 70] Alur et al. 71] Nerode et al. [72], 73] Dogruel Ozguner [74] Branicky [51] 75] 76] and, more recently, Pettersson et al. 49] 77] 78] A review of these models is beyond the scope of this paper. Nevertheless, the pertinent fruit of the modeling evolution can be summarized by the dynamics (2.1a) 2.1b) 2.1c) where ....

R. Grossman, A. Nerode, A. Ravn, and H. Rischel, Hybrid Systems, H. Rischel, Ed. New York: Springer-Verlag, 1993, vol. 736, Lecture Notes in Computer Science.

....systems, resulting in a hybrid control system. The interaction and information exchange of all of the aircraft involved in the maneuver results in a multiagent hybrid control system. There are several approaches to hybrid system modeling, verification, and controller design (see, for example, [16] [19] The computer science approach is to extend models of finite state automata to timed automata [20] linear hybrid automata [21] and hybrid input output automata [22] Linear hybrid automata model or abstract the continuous dynamics by differential inclusions of the form and verify ....

R. L. Grossman, A. Nerode, A. P. Ravn, and H. Rischel, Eds., Hybrid Systems, Lecture Notes in Computer Science 736. New York: SpringerVerlag, 1993.

....and empty recover all these. 2) Hybrid Systems: The case of a GHDS with finite, where each is a subset of and each largely corresponds to the usual notion of a hybrid system, viz, a 1 Precise statements appear in [1, Sec. 4. 3] coupling of finite automata and differential equations [9] 12] [36]. Herein, a hybrid system is a GHDS with countable and with (or ) and , for all : where is a vector field on . 2 3) Changing State Space: The state space may change. This is useful in modeling component failures or changes in dynamical description based on autonomous or controlled events which ....

R. L. Grossman, A. Nerode, A. P. Ravn, and H. Rischel, Eds., Hybrid Systems, Lecture Notes in Computer Science, vol. 736. New York: Springer, 1993.

....process for large scale systems consists of imposing an overall system architecture as well as designing communication and control algorithms for achieving a desired overall system performance. The merging of discrete communication protocols and continuous control laws results in hybrid systems ([3, 4, 5]) The analysis process for complex, hybrid systems consists of proving or verifying that the designed system indeed meets certain specifications. However, both the design and the analysis may be formidable due to the complexity and magnitude of the system. In the design process, complexity is ....

Robert L. Grossman, Anil Nerode, Anders P. Ravn, and Hans Rischel, editors. Hybrid Systems. Lecture Notes in Computer Science. Springer-Verlag, 1993.

....known to lie to reasonable uncertain sets. Conflict resolution maneuvers are therefore modeled by a finite state automaton interacting with control systems, the so called hybrid 3 control systems. There are several approaches to hybrid system design and verification (see, for example, [12, 13, 14, 15]) One approach is to extend verification techniques which exist for finite state machines [16] to include timed and dynamical systems [17, 18] These approaches abstract the differential equations by clocks [19] or differential inclusions [20, 21, 22] and verify the resulting abstracted system. ....

Robert L. Grossman, Anil Nerode, Anders P. Ravn, and Hans Rischel, editors. Hybrid Systems. Lecture Notes in Computer Science. Springer-Verlag, 1993.

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R.L. Grossman, A. Nerode, A.P. Ravn, and H. Rischel, editors. Hybrid Systems, Lecture Notes in Computer Science 736. Springer-Verlag, 1993.

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R.L. Grossman, A. Nerode, A.P. Ravn, and H. Rischel, editors. Hybrid Systems I. Lecture Notes in Computer Science 736. Springer-Verlag, 1993.

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R.L. Grossman, A. Nerode, A.P.Ravn, and H. Rischel. Hybrid Systems, volume736 Springer Verlag, 1993. Lecture Notes in Computer Science.

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R.L. Grossman, A. Nerode, A.P. Ravn, H. Rischel (Eds.), Hybrid Systems, Lecture Notes in Computer Science, vol. 736, Springer, Berlin, 1993.

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R. L. Grossman, A. Nerode, A. P. Ravn, and H. Rishel, eds., Hybrid Systems, vol. 736 of Lecture Notes in Computer Science. New York: Springer-Verlag, 1993. 10

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Grossman, R. L., Nerode, A., Ravn, A. P., Rischel, H. (editors): Hybrid Systems, Lecture Notes in Computer Science, Vol. 736. Springer-Verlag, 1993.

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R. L. Grossman, A. Nerode, A. P. Ravn, and H. Rishel, editors. Hybrid Systems, vol. 736 of Lecture Notes in Computer Science. Springer-Verlag, 1993.

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