M. Branicky, Studies in Hybrid Systems: Modeling, Analysis and Control. PhD thesis, MIT, Cambridge, MA, 1995.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....satisfies this requirement on C #,#1 , n,1 X i=1 # 2 i # 1=2 rV #q# n,1 X i=1 # i #rV #q## i # # n#q# = #1 , n,1 X i=1 # 2 i # 1=2 # 0 : Since #1 , P n,1 i=1 # 2 i # 1=2 # 0 the new vector also points away from the obstacle. It is well know (see for example [10]) that if a set of stable differential equations share a common Lyapunov function, as the set of equations q = u# , 8# i such that P n,1 i=1 # 2 i # 1,shareV #q# as a Lyapunov function, then a system whose dynamics switches between the right hand sides of those differential equations shares ....

M. Branicky, Studies in Hybrid Systems: Modeling, Analysis and Control. PhD thesis, MIT, Cambridge,

....that they introduce on a purely continuous systems. Also there are real life systems that are inherently hybrid, for instance the transmission system of a car, walking robots, flight controllers, industrial processes and many others. In a survey of the current hybrid system models, Branicky ([9]) distinguishes four kind of discrete behavior in a hybrid systems: 1. autonomous jumps when the continuous state jumps discontinuously on hitting prescribed regions of the state space; 2. autonomous switch the vector field changes discontinuously when the continuous state hits certain ....

....events are recorded. This approach allows for design specification and verifiability, but fails to answer questions regarding stability and controllability. Next we briefly describe a few models from each approach. For a more complete survey of the first approach, the reader is directed to [9]. Most of the second approach models can be found in [8] 15] 4] 3] 5] 17] 1.3.1 Witsenhausen Model In [37] Witsenhausen introduced a simple model for continuous time hybrid systems. The state of the system has two components: a continuous part and a discrete part. 7 The continuous ....

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M.S. Branicky. Studies in hybrid systems: modeling, analysis, and control. PhD thesis, MIT, 1995.

....enabling conditions and any necessary reset of the continuous state that must take place when the transition occurs. We assume here that a jump always occurs when the transition condition is enabled. This model falls in several of the general hybrid systems frameworks proposed in the literature [7, 8, 9, 10, 11, 12, 13, 14, 15]. For simplicity we assume here that the PSfrag replacements queue not full: q = B P i w i BTp q 1 w i = aB BTp q tT = 0 queue full: q = 0 w i = aB BTp q tT = 1 q qmax and P i w i BTp q 1 tT : 0 tT Tp q B w i : mw i Figure 2: Hybrid model for ....

M. S. Branicky, Studies in Hybrid Systems: Modeling, Analysis, and Control. PhD thesis, MIT, Cambridge, MA, June 1995.

....of space limitations, a discussion of synchronization and of interconnections of hybrid control systems is omitted. The synchronization may take rather complex forms. Other definitions of hybrid systems or hybrid control systems have been proposed. For an overview see the thesis of M. Branicky, [6]. Definitions similar in character to the above are [6, Ch. 5] and [9, 17, 21, 23] 3.2 Subclasses of the class of hybrid control systems An example of a hybrid control system is the conveyor belt model of Example 2.1. E.D. Sontag has introduced a class of hybrid control systems in a paper that ....

M.S. Branicky. Studies in hybrid systems: Modeling, analysis, and control. PhD thesis, M.I.T., Cambridge, MA, 1995.

....led not only to diverse techniques, but also to different terminology. A good example of this is the variety of terms used to essentially describe the discrete part (or object) of a hybrid system, some of these being discrete state , mode , location , node and vertex . The work of Branicky (Branicky 1995), Branicky 1996) provides a taxonomy for hybrid dynamical systems based on his development of a general hybrid dynamical system (GHDS) Earlier work (Branicky et al. 1994) introduced some aspects of the overall classification approach. The full taxonomy considers a wide variety of attributes that ....

....corresponds to a unit rise in level. Table 1 List of models and references Reference Authors (Alur et al. 1993) Alur, Courcoubetis, Henzinger, Ho (Asarin et al. 1995) Asarin, Maler, Pneuli (Antsaklis et al. 1993) Stiver and Antsaklis 1993) Antsaklis, Stiver, Lemmon (Branicky et al. 1994) (Branicky 1995) Branicky, Borkar, Mitter (Back et al. 1993) Back, Guckenheimer, Meyers (Brockett 1993) Brockett (Wei 1995) Caines and Wei 1996) Caines, Wei (Chaochen et al. 1993) Chaochen, Ravn, Hansen (DiGennaro et al. 1994) DiGennaro, Horn, Kulkarni, Ramadge (Dogruel and Ozguner 1994) Dogruel, Ozguner ....

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Branicky, M.S. (1995). Studies in Hybrid Systems: Modeling, Analysis, and Control. PhD Thesis. Massachusetts Institute of Technology, Laboratory for Information and Decision Systems. Cambridge, MA. LIDS-TH-2304.

.... are applied to this simple Table 1 List of model acronyms and references Model Code Reference Authors ACHH (Alur et al. 1993) Alur Courcoubetis Henzinger Ho AMP (Asarin et al. 1995) Asarin Maler Pneuli ASL (Antsaklis et al. 1993) Stiver and Antsaklis 1993) Antsaklis Stiver Lemmon BBM (Branicky 1995), Branicky et al. 1994) Branicky Borkar Mitter BGM (Back et al. 1993) Back Guckenheimer Meyers Bro (Brockett 1993) Brockett CRH (Chaochen et al. 1993) Chaochen Ravn Hansen DHKR (DiGennaro et al. 1994) DiGennaro Horn Kulkarni Ramadge DO (Dogruel and Ozguner 1994) Dogruel Ozguner Dra ....

....that only 3 distinct vector fields are used in the assignment as expected since the server can be positioned in only three locations. As a final remark, the exact values for the vector fields are defined by the system parameters (i.e. ae; ae 1 ; ae 2 ; ae 3 ) Branicky Borkar Mitter (BBM) In (Branicky 1995), Branicky et al. 1994) a model referred to as the abstract model is introduced. The three tank system exhibits a transition behaviour which is referred to as autonomous switching in which the vector field describing the state evolution changes discontinuously when the state x(t) hits the ....

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Branicky, M. S. (1995). Studies in Hybrid Systems: Modeling, Analysis, and Control. PhD thesis. Massachusetts Institute of Technology, Laboratory for Information and Decision Systems. Cambridge, MA. LIDS-TH-2304.

....of control theory. E.D. Sontag has introduced the class of piecewise linear systems in a paper published in 1981, see [48] A subclass of this class forms the piecewise linear hybrid systems as defined elsewhere in this report, see [50] Hybrid systems have been considered since the 1980 s, see [14] for references and [55] for a definition. Piecewise linear hybrid systems are, in regard to the geometry of the spaces, based on polyhedral sets. The fact that polyhedral sets can be described by finite dimensional parameters, makes these sets a suitable class of objects for control and system ....

....a piecewise linear system has been introduced by E.D. Sontag in 1981, see [48] As a special case, it contains the definition of a piecewise linear hybrid system as argued by the author in [50] A proof of this statement is provided in Appendix B. There are many definitions of hybrid systems, see [14] for an overview. Since then other definitions have been introduced that are more suitable for control theory, see [34, 55] The concept of a mixed logic dynamical (MLD) system has been introduced by A. Bemporad and M. Morari, see [9, 8] It is established in [8] that the concept of a MLD system ....

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M.S. Branicky. Studies in hybrid systems: Modeling, analysis, and control. PhD thesis, M.I.T., Cambridge, MA, 1995.

....conditions for the game, we encode the desirability of each possible system trajectory for each player. We seek to most generally and formally express what it means to play a control game with a hybrid system. Our formalism is based on that of Branicky s controlled hybrid dynamical system (CHDS) (Branicky, 1995). With a desire to both (1) preserve the expressive power of a CHDS, and (2) create a formal language suited to expressing hybrid system game play, we have found it most natural to describe transitions in terms of actions, 1 for practical purposes of modeling and simulation and allow for the ....

Branicky, Michael S. (1995). Studies in Hybrid Systems: modeling, analysis, and control. PhD thesis. Massachusetts Institute of Technology. Cambridge, MA, USA.

.... [Bournez and Cosnard, 1996] for simulation by analog automata, Garzon, 1995] for simulation by cellular automata, Siegelmann and Sontag, 1994] and [Siegelmann, 1998] for simulation by saturated linear systems that can involve arbitrary real (not necessarily rational) numbers, Branicky, 1995b] Branicky, 1995a] Ruohonen, 1997] and [Moore, 1991] for simulation by di#erential equations, Moore, 1990] for simulation by continuous time physical devices in dimension three, and 13 In high order neural nets, activations are combined using multiplication as opposed to just linear combinations. 34 [Koiran ....

Branicky, M. S. (1995). Studies in Hybrid Systems: Modeling, Analysis, and Control, Ph.D. Thesis, Center for Intelligent Control Systems, M.I.T., Cambridge, MA.

....dynamics using logic based decision rules. Only in the last 10 years has the theoretical analysis of hybrid systems (i.e. systems with both continuous dynamics and discrete logic) been pursued in a systematic fashion. A fair amount of research has been done on the modeling of hybrid systems [1, 2, 3, 4, 5, 6, 7], but only more recently has the analysis and synthesis of hybrid control laws begun to emerge in the literature. One of the main goals of this thesis is to broaden the body of knowledge concerned with hybrid systems. Toward this end we develop tools to expedite the analysis and design of hybrid ....

....(1.1) if for any x 0 2 Z , the solution x to (1.1) with x(t 0 ) x 0 remains in Z for all times t t 0 for which the solution is defined [8] In Chapter 2 the above definition of an invariant set is extended to hybrid systems. The use of invariance in a hybrid systems context is touched upon in [7]. In this thesis, a hybrid system Sigma is characterized by four entities: A finite dimensional linear space X called the continuous state space; an arbitrary set S called the discrete statespace; a family ff s : s 2 Sg of locally Lipschitz continuous functions from X to X called the family of ....

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M. S. Branicky. Studies in Hybrid Systems: Modeling, Analysis, and Control. PhD thesis, MIT, Cambridge, MA, June 1995.

....how to diagnose hybrid systems complex dynamical systems whose behavior is modeled as a hybrid system. Hybrid models comprise both discrete and continuous behavior. They are typically represented as a sequence of piecewise continuous behaviors interleaved with discrete transitions (e.g. (Branicky 1995)) Each period of continuous behavior represents a so called mode of the system. For example, in the case of NASA s Sprint AERCam, modes might include translate X axis, rotate X axis, translate Y axis, etc. Alenius Gupta 1998) In the case of an Airbus fly by wire system, modes might include ....

.... with discrete transitions that are simpler to analyze and interpret (e.g. Mosterman Biswas 1997a) In the examples above, hybrid models use discrete transitions to model both controller actions, and so called autonomous jumps, i.e. model induced jumps from one continuous behavior to another (Branicky 1995). As we shall see in this paper, we may also use discrete transitions to model exogenous actions, i.e. unpredicted actions that cause components of our system to fail. The problem we address in this paper is how to diagnose such hybrid systems. For the purposes of this paper, we consider the ....

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Branicky, M. 1995. Studies in Hybrid Systems: Modeling, Analysis, and Control. Ph.D. Dissertation, Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology.

....paper introduces tests to determine if a given set is invariant for a certain hybrid system. These tests do not require the computation of the hybrid system s state trajectory and their use goes beyond the present application. The use of invariance in a hybrid systems context was touched upon by Branicky (1995). The remaining of the paper is organized as follows. In Section 2 the proposed hybrid control law is presented and briefly motivated. The main result of the paper is stated in Section 3, namely that the control law described in Section 2 makes the closed loop hybrid system asymptotically stable ....

Branicky, M. S. (1995). Studies in Hybrid Systems: Modeling, Analysis, and Control.

....many papers have covered the problem of modelling and simulation according to the hybrid approach. A majority of these papers deals with mathematical and computational issues such as the mathematical representation, the interpretation, the analysis and the practical execution of hybrid systems [6, 4, 5, 1, 14, 2]. In our work, which started in 1990, we have adopted a slightly different view. Instead of emphasising the hardcore computational matters, we have emphasised the conceptual side [12, 11, 15, 13, 8] of the modelling process. As expected, such an approach raises much debate since simulation is ....

M.S. Branicky. Studies in Hybrid Systems: Modeling, Analysis, and Control. PhD thesis, MIT, 1995.

....systems. An example is given to illustrate the theoretical results. 1 Introduction A vast amount of literature about analysis, modeling and control of hybrid systems, i.e. systems with both continuous and discrete parts, can be found in both the field of control and computer science ( 1] [3], 4] 9] 11] 13] A special class of hybrid systems is the class of switched systems, which can be thought of as a collection of differential equations together with rules to switch between them [12] 11] During the switching, the continuous state is assumed to be continuous, but there ....

.... A special class of hybrid systems is the class of switched systems, which can be thought of as a collection of differential equations together with rules to switch between them [12] 11] During the switching, the continuous state is assumed to be continuous, but there are some extensions ( 1] [3]) that allow for jumps in the continuous state and even for different state spaces for different vector fields. Examples in real life include car transmission systems, process control systems, mobile robots etc. We are interested in developing a new, general methodology for designing controllers ....

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M. S. Branicky. Studies in hybrid systems: modeling, analysis, and control. PhD thesis, MIT, 1995.

....algebraic equation models the state of the decision making logic. The discrete state i(t) 2 I is piecewise constant. The notation t Gamma indicates that the discrete state is piecewise continuous from the right. For a broad review of hybrid phenomena and associated models, we refer to the thesis [14]. So far, the discrete state has been playing the role of an index variable that keeps track of which cell the continuous state is currently evolving in. For systems with hysteresis, the discrete state will play a more crucial role. We give the following example. Example 2 Figure 4 (left) shows a ....

M. S. Branicky, Studies in Hybrid Systems: Modeling, Analysis and Control, Ph.D. thesis, MIT, 1995.

....Dept. of Electrical Engineering Linkoping University S 581 83 Linkoping, Sweden 1 Introduction Hybrid system is a term used in many different areas to describe system combining different properties. In this context, hybrid systems are systems that are both continuous and discrete to their nature [3]. This paper deals with the problem of modeling and simulating hybrid systems [2, 6, 4] More particularly, it deals with initializations of the continuous state variables after a discrete state change. The tool used for describing the hybrid systems is switched bond graphs. It is a tool for ....

M.S. Branicky. Studies in hybrid systems: modeling, analysis, and control. PhD thesis, MIT, 1995.

....has recently been a very active area of research. The development of computers and discrete controllers has increased the importance of hybrid systems. A vast amount of literature about analysis, modeling and control of hybrid systems can be found in both the field of control and computer science ([2], 1] 7] 8] 3] 4] However a general methodology for designing hybrid controllers is lacking; most of the controllers are being designed specificly to the problem. In this paper we study some mathematic properties of a special class of hybrid system, Witsenhausen systems or switched ....

....discrete state. The condition of well defined is essential for stability. Next we give an example of a Witsenhausen system that is not well defined, having an unstable equilibrium point, although this point is stable for all of the individual differential equations. Example 1 (Due to Branicky [2]) Consider f 1 (x) Ax and f 2 (x) Bx where: A = Gamma0:1 1 Gamma10 Gamma0:1 250 200 150 100 50 0 50 80 60 40 20 0 20 40 60 80 100 120 x Figure 2: Trajectory for switched system with initial condition (0.1,0.1) B = Gamma0:1 10 Gamma1 Gamma0:1 For the switched system we ....

M.S. Branicky. Studies in hybrid systems: modeling, analysis, and control. PhD thesis, MIT, 1995.

....the algebraic equation models the state of the decision making logic. The discrete state i#t# I is piecewise constant. The notation t indicates that the discrete state is piecewise continuous from the right. For a broad review of hybrid phenomena and associated models, we refer to the thesis [5]. So far, the discrete state has been playing the role of an index variable that keeps track of which cell the continuous state is evolving in. For systems with hysteresis, the discrete state will play a more crucial role. Inspired by [13] we give the following example. EXAMPLE 3 SWITCHING ....

M. S. Branicky. Studies in Hybrid Systems: Modeling, Analysis and Control. PhD thesis, MIT, 1995.

....a polytope p c bounding f(c) can be achieved in many ways. One of the simplest and most efficient ways to find a suitable p c is to compute the minimum and maximum values for each component of F over the cell c and form a bounding box for f(c) using these values. In hybrid systems terms (see e.g. (Branicky, 1995)) each cell can be thought of as a discrete state, and the bounding polytope is determined by approximating system dynamics with a rectangular differential inclusion. In step 3, we are checking for two properties: 1) 8x 2 c : f n (x) 2 c for some n 2 N. That is, all trajectories of the ....

Branicky, M. (1995). Studies in Hybrid Systems: Modeling, Analysis, and Control. PhD thesis.

....be used to obtain bounds on an external disturbance that affects the system. The presented stability results are quite general and can be applied also to fuzzy systems. Fuzzy systems may be viewed as hybrid systems where the finite rule bases are related to the discrete states of the hybrid system [5, 15]. In this paper we will illustrate the flexibility of the stability result by applying it to a Takagi Sugeno fuzzy system [28, 31] which consists of fuzzy blending of linear subsystems. The stability result for fuzzy systems presented in [28, 31] requires the existence of one common positive ....

....in the literature [20, 6, 2, 7, 17, 1, 19, 12, 18] to name a few. In this paper, stability is studied for autonomous hybrid systems, obtained for instance when a controller has been designed resulting in a closed loop hybrid system [20] Models for autonomous hybrid systems can be found in [33, 29, 5]. The evolution of an autonomous hybrid system can be described by (1) combined with a discrete event system whose output determines which vector field is active, that is x(t) f(x(t) m(t) 2) m(t) OE(x(t) m(t Gamma ) 3) where x 2 n , m 2 M = fm 1 ; m g and each m i = m ....

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M. S. Branicky. Studies in Hybrid Systems: Modeling, Analysis, and Control. PhD thesis, Massachusetts Institute of Tech., 1995.

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M. S. Branicky. Studies in Hybrid Systems: Modeling, Analysis, and Control. Sc.D. thesis, M.I.T., Cambridge, MA, June 1995.

....software tools (Hybrid cc, HyTech, and CEtool) for the simulation and verification of these strategies. We describe the computational environment we developed at Case to synthesize and implement real world assembly strategies. 1. Introduction Robotic assemblies are inherently hybrid systems [1] because they involve the making and breaking of contacts [2,3] This paper pursues a class of such assemblies that we call peg in maze assemblies, which includes realworld examples such as clutch mating and gear meshing. These are multi tiered versions of traditional peg in hole assembly ....

M.S. Branicky, Studies in Hybrid Systems: Modeling, Analysis, and Control, Sc.D. Thesis, Electrical Eng. and Computer Science Dept., M.I.T., June 1995.

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M. Branicky, Studies in Hybrid Systems: Modeling, Analysis and Control. PhD thesis, MIT, Cambridge, MA, 1995.

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M. Branicky. Studies in Hybrid Systems: Modeling, Analysis, and Control. PhD thesis, MIT, Cambridge, MA, 1995.

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M.S. Branicky. Studies in hybrid systems: Modeling, analysis, and control. PhD thesis, M.I.T., Cambridge, MA, 1995.

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