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168
Observability and Controllability of Piecewise Affine and Hybrid Systems
 IEEE Transactions on Automatic Control
, 1999
"... In this pap e we prove in a constructive way, the ee ale b e we e pie a#ne syste and a broad class of hybridsyste de e d by inte line dynamics, automata, and propositional logic. By focusing our inveon the forme class, we show through countethat obse ability and controllability prope rtie cannot b ..."
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Cited by 140 (21 self)
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In this pap e we prove in a constructive way, the ee ale b e we e pie a#ne syste and a broad class of hybridsyste de e d by inte line dynamics, automata, and propositional logic. By focusing our inveon the forme class, we show through countethat obse ability and controllability prope rtie cannot be e asilydely from those of the comp tline subsyste Inste we propose practical nume te base onmixe te line programming. Keywords Hybrid syste controllability,obse ability, pie line syste pie a#ne syste mixe teline programming I. Introducti In recent yearsb oth control and computer science haveb een attractedb y hybridsystem [1], [2], [23], [25], [26],b ecause they provide a unified framework fordescribgARB( cesses evolving accordingto continuous dynamics, discrete dynamics, and logic rules. The interest is mainly motivatedb y the large variety of practical situations, for instance realtime systems, where physical processes interact with digital controllers. Several modelingformalisms h...
A game theoretic approach to controller design for hybrid systems
 Proceedings of the IEEE
, 2000
"... We present a method to design controllers for safety specifications in hybrid systems. The hybrid system combines discrete event dynamics with nonlinear continuous dynamics: the discrete event dynamics model linguistic and qualitative information and naturally accommodate mode switching logic, and t ..."
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Cited by 126 (36 self)
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We present a method to design controllers for safety specifications in hybrid systems. The hybrid system combines discrete event dynamics with nonlinear continuous dynamics: the discrete event dynamics model linguistic and qualitative information and naturally accommodate mode switching logic, and the continuous dynamics model the physical processes themselves, such as the continuous response of an aircraft to the forces of aileron and throttle. Input variables model both continuous and discrete control and disturbance parameters. We translate safety specifications into restrictions on the system’s reachable sets of states. Then, using analysis based on optimal control and game theory for automata and continuous dynamical systems, we derive Hamilton–Jacobi equations whose solutions describe the boundaries of reachable sets. These equations are the heart of our general controller synthesis technique for hybrid systems, in which we calculate feedback control laws for
Optimal Paths in Weighted Timed Automata
 HSCC
, 2001
"... We consider an optimalreachability problem for a timed automaton with respect to a linear cost function which results in a weighted timed automaton. Our solution to this optimization problem consists of reducing it to a (parametric) shortestpath problem for a finite directed graph. The directed gr ..."
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Cited by 122 (5 self)
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We consider an optimalreachability problem for a timed automaton with respect to a linear cost function which results in a weighted timed automaton. Our solution to this optimization problem consists of reducing it to a (parametric) shortestpath problem for a finite directed graph. The directed graph we construct is a refinement of the region automaton due to Alur and Dill. We present an exponential time algorithm to solve the shortestpath problem for weighted timed automata starting from a single state, and a doublyexponential time algorithm to solve this problem starting from a zone of the state space.
Effective Synthesis of Switching Controllers for Linear Systems
, 2000
"... In this work we suggest a novel methodology for synthesizing switching controllers for continuous and hybrid systems whose dynamics are defined by linear differential equations. We formulate the synthesis problem as finding the conditions upon which a controller should switch the behavior of the sys ..."
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Cited by 108 (8 self)
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In this work we suggest a novel methodology for synthesizing switching controllers for continuous and hybrid systems whose dynamics are defined by linear differential equations. We formulate the synthesis problem as finding the conditions upon which a controller should switch the behavior of the system from one "mode" to another in order to avoid a set of bad states, and propose an abstract algorithm which solves the problem by an iterative computation of reachable states. We have implemented a concrete version of the algorithm, which uses a new approximation scheme for reachability analysis of linear systems.
Distributed control applications within sensor networks
 IEEE PROCEEDINGS SPECIAL ISSUE ON DISTRIBUTED SENSOR NETWORKS
, 2003
"... Sensor networks are gaining a central role in the research community. This paper addresses some of the issues arising from the use of sensor networks in control applications. Classical control theory proves to be insufficient in modeling distributed control problems where issues of communication del ..."
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Cited by 100 (28 self)
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Sensor networks are gaining a central role in the research community. This paper addresses some of the issues arising from the use of sensor networks in control applications. Classical control theory proves to be insufficient in modeling distributed control problems where issues of communication delay, jitter, and time synchronization between components are not negligible. After discussing our hardware and software platform and our target application, we review useful models of computation and then suggest a mixed model for design, analysis, and synthesis of control algorithms within sensor networks. We present a hierarchical model composed of continuous timetrigger components at the low level and discrete eventtriggered components at the high level.
A timedependent HamiltonJacobi formulation of reachable sets for continuous dynamic games
 IEEE Transactions on Automatic Control
, 2005
"... Abstract—We describe and implement an algorithm for computing the set of reachable states of a continuous dynamic game. The algorithm is based on a proof that the reachable set is the zero sublevel set of the viscosity solution of a particular timedependent Hamilton–Jacobi–Isaacs partial differenti ..."
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Cited by 98 (25 self)
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Abstract—We describe and implement an algorithm for computing the set of reachable states of a continuous dynamic game. The algorithm is based on a proof that the reachable set is the zero sublevel set of the viscosity solution of a particular timedependent Hamilton–Jacobi–Isaacs partial differential equation. While alternative techniques for computing the reachable set have been proposed, the differential game formulation allows treatment of nonlinear systems with inputs and uncertain parameters. Because the timedependent equation’s solution is continuous and defined throughout the state space, methods from the level set literature can be used to generate more accurate approximations than are possible for formulations with potentially discontinuous solutions. A numerical implementation of our formulation is described and has been released on the web. Its correctness is verified through a two vehicle, three dimensional collision avoidance example for which an analytic solution is available. Index Terms—Differential games, Hamilton–Jacobi equations, reachability, verification.
Stochastic Hybrid Systems: Application to Communication Networks
 in Hybrid Systems: Computation and Control, ser. Lect. Notes in Comput. Science
, 2004
"... Abstract. We propose a model for Stochastic Hybrid Systems (SHSs) where transitions between discrete modes are triggered by stochastic events much like transitions between states of a continuoustime Markov chains. However, the rate at which transitions occur is allowed to depend both on the continu ..."
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Cited by 69 (14 self)
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Abstract. We propose a model for Stochastic Hybrid Systems (SHSs) where transitions between discrete modes are triggered by stochastic events much like transitions between states of a continuoustime Markov chains. However, the rate at which transitions occur is allowed to depend both on the continuous and the discrete states of the SHS. Based on results available for PiecewiseDeterministic Markov Process (PDPs), we provide a formula for the extended generator of the SHS, which can be used to compute expectations and the overall distribution of the state. As an application, we construct a stochastic model for onoff TCP flows that considers both the congestionavoidance and slowstart modes and takes directly into account the distribution of the number of bytes transmitted. Using the tools derived for SHSs, we model the dynamics of the moments of the sending rate by an infinite system of ODEs, which can be truncated to obtain an approximate finitedimensional model. This model shows that, for transfersize distributions reported in the literature, the standard deviation of the sending rate is much larger than its average. Moreover, the later seems to vary little with the probability of packet drop. This has significant implications for the design of congestion control mechanisms. 1
Computational techniques for the verification of hybrid systems
 Proceedings of the IEEE
, 2003
"... Hybrid system theory lies at the intersection of the fields of engineering control theory and computer science verification. It is defined as the modeling, analysis, and control of systems that involve the interaction of both discrete state systems, represented by finite automata, and continuous sta ..."
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Cited by 67 (8 self)
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Hybrid system theory lies at the intersection of the fields of engineering control theory and computer science verification. It is defined as the modeling, analysis, and control of systems that involve the interaction of both discrete state systems, represented by finite automata, and continuous state dynamics, represented by differential equations. The embedded autopilot of a modern commercial jet is a prime example of a hybrid system: the autopilot modes correspond to the application of different control laws, and the logic of mode switching is determined by the continuous state dynamics of the aircraft, as well as through interaction with the pilot. To understand the behavior of hybrid systems, to simulate, and to control these systems, theoretical advances, analyses, and numerical tools are needed. In this paper, we first present a general model for a hybrid system along with an overview of methods for verifying continuous and hybrid systems. We describe a particular verification
Automotive engine control and hybrid systems: challenges and opportunities
 Proceedings of the IEEE
, 2000
"... The design of engine control systems has been traditionally carried out using a mix of heuristic techniques validated by simulation and prototyping using approximate averagevalue models. However, the ever increasing demands on passengers ’ comfort, safety, emissions, and fuel consumption imposed by ..."
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Cited by 57 (15 self)
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The design of engine control systems has been traditionally carried out using a mix of heuristic techniques validated by simulation and prototyping using approximate averagevalue models. However, the ever increasing demands on passengers ’ comfort, safety, emissions, and fuel consumption imposed by car manufacturers and regulations call for more robust techniques and the use of cycleaccurate models. We argue that these models must be hybrid because of the combination of timedomain and eventbased behaviors. In this paper, we present a hybrid model of the engine in which both continuous and discrete timedomain as well as eventbased phenomena are modeled in a separate but integrated manner. Based on this model, we formalize the specification of the overall engine control by defining a number of hybrid control problems. To cope with the difficulties arising in the design of hybrid controllers, a design methodology is proposed. This methodology consists of a relaxation