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Logics for Hybrid Systems
 Proceedings of the IEEE
, 2000
"... This paper offers a synthetic overview of, and original contributions to, the use of logics and formal methods in the analysis of hybrid systems ..."
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Cited by 138 (13 self)
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This paper offers a synthetic overview of, and original contributions to, the use of logics and formal methods in the analysis of hybrid systems
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.
Bisimilar Linear Systems
, 2001
"... The notion of bisimulation in theoretical computer science is one of the main complexity reduction methods for the analysis and synthesis of labeled transition systems. Bisimulations are special quotients of the state space that preserve many important properties expressible in temporal logics, and, ..."
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Cited by 74 (11 self)
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The notion of bisimulation in theoretical computer science is one of the main complexity reduction methods for the analysis and synthesis of labeled transition systems. Bisimulations are special quotients of the state space that preserve many important properties expressible in temporal logics, and, in particular, reachability. In this paper, the framework of bisimilar transition systems is applied to various transition systems that are generated by linear control systems. Given a discretetime or continuoustime linear system, and a finite observation map, we characterize linear quotient maps that result in quotient transition systems that are bisimilar to the original system. Interestingly, the characterizations for discretetime systems are more restrictive than for continuoustime systems, due to the existence of an atomic time step. We show that computing the coarsest bisimulation, which results in maximum complexity reduction, corresponds to computing the maximal controlled or reachability invariant subspace inside the kernel of the observations map. These results establish strong connections between complexity reduction concepts in control theory and computer science.
Temporal Logic Motion Planning for Dynamic Robots
, 2007
"... In this paper, we address the temporal logic motion planning problem for point robots that are modeled by second order dynamics. Temporal logic specifications can capture the usual control specifications such as reachability and invariance as well as more complex specifications like sequencing and o ..."
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Cited by 51 (14 self)
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In this paper, we address the temporal logic motion planning problem for point robots that are modeled by second order dynamics. Temporal logic specifications can capture the usual control specifications such as reachability and invariance as well as more complex specifications like sequencing and obstacle avoidance. In order to solve this problem, we follow a hierarchical approach that enables the control of the second order system by designing control laws for a fully actuated kinematic model. Our approach consists of three basic steps. First, we design a control law that enables the dynamic model to track a simpler kinematic model with a globally bounded error. Second, we built a robust temporal logic specification that takes into account the tracking errors of the first step. Finally, we solve the new robust temporal logic path planning problem for the kinematic model using automata theory and simple local vector fields. The resulting continuous time trajectory is provably guaranteed to satisfy the initial user specification.
Impulse differential inclusions: A viability approach to hybrid systems
 IEEE Transactions on Automatic Control
, 2002
"... Abstract. Impulse differential inclusions are introduced as a framework for modelling hybrid phenomena. Connections to standard problems in area of hybrid systems are discussed. Conditions are derived that allow one to determine whether a set of states is viable or invariant under the action of an i ..."
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Cited by 47 (7 self)
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Abstract. Impulse differential inclusions are introduced as a framework for modelling hybrid phenomena. Connections to standard problems in area of hybrid systems are discussed. Conditions are derived that allow one to determine whether a set of states is viable or invariant under the action of an impulse differential inclusion. For sets that violate these conditions, methods are developed for approximating their viability and invariance kernels, that is the largest subset that is viable or invariant under the action of the impulse differential inclusion. The results are demonstrated on examples. 1.
Symbolic models for nonlinear control systems using approximate bisimulation
, 2007
"... Symbolic models for nonlinear control systems using approximate bisimulation Abstract — Control systems are usually modeled by differential equations describing how physical phenomena can be influenced by certain control parameters or inputs. Although these models are very powerful when dealing with ..."
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Cited by 42 (12 self)
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Symbolic models for nonlinear control systems using approximate bisimulation Abstract — Control systems are usually modeled by differential equations describing how physical phenomena can be influenced by certain control parameters or inputs. Although these models are very powerful when dealing with physical phenomena, they are less suitable to describe software and hardware interfacing the physical world. This has spurred a recent interest in describing control systems through symbolic models that are abstract descriptions of the continuous dynamics, where each “symbol” corresponds to an “aggregate” of continuous states in the continuous model. Since these symbolic models are of the same nature of the models used in computer science to describe software and hardware, they provided a unified language to study problems of control in which software and hardware interact with the physical world. In this paper we show that every incrementally globally asymptotically stable nonlinear control system is approximately equivalent (bisimilar) to symbolic model with a precision that can be chosen a–priori. We also show that for digital controlled systems, in which inputs are piecewise–constant, and under the stronger assumption of incremental input–to–state stability, the symbolic models can be obtained, based on a suitable quantization of the inputs.
Robust Controller Synthesis for Hybrid Systems Using Modal Logic
 Hybrid Systems: Computation and Control (HSCC’01), volume 2034 of LNCS
, 2001
"... . In this paper, we formulate and robustly solve a quite general class of hybrid controller synthesis problems. The type of controller we investigate is the switching control mechanism of a hybrid automaton (via guard and mode invariant sets), and the robustness result is with respect to variations ..."
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Cited by 23 (3 self)
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. In this paper, we formulate and robustly solve a quite general class of hybrid controller synthesis problems. The type of controller we investigate is the switching control mechanism of a hybrid automaton (via guard and mode invariant sets), and the robustness result is with respect to variations in the right hand sides of the dierential equations that depend continuously on a parameter. We present a novel methodology for controller design and synthesis which uses modal logic as a formalism for reasoning about sets of plant states, and various operators on sets arising from the dierential equations and from metric tolerance relations on the state space. 1 Introduction In general terms, a hybrid system H can be said to satisfy a performance speci cation robustly if every system H 0 in some nominated variation class around H also satis es that speci cation. Likewise, a synthesis procedure for a class of control problems can be called robust if the nominal closedloop hyb...
Lecture notes on hybrid systems
, 2004
"... The aim of this course is to introduce some fundamental concepts from the area of hybrid systems, that is dynamical systems that involve the interaction of continuous (real valued) states and discrete (finite valued) states. Applications where these types of dynamics play a prominent role will be hi ..."
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Cited by 22 (0 self)
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The aim of this course is to introduce some fundamental concepts from the area of hybrid systems, that is dynamical systems that involve the interaction of continuous (real valued) states and discrete (finite valued) states. Applications where these types of dynamics play a prominent role will be highlighted. We will introduce general methods for investigating properties such as existence of solutions, reachability and decidability of hybrid systems. The methods will be demonstrated on the motivating applications. Students who successfully complete the course should be able to appreciate the diversity of phenomena that arise in hybrid systems and how discrete “discrete ” entities and concepts such as automata, decidability and bisimulation can coexist with continuous entities and
A QUALITATIVE EVENTBASED APPROACH TO FAULT DIAGNOSIS OF HYBRID SYSTEMS
, 2008
"... Fault diagnosis is crucial for ensuring the safe operation of complex engineering systems. Many ..."
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Cited by 21 (14 self)
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Fault diagnosis is crucial for ensuring the safe operation of complex engineering systems. Many
A qualitative eventbased approach to continuous systems diagnosis
 IEEE TRANSACTIONS ON CONTROL SYSTEMS TECHNOLOGY
, 2009
"... Fault diagnosis is crucial for ensuring the safe operation of complex engineering systems. Although discreteevent diagnosis methods are used extensively, they do not easily address parametric fault isolation in systems with complex continuous dynamics. This paper presents a novel eventbased approa ..."
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Cited by 16 (12 self)
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Fault diagnosis is crucial for ensuring the safe operation of complex engineering systems. Although discreteevent diagnosis methods are used extensively, they do not easily address parametric fault isolation in systems with complex continuous dynamics. This paper presents a novel eventbased approach for diagnosis of abrupt parametric faults in continuous systems, based on a qualitative abstraction of measurement deviations from the nominal behavior. From a continuous model of the system, we systematically derive dynamic fault signatures expressed as eventbased fault models, which are used, in turn, for designing an eventbased diagnoser of the system and determining system diagnosability. The proposed approach is applied to a subset of the Advanced Diagnostics and Prognostics Testbed, which is representative of a spacecraft’s electrical power system. We present experimental results from the actual testbed, as well as detailed simulation experiments that examine the performance of our diagnosis algorithms under different fault magnitudes and noise levels.