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72
A fully automated framework for control of linear systems from ltl specifications
 In HSCC, volume 3927 of LNCS
, 2006
"... Abstract. We consider the following problem: given a linear system and an LTL−X formula over a set of linear predicates in its state variables, find a feedback control law with polyhedral bounds and a set of initial states so that all trajectories of the closed loop system satisfy the formula. Our ..."
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Cited by 140 (27 self)
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Abstract. We consider the following problem: given a linear system and an LTL−X formula over a set of linear predicates in its state variables, find a feedback control law with polyhedral bounds and a set of initial states so that all trajectories of the closed loop system satisfy the formula. Our solution to this problem consists of three main steps. First, we partition the state space in accordance with the predicates in the formula and construct a transition system over the partition quotient, which captures our capability of designing controllers. Second, using model checking, we determine runs of the transition system satisfying the formula. Third, we generate the control strategy. Illustrative examples are included. 1
Approximation metrics for discrete and continuous systems
 IEEE Transactions on Automatic Control
, 2005
"... Established system relationships for discrete systems, such as language inclusion, simulation, and bisimulation, require system observations to be identical. When interacting with the physical world, modeled by continuous or hybrid systems, exact relationships are restrictive and not robust. In thi ..."
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Cited by 103 (16 self)
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Established system relationships for discrete systems, such as language inclusion, simulation, and bisimulation, require system observations to be identical. When interacting with the physical world, modeled by continuous or hybrid systems, exact relationships are restrictive and not robust. In this paper, we develop the first framework of system approximation that applies to both discrete and continuous systems by developing notions of approximate language inclusion, approximate simulation, and approximate bisimulation relations. We define a hierarchy of approximation pseudometrics between two systems that quantify the quality of the approximation, and capture the established exact relationships as zero sections. Our approximation framework is compositional for a synchronous composition operator. Algorithms are developed for computing the proposed pseudometrics, both exactly and approximately. The exact algorithms require the generalization of the fixed point algorithms for computing simulation and bisimulation relations, or dually, the solution of a static game whose cost is the socalled branching distance between the systems. Approximations for the pseudometrics can be obtained by considering Lyapunovlike functions called simulation and bisimulation functions. We illustrate our approximation framework in reducing the complexity of safety verification problems for both deterministic and nondeterministic continuous systems.
Discrete abstractions for robot motion planning and control in polygonal environments
 IEEE Transactions on Robotics
, 2005
"... In this paper, we present a computational framework for automatic generation of provably correct control laws for planar robots in polygonal environments. Using polygon triangulation and discrete abstractions, we map continuous motion planning and control problems specified in terms of triangles to ..."
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Cited by 57 (7 self)
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In this paper, we present a computational framework for automatic generation of provably correct control laws for planar robots in polygonal environments. Using polygon triangulation and discrete abstractions, we map continuous motion planning and control problems specified in terms of triangles to computationally inexpensive finite state transition systems. In this framework, powerful discrete planning algorithms in complex environments can be seamlessly linked to automatic generation of feedback control laws for robots with underactuation constraints and control bounds. We focus on fullyactuated kinematic robots with velocity bounds and (underactuated) unicycles with forward and turning speed bounds.
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.
Reachability analysis of multiaffine systems (ramas),” URL http://iasi.bu.edu/∼software/reachma.htm
"... Abstract. We present a technique for reachability analysis of continuous multiaffine systems based on rectangular partitions. The method is iterative. At each step, finer partitions and larger discrete quotients are produced. We exploit some interesting convexity properties of multiaffine functio ..."
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Cited by 31 (3 self)
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Abstract. We present a technique for reachability analysis of continuous multiaffine systems based on rectangular partitions. The method is iterative. At each step, finer partitions and larger discrete quotients are produced. We exploit some interesting convexity properties of multiaffine functions on rectangles to show that the construction of the discrete quotient at each step requires only the evaluation of the vector field at the set of all vertices of all rectangles in the partition and finding the roots of a finite set of scalar affine functions. The methodology promises to be easily extendable to rectangular hybrid automata with multiaffine vector fields and is expected to find important applications in analysis of biological networks and robot control. 1
Model checking LTL over controllable linear systems is decidable
 of Lecture Notes in Computer Science
, 2003
"... Abstract. The use of algorithmic verification and synthesis tools for hybrid systems is currently limited to systems exhibiting simple continuous dynamics such as timed automata or rectangular hybrid systems. In this paper we enlarge the class of systems amenable to algorithmic analysis and synthesi ..."
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Cited by 30 (2 self)
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Abstract. The use of algorithmic verification and synthesis tools for hybrid systems is currently limited to systems exhibiting simple continuous dynamics such as timed automata or rectangular hybrid systems. In this paper we enlarge the class of systems amenable to algorithmic analysis and synthesis by showing decidability of model checking Linear Temporal Logic (LTL) formulas over discrete time, controllable, linear systems. This result follows from the construction of a language equivalent, finite abstraction of a control system based on a set of finite observations which correspond to the atomic propositions appearing in a given LTL formula. Furthermore, the size of this abstraction is shown to be polynomial in the dimension of the control system and the number of observations. These results open the doors for verification and synthesis of continuous and hybrid control systems from LTL specifications. 1
Bisimilar Control Affine Systems
 Systems and Control Letters
, 2002
"... The notion of bisimulation plays a very important role in theoretical computer science where it provides several notions of equivalence between models of computation. These equivalences are in turn used to simplify analysis and synthesis for these models. In system theory, a similar notion is also o ..."
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Cited by 29 (12 self)
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The notion of bisimulation plays a very important role in theoretical computer science where it provides several notions of equivalence between models of computation. These equivalences are in turn used to simplify analysis and synthesis for these models. In system theory, a similar notion is also of interest in order to develop modular analysis and design tools for purely continuous or hybrid control systems. In this paper, we introduce two notions of bisimulation for nonlinear systems. We present a differentialalgebraic characterization of these notions and show that bisimilar systems of different dimensions are obtained by factoring out certain invariant distributions. Furthermore, we also show that all bisimilar systems of different dimension are of this form.
Bisimulation Relations for Dynamical and Control Systems
, 2002
"... In this paper we propose a new equivalence relation for dynamical and control systems called bisimulation. As the name implies this definition is inspired by the fundamental notion of bisimulation introduced by R. Milner for labeled transition systems. It is however, more subtle than its namesake in ..."
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Cited by 25 (9 self)
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In this paper we propose a new equivalence relation for dynamical and control systems called bisimulation. As the name implies this definition is inspired by the fundamental notion of bisimulation introduced by R. Milner for labeled transition systems. It is however, more subtle than its namesake in concurrency theory, mainly due to the fact that here, one deals with relations on manifolds. We further show that the bisimulation relations for dynamical and control systems defined in this paper are captured by the notion of abstract bisimulation of Joyal, Nielsen and Winskel (JNW). This result not only shows that our equivalence notion is on the right track, but also confirms that the abstract bisimulation of JNW is general enough to capture equivalence notions in the domain of continuous systems. We believe that the unification of the bisimulation relation for labeled transition systems and dynamical systems under the umbrella of abstract bisimulation, as achieved in this work, is a first step towards a unified approach to modeling of and reasoning about the dynamics of discrete and continuous structures in computer science and control theory.
Observability of switched linear systems in continuous time
 of Lecture Notes in Computer Sciences
, 2005
"... Abstract. We study continuoustime switched linear systems with unobserved and exogenous mode signals. We analyze the observability of the initial state and initial mode under arbitrary switching, and characterize both properties in both the autonomous and nonautonomous cases. 1 ..."
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Cited by 25 (1 self)
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Abstract. We study continuoustime switched linear systems with unobserved and exogenous mode signals. We analyze the observability of the initial state and initial mode under arbitrary switching, and characterize both properties in both the autonomous and nonautonomous cases. 1
Approximate bisimulation relations for constrained linear systems
 AUTOMATICA
, 2007
"... In this paper, we define the notion of approximate bisimulation relation between two systems, extending the well established exact bisimulation relations for discrete and continuous systems. Exact bisimulation requires that the observations of two systems are and remain identical, approximate bisi ..."
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Cited by 18 (5 self)
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In this paper, we define the notion of approximate bisimulation relation between two systems, extending the well established exact bisimulation relations for discrete and continuous systems. Exact bisimulation requires that the observations of two systems are and remain identical, approximate bisimulation allows the observation to be different provided they are and remain arbitrarily close. Approximate bisimulation relations are conveniently defined as level sets of a function called bisimulation function. For the class of linear systems with constrained initial states and constrained inputs, we develop effective characterizations for bisimulation functions that can be interpreted in terms of linear matrix inequalities, set inclusion and games. We derive a computationally effective algorithm to evaluate the precision of the approximate bisimulation between a constrained linear system and its projection. This algorithm has been implemented in a MATLAB toolbox: MATISSE. Two examples of use of the toolbox in the context of safety verification are shown.