Results 1  10
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34
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 105 (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.
Receding horizon control for temporal logic specifications.
 In 13th ACM international conference on Hybrid systems: computation and control,
, 2010
"... ABSTRACT In this paper, we describe a receding horizon framework that satisfies a class of linear temporal logic specifications sufficient to describe a wide range of properties including safety, stability, progress, obligation, response and guarantee. The resulting embedded control software consis ..."
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Cited by 61 (9 self)
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ABSTRACT In this paper, we describe a receding horizon framework that satisfies a class of linear temporal logic specifications sufficient to describe a wide range of properties including safety, stability, progress, obligation, response and guarantee. The resulting embedded control software consists of a goal generator, a trajectory planner, and a continuous controller. The goal generator essentially reduces the trajectory generation problem to a sequence of smaller problems of short horizon while preserving the desired systemlevel temporal properties. Subsequently, in each iteration, the trajectory planner solves the corresponding shorthorizon problem with the currently observed state as the initial state and generates a feasible trajectory to be implemented by the continuous controller. Based on the simulation property, we show that the composition of the goal generator, trajectory planner and continuous controller and the corresponding receding horizon framework guarantee the correctness of the system. To handle failures that may occur due to a mismatch between the actual system and its model, we propose a response mechanism and illustrate, through an example, how the system is capable of responding to certain failures and continues to exhibit a correct behavior.
Receding Horizon Temporal Logic Planning for Dynamical Systems
 In 48th IEEE Conference on Decision and Control (CDC) 2009
, 2009
"... Abstract—This paper bridges the advances in computer science and control to allow automatic synthesis of complex dynamical systems which are guaranteed, by construction, to satisfy the desired properties even in the presence of adversary. The desired properties are expressed in the language of tempo ..."
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Cited by 37 (7 self)
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Abstract—This paper bridges the advances in computer science and control to allow automatic synthesis of complex dynamical systems which are guaranteed, by construction, to satisfy the desired properties even in the presence of adversary. The desired properties are expressed in the language of temporal logic. With its expressive power, a wider class of properties than safety and stability can be specified. The resulting system consists of a discrete planner which plans, in the abstracted discrete domain, a set of transitions of the system to ensure the correct behaviors and a continuous controller which continuously implements the plan. For a system with certain structure, we present an approach, based on a receding horizon scheme, to overcome computational difficulties in the synthesis of a discrete planner and allow more complex problems to be solved. I.
Receding horizon temporal logic planning
 IEEE Transactions on Automatic Control
, 2012
"... Abstract We present a methodology for automatic synthesis of embedded control software that incorporates a class of linear temporal logic (LTL) specifications sufficient to describe a wide range of properties including safety, stability, progress, obligation, response and guarantee. To alleviate th ..."
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Cited by 35 (11 self)
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Abstract We present a methodology for automatic synthesis of embedded control software that incorporates a class of linear temporal logic (LTL) specifications sufficient to describe a wide range of properties including safety, stability, progress, obligation, response and guarantee. To alleviate the associated computational complexity of LTL synthesis, we propose a receding horizon framework that effectively reduces the synthesis problem into a set of smaller problems. The proposed control architecture consists of a goal generator, a trajectory planner, and a continuous controller. The goal generator reduces the trajectory generation problem into a sequence of smaller problems of short horizon while preserving the desired systemlevel temporal properties. Subsequently, in each iteration, the trajectory planner solves the corresponding shorthorizon problem with the currently observed state as the initial state and generates a feasible trajectory to be implemented by the continuous controller. Based on the simulation property, we show that the composition of the goal generator, trajectory planner and continuous controller and the corresponding receding horizon framework guarantee the correctness of the system with respect to its specification regardless of the environment in which the system operates. In addition, we present a response mechanism to handle failures that may occur due to a mismatch between the actual system and its model. The effectiveness of the proposed technique is demonstrated through an example of an autonomous vehicle navigating an urban environment. This example also illustrates that the system is not only robust with respect to exogenous disturbances but is also capable of properly handling violation of the environment assumption that is explicitly stated as part of the system specification .
Robust ReachAvoid Controller Synthesis for Switched Nonlinear Systems
"... Abstract — In this paper, we describe a method to automatically synthesize controllers that provide hard guarantees of safety and target reachability for sampleddata switched systems under bounded continuous disturbances. Techniques from hybrid system verification are used to perform continuous tim ..."
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Cited by 10 (3 self)
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Abstract — In this paper, we describe a method to automatically synthesize controllers that provide hard guarantees of safety and target reachability for sampleddata switched systems under bounded continuous disturbances. Techniques from hybrid system verification are used to perform continuous time differential game calculations on each sampling interval. Iterative procedures are given for computing the set of states for which there exists an admissible control policy so that the closedloop system satisfies the properties of safety and reachability over a finite time horizon. From this computation, we show how to obtain an explicit state feedback policy in the form of multiple reachable sets, and an algorithm is given for using this feedback law in closedloop control of the switched system. A simulation example of automated aerial refueling is used to illustrate the application of our approach. I.
Controllability Decompositions of Networked Systems Through Quotient Graphs
"... Abstract — In this paper we study decentralized, networked systems whose interaction dynamics are given by a nearestneighbor averaging rule. By letting one node in the network take on the role of a leader in the sense that this node provides the control input to the entire system, we can ask questi ..."
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Cited by 10 (2 self)
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Abstract — In this paper we study decentralized, networked systems whose interaction dynamics are given by a nearestneighbor averaging rule. By letting one node in the network take on the role of a leader in the sense that this node provides the control input to the entire system, we can ask questions concerning the controllability. In particular, we show that the controllable subspaces associated with such systems have a direct, graph theoretic interpretation in terms of socalled quotient graphs, providing us with a smaller, approximate bisimulation of the original network. Index Terms — Networked control systems, Network analysis and control, Communication networks
Approximate simulations for taskstructured probabilistic I/O automata
 In LICS workshop on Probabilistic Automata and Logics (PAul06
, 2006
"... A Probabilistic I/O Automaton (PIOA) is a countablestate automaton model that allows nondeterministic and probabilistic choices in state transitions. A taskPIOA adds a task structure on the locally controlled actions of a PIOA as a means for restricting the nondeterminism in the model. The taskPI ..."
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Cited by 6 (4 self)
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A Probabilistic I/O Automaton (PIOA) is a countablestate automaton model that allows nondeterministic and probabilistic choices in state transitions. A taskPIOA adds a task structure on the locally controlled actions of a PIOA as a means for restricting the nondeterminism in the model. The taskPIOA framework defines exact implementation relations based on inclusion of sets of trace distributions. In this paper we develop the theory of approximate implementations and equivalences for taskPIOAs. We propose a new kind of approximate simulation between taskPIOAs and prove that it is sound with respect to approximate implementations. Our notion of similarity of traces is based on a metric on trace distributions and therefore, we do not require the state spaces nor the space of external actions (output alphabet) of the underlying automata to be metric spaces. We discuss applications of approximate implementations to probabilistic safety verification.
Verifying tolerant systems using polynomial approximations.
 In Proceedings of the IEEE RealTime Systems Symposium,
, 2009
"... AbstractIn this paper, we approximate a hybrid system with arbitrary flow functions by systems with polynomial flows; the verification of certain properties in systems with polynomial flows can be reduced to the first order theory of reals, and is therefore decidable. The polynomial approximations ..."
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Cited by 6 (3 self)
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AbstractIn this paper, we approximate a hybrid system with arbitrary flow functions by systems with polynomial flows; the verification of certain properties in systems with polynomial flows can be reduced to the first order theory of reals, and is therefore decidable. The polynomial approximations that we constructsimulate (as opposed to "simulate") the original system, and at the same time are tight. We show that for systems that we call tolerant, safety verification of a system can be reduced to the safety verification of the polynomial approximation. Our main technical tool in proving this result is a logical characterization of simulations. We demonstrate the construction of the polynomial approximation, as well as the verification process, by applying it to an example protocol in air traffic coordination.
Conformance testing as falsification for cyberphysical systems
 In ICCPS 2014
, 2014
"... In ModelBased Design of CyberPhysical Systems (CPS), it is often desirable to develop several models of varying fidelity. Models of different fidelity levels can enable mathematical analysis of the model, control synthesis, faster simulation etc. Furthermore, when (automatically or manually) tra ..."
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Cited by 6 (3 self)
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In ModelBased Design of CyberPhysical Systems (CPS), it is often desirable to develop several models of varying fidelity. Models of different fidelity levels can enable mathematical analysis of the model, control synthesis, faster simulation etc. Furthermore, when (automatically or manually) transitioning from a model to its implementation on an actual computational platform, then again two different versions of the same system are being developed. In all previous cases, it is necessary to define a rigorous notion of conformance between different models and between models and their implementations. This paper argues that conformance should be a measure of distance between systems. Albeit a range of theoretical distance notions exists, a way to compute such distances for industrial size systems and models has not been proposed yet. This paper addresses exactly this problem. A universal notion of conformance as closeness between systems is rigorously defined, and evidence is presented that this implies a number of other applicationdependent conformance notions. An algorithm for detecting that two systems are not conformant is then proposed, which uses existing proven tools. A method is also proposed to measure the degree of conformance between two systems. The results are demonstrated on a range of models. 1.
Automatic synthesis of robust embedded control software
 in AAAI Spring Symposium on Embedded Reasoning: Intelligence in Embedded Systems, 2010
"... We propose a methodology for automatic synthesis of embedded control software that accounts for exogenous disturbances. The resulting system is guaranteed, by construction, to satisfy a given specification expressed in linear temporal logic. The embedded control software consists of three component ..."
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Cited by 5 (3 self)
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We propose a methodology for automatic synthesis of embedded control software that accounts for exogenous disturbances. The resulting system is guaranteed, by construction, to satisfy a given specification expressed in linear temporal logic. The embedded control software consists of three components: a goal generator, a trajectory planner, and a continuous controller. We demonstrate the effectiveness of the proposed technique through an example of an autonomous vehicle navigating an urban environment. This example also illustrates that the system is not only robust with respect to exogenous disturbances but also capable of handling violation of the environment assumptions. 1.