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105
Approximately Bisimilar Symbolic Models for Incrementally Stable Switched Systems
"... Switched systems constitute an important modeling paradigm faithfully describing many engineering systems in which software interacts with the physical world. Despite considerable progress on stability and stabilization of switched systems, the constant evolution of technology demands that we make s ..."
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Cited by 53 (12 self)
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Switched systems constitute an important modeling paradigm faithfully describing many engineering systems in which software interacts with the physical world. Despite considerable progress on stability and stabilization of switched systems, the constant evolution of technology demands that we make similar progress with respect to different, and perhaps more complex, objectives. This paper describes one particular approach to address these different objectives based on the construction of approximately equivalent (bisimilar) symbolic models for a switched system. The main contribution of this paper consists in showing that under standard assumptions ensuring incremental stability of a switched system (i.e. existence of common or multiple Lyapunov functions), it is possible to construct a symbolic model that is approximately bisimilar to the original switched system with a precision that can be chosen a priori. To support the computational merits of the proposed approach we present a realistic example of a boost dcdc converter and show how to synthesize a switched controller that regulates the output voltage at a desired level.
Approximately bisimilar symbolic models for nonlinear control systems
 In 46th IEEE Conference on Decision and Control
, 2007
"... 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 ..."
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Cited by 52 (19 self)
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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. For this reason there is a growing interest in describing control systems through symbolic models that are abstract descriptions of the continuous dynamics, where each “symbol ” corresponds to an “aggregate ” of 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 provide a unified language to study problems of control in which software and hardware interact with the physical world. Furthermore the use of symbolic models enables one to leverage techniques from supervisory control and algorithms from game theory for controller synthesis purposes. In this paper we show that every incrementally globally asymptotically stable nonlinear control system is approximately equivalent (bisimilar) to symbolic model. The approximation error is a design parameter in the construction of the symbolic model and can be rendered as small as desired. We also show that for digital control systems, and under the stronger assumption of incremental input–to–state stability, the symbolic models can be constructed through a suitable quantization of the inputs. 1.
Temporal logic motion planning for dynamic robots,”
 Automatica,
, 2009
"... Abstract In this paper, we address the temporal logic motion planning problem for mobile 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 seque ..."
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Cited by 51 (13 self)
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Abstract In this paper, we address the temporal logic motion planning problem for mobile 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. 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.
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 45 (13 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 Test Generation and Coverage for Hybrid Systems
, 2007
"... Testing is an important tool for validation of the system design and its implementation. Modelbased test generation allows to systematically ascertain whether the system meets its design requirements, particularly the safety and correctness requirements of the system. In this paper, we develop a fr ..."
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Cited by 42 (13 self)
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Testing is an important tool for validation of the system design and its implementation. Modelbased test generation allows to systematically ascertain whether the system meets its design requirements, particularly the safety and correctness requirements of the system. In this paper, we develop a framework for generating tests from hybrid systems’ models. The core idea of the framework is to develop a notion of robust test, where one nominal test can be guaranteed to yield the same qualitative behavior with any other test that is close to it. Our approach offers three distinct advantages. 1) It allows for computing and formally quantifying the robustness of some properties, 2) it establishes a method to quantify the test coverage for every test case, and 3) the procedure is parallelizable and therefore, very scalable. We demonstrate our framework by generating tests for a navigation benchmark application.
Robustness of Temporal Logic Specifications for ContinuousTime Signals
, 2009
"... In this paper, we consider the robust interpretation of Metric Temporal Logic (MTL) formulas over signals that take values in metric spaces. For such signals, which are generated by systems whose states are equipped with nontrivial metrics, for example continuous or hybrid, robustness is not only na ..."
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Cited by 42 (18 self)
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In this paper, we consider the robust interpretation of Metric Temporal Logic (MTL) formulas over signals that take values in metric spaces. For such signals, which are generated by systems whose states are equipped with nontrivial metrics, for example continuous or hybrid, robustness is not only natural, but also a critical measure of system performance. Thus, we propose multivalued semantics for MTL formulas, which capture not only the usual Boolean satisfiability of the formula, but also topological information regarding the distance, ε, from unsatisfiability. We prove that any other signal that remains εclose to the initial one also satisfies the same MTL specification under the usual Boolean semantics. Finally, our framework is applied to the problem of testing formulas of two fragments of MTL, namely Metric Interval Temporal Logic (MITL) and closed Metric Temporal Logic (clMTL), over continuoustime signals using only discretetime analysis. The motivating idea behind our approach is that if the continuoustime signal fulfills certain conditions and the discrete time signal robustly satisfies the temporal logic specification, then the corresponding continuoustime signal should also satisfy the same temporal logic specification.
Symbolic analysis for improving simulation coverage of simulink/stateflow models
 in EMSOFT ’08: Proceedings of the 8th ACM international conference on Embedded software, 2008
"... Aimed at verifying safety properties and improving simulation coverage for hybrid systems models of embedded control software, we propose a technique that combines numerical simulation and symbolic methods for computing statesets. We consider systems with linear dynamics described in the commercial ..."
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Cited by 37 (4 self)
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Aimed at verifying safety properties and improving simulation coverage for hybrid systems models of embedded control software, we propose a technique that combines numerical simulation and symbolic methods for computing statesets. We consider systems with linear dynamics described in the commercial modeling tool Simulink/Stateflow. Given an initial state x, and a discretetime simulation trajectory, our method computes a set of initial states that are guaranteed to be equivalent to x, where two initial states are considered to be equivalent if the resulting simulation trajectories contain the same discrete components at each step of the simulation. We illustrate the benefits of our method on two case studies. One case study is a benchmark proposed in the literature for hybrid systems verification and another is a Simulink demo model from Mathworks.
Formal verification of hybrid systems
, 2011
"... In formal verification, a designer first constructs a model, with mathematically precise semantics, of the system under design, and performs extensive analysis with respect to correctness requirements. The appropriate mathematical model for embedded control systems is hybrid systems that combines th ..."
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Cited by 34 (0 self)
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In formal verification, a designer first constructs a model, with mathematically precise semantics, of the system under design, and performs extensive analysis with respect to correctness requirements. The appropriate mathematical model for embedded control systems is hybrid systems that combines the traditional statemachine based models for discrete control with classical differentialequations based models for continuously evolving physical activities. In this article, we briefly review selected existing approaches to formal verification of hybrid systems, along with directions for future research.
Approximately bisimilar finite abstractions of stable linear systems
 in Hybrid Systems: Computation and Control, ser. Lecture
, 2007
"... The use of bisimilar finite abstractions of continuous and hybrid systems, greatly simplifies complex computational tasks such as verification or control synthesis. Unfortunately, because of the strong requirements of bisimulation relations, such abstractions exist only for quite restrictive class ..."
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Cited by 20 (4 self)
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The use of bisimilar finite abstractions of continuous and hybrid systems, greatly simplifies complex computational tasks such as verification or control synthesis. Unfortunately, because of the strong requirements of bisimulation relations, such abstractions exist only for quite restrictive classes of systems. Recently, the notion of approximate bisimulation relations has been introduced, allowing the definition of less rigid relationships between systems. This relaxed notion should certainly allow us to build approximately bisimilar finite abstractions for more general classes of continuous and hybrid systems. In this paper, we show that for the class of stable discretetime linear systems with constrained inputs, there exists an approximately bisimilar finite state system of any desired precision. We describe an effective procedure for the construction of this abstraction, based on compositional reasoning and samples of the set of initial states and inputs. Finally, we briefly show how our finite abstractions can be used for verification or control synthesis.