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45
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.
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 .
Synthesis using approximately bisimilar abstractions: statefeedback controllers for safety specifications
 in Proceedings of 13th International Conference on Hybrid Systems: Computation and Control
, 2010
"... AbstractIn this paper, we present a hierarchical approach to timeoptimal control using approximately bisimilar abstractions. Given a timeoptimal controller for an abstraction, we present a specific procedure that allows us to compute a suboptimal controller for the original system. While the usu ..."
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Cited by 12 (2 self)
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AbstractIn this paper, we present a hierarchical approach to timeoptimal control using approximately bisimilar abstractions. Given a timeoptimal controller for an abstraction, we present a specific procedure that allows us to compute a suboptimal controller for the original system. While the usual controller refinement procedure produces dynamic controllers that may have limitations in terms of implementation cost and robustness, the static controllers we synthesize do not suffer from these issues. Moreover, we provide guarantees by bounding below and above the performances of the synthesized controller between performances of two timeoptimal controllers for problems that can be made arbitrarily close by choosing sufficiently precise abstractions. Finally, we show the effectiveness of our approach by solving timeoptimal control problems for switched systems.
Approximate Bisimulation: A Bridge Between Computer Science and Control Theory
 EUROPEAN JOURNAL OF CONTROL (2011)56:568–578
, 2011
"... Fifty years ago, control and computing were part of a broader system science. After a long period of separate development within each discipline, embedded and hybrid systems have challenged us to reunite the, now sophisticated theories of continuous control and discrete computing on a broader syste ..."
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Cited by 12 (0 self)
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Fifty years ago, control and computing were part of a broader system science. After a long period of separate development within each discipline, embedded and hybrid systems have challenged us to reunite the, now sophisticated theories of continuous control and discrete computing on a broader system theoretic basis. In this paper, we present a framework of system approximation that applies to both discrete and continuous systems. We define a hierarchy of approximation metrics between two systems that quantify the quality of the approximation, and capture the established notions in computer science as zero sections. The central notions in this framework are that of approximate simulation and bisimulation relations and their functional characterizations called simulation and bisimulation functions and defined by Lyapunovtype inequalities. In particular, these functions can provide computable upperbounds on the approximation metrics by solving a static game. Our approximation framework will be illustrated by showing some of its applications in various problems such as reachability analysis of continuous systems and hybrid systems, approximation of continuous and hybrid systems by discrete systems, hierarchical control design, and simulationbased approaches to verification of continuous and hybrid systems.
P.: Symbolic approximate timeoptimal control
 Systems & Control Letters
, 2011
"... Abstract. There is an increasing demand for controller design techniques capable of addressing the complex requirements of todays embedded applications. This demand has sparked the interest in symbolic control where lower complexity models of control systems are used to cater for complex specifica ..."
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Cited by 10 (0 self)
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Abstract. There is an increasing demand for controller design techniques capable of addressing the complex requirements of todays embedded applications. This demand has sparked the interest in symbolic control where lower complexity models of control systems are used to cater for complex specifications given by temporal logics, regular languages, or automata. These specification mechanisms can be regarded as qualitative since they divide the trajectories of the plant into bad trajectories (those that need to be avoided) and good trajectories. However, many applications require also the optimization of quantitative measures of the trajectories retained by the controller, as specified by a cost or utility function. As a first step towards the synthesis of controllers reconciling both qualitative and quantitative specifications, we investigate in this paper the use of symbolic models for timeoptimal controller synthesis. We consider systems related by approximate (alternating) simulation relations and show how such relations enable the transfer of timeoptimality information between the systems. We then use this insight to synthesize approximately timeoptimal controllers for a control system by working with a lower complexity symbolic model. The resulting approximately timeoptimal controllers are equipped with upper and lower bounds for the time to reach a target, describing the quality of the controller. The results described in this paper were implemented in the Matlab Toolbox Pessoa [1] which we used to workout several illustrative examples reported in this paper. 1.
Imura; Finite Abstractions of Discretetime Linear Systems and Its Application to
 Optimal Control, 17th IFAC World Congress
, 2008
"... Abstract: Optimal control and reachability analysis of continuousstate systems often require computational algorithms with high complexity. The use of finite abstractions of continuousstate systems reduces such problems to pathplanning problems on directed graphs with a finite number of nodes, w ..."
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Cited by 9 (1 self)
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Abstract: Optimal control and reachability analysis of continuousstate systems often require computational algorithms with high complexity. The use of finite abstractions of continuousstate systems reduces such problems to pathplanning problems on directed graphs with a finite number of nodes, which can be computed efficiently. In this research, we discuss the design of finite abstractions of stabilizable discretetime linear systems based on approximately bisimulation. First, we focus our attention to a class of finitestate system that are expressed by the statequantization of the original system. Then, the original problem reduces to the design of a quantization function, which is formulated as a kind of semidefinite programming problem. Moreover, we show that a suboptimal solution to optimal control problems with a known error bound is obtained by simulating the optimal path of an approximately bisimilar finite abstraction. 1.
Discretestate abstractions of nonlinear systems using multiresolution quantizer
 Hybrid Systems: Computation and Control
, 2009
"... Abstract. This paper proposes a design method for discrete abstractions of nonlinear systems using multiresolution quantizer, which is capable of handling state dependent approximation precision requirements. To this aim, we extend the notion of quantizer embedding, which has been proposed by the ..."
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Cited by 6 (1 self)
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Abstract. This paper proposes a design method for discrete abstractions of nonlinear systems using multiresolution quantizer, which is capable of handling state dependent approximation precision requirements. To this aim, we extend the notion of quantizer embedding, which has been proposed by the authors ’ previous works as a transformation from continuousstate systems to discretestate systems, to a multiresolution setting. Then, we propose a computational method that analyzes how a locally generated quantization error is propagated through the state space. Based on this method, we present an algorithm that generates a multiresolution quantizer with a specified error precision by finite refinements. Discrete abstractions produced by the proposed method exhibit nonuniform distribution of discrete states and inputs. 1
PESSOA: A tool for embedded control software synthesis ∗
"... In the past years several different abstraction techniques were developed to facilitate the analysis and design of hybrid systems. In this paper we complement the theoretical work underlying abstractions based on approximate simulations and bisimulations by moving from theory to practice. We introdu ..."
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Cited by 3 (0 self)
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In the past years several different abstraction techniques were developed to facilitate the analysis and design of hybrid systems. In this paper we complement the theoretical work underlying abstractions based on approximate simulations and bisimulations by moving from theory to practice. We introduce a tool, named Pessoa, for the synthesis of correctbydesign embedded control software. We describe the theoretical underpinnings of Pessoa, its algorithmic implementation, and illustrate its use on the synthesis of control software for several examples. 1.
Abstraction, Discretization, and Robustness in Temporal Logic Control of Dynamical Systems∗
"... Abstractionbased, hierarchical approaches to control synthesis from temporal logic specifications for dynamical systems have gained increased popularity over the last decade. Yet various issues commonly encountered and extensively dealt with in control systems have not been adequately discussed ..."
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Abstractionbased, hierarchical approaches to control synthesis from temporal logic specifications for dynamical systems have gained increased popularity over the last decade. Yet various issues commonly encountered and extensively dealt with in control systems have not been adequately discussed in the context of temporal logic control of dynamical systems, such as intersample behaviors of a sampleddata system, effects of imperfect state measurements and unmodeled dynamics, and the use of timediscretized models to design controllers for continuoustime dynamical systems. We discuss these issues in this paper. The main motivation is to demonstrate the possibility of accounting for the mismatches between a continuoustime control system and its various types of abstract models used for control synthesis. We do this by incorporating additional robustness measures in the abstract models. Such robustness measures are gained at the price of either increased nondeterminism in the abstracted models or relaxed versions of the specification being realized. Under a unified notion of abstraction, we provide concrete means of incorporating these robustness measures and establish results that demonstrate their effectiveness in dealing with the above mentioned issues.