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52
Temporal-Logic-Based Reactive Mission and Motion Planning
, 2009
"... This paper provides a framework to automatically generate a hybrid controller that guarantees that the robot can achieve its task when a robot model, a class of admissible environments, and a high-level task or behavior for the robot are provided. The desired task specifications, which are expresse ..."
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Cited by 58 (11 self)
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This paper provides a framework to automatically generate a hybrid controller that guarantees that the robot can achieve its task when a robot model, a class of admissible environments, and a high-level task or behavior for the robot are provided. The desired task specifications, which are expressed in a fragment of linear temporal logic (LTL), can capture complex robot behaviors such as search and rescue, coverage, and collision avoidance. In addition, our framework explicitly captures sensor specifications that depend on the environment with which the robot is interacting, which results in a novel paradigm for sensor-based temporal-logic-motion planning. As one robot is part of the environment of another robot, our sensor-based framework very naturally captures multirobot specifications in a decentralized manner. Our computational approach is based on first creating discrete controllers satisfying specific LTL formulas. If feasible, the discrete controller is then used to guide the sensor-based composition of continuous controllers, which results in a hybrid controller satisfying the high-level specification but only if the environment is admissible.
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 dc-dc converter and show how to synthesize a switched controller that regulates the output voltage at a desired level.
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.
Temporal Logic-based Reactive Mission and Motion Planning
"... Given a robot model, a class of admissible environments and a high level task or behavior for the robot, this paper provides a framework for automatically generating a hybrid controller that guarantees the robot can achieve its task. The desired task specifications, expressed in a fragment of linea ..."
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Cited by 19 (0 self)
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Given a robot model, a class of admissible environments and a high level task or behavior for the robot, this paper provides a framework for automatically generating a hybrid controller that guarantees the robot can achieve its task. The desired task specifications, expressed in a fragment of linear temporal logic, can capture complex robot behaviors such as search and rescue, coverage, and collision avoidance. In addition, our framework explicitly captures sensor specifications that depend on the environment with which the robot is interacting, resulting in a novel paradigm for sensor-based temporal logic motion planning. As one robot is part of the environment of another robot, our sensor-based framework very naturally captures multi-robot specifications in a decentralized manner. Our computational approach is based on first creating discrete controllers satisfying specific Linear Temporal Logic formulas. If feasible, the discrete controller is then used to guide the sensor-based composition of continuous controllers, resulting in a hybrid controller satisfying the high-level specification, but only if the environment is admissible.
Synthesis using approximately bisimilar abstractions: state-feedback controllers for safety specifications
- in Proceedings of 13th International Conference on Hybrid Systems: Computation and Control
, 2010
"... Abstract-In this paper, we present a hierarchical approach to time-optimal control using approximately bisimilar abstractions. Given a time-optimal 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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Abstract-In this paper, we present a hierarchical approach to time-optimal control using approximately bisimilar abstractions. Given a time-optimal 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 time-optimal controllers for problems that can be made arbitrarily close by choosing sufficiently precise abstractions. Finally, we show the effectiveness of our approach by solving time-optimal control problems for switched systems.
Approximate Bisimulation: A Bridge Between Computer Science and Control Theory
- EUROPEAN JOURNAL OF CONTROL (2011)5-6:568–578
, 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 re-unite 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 re-unite 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 Lyapunov-type inequalities. In particular, these functions can provide computable upper-bounds 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 simulation-based approaches to verification of continuous and hybrid systems.
P.: Symbolic approximate time-optimal control
- Systems & Control Letters
, 2011
"... Abstract. There is an increasing demand for controller design techniques ca-pable of addressing the complex requirements of todays embedded applications. This demand has sparked the interest in symbolic control where lower complex-ity 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 ca-pable of addressing the complex requirements of todays embedded applications. This demand has sparked the interest in symbolic control where lower complex-ity models of control systems are used to cater for complex specifications given by temporal logics, regular languages, or automata. These specification mech-anisms can be regarded as qualitative since they divide the trajectories of the plant into bad trajectories (those that need to be avoided) and good trajecto-ries. 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 time-optimal controller synthesis. We con-sider systems related by approximate (alternating) simulation relations and show how such relations enable the transfer of time-optimality information between the systems. We then use this insight to synthesize approximately time-optimal controllers for a control system by working with a lower com-plexity symbolic model. The resulting approximately time-optimal 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.
Controller synthesis for safety and reachability via approximate bisimulation
- In: Automatica 48.5 (2012
"... Abstract. In this paper, we consider the problem of controller design using approximately bisimilar abstractions with an emphasis on safety and reachability specifications. We propose abstraction-based approaches to solve both classes of problems. We start by synthesizing a controller for an approxi ..."
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Cited by 8 (0 self)
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Abstract. In this paper, we consider the problem of controller design using approximately bisimilar abstractions with an emphasis on safety and reachability specifications. We propose abstraction-based approaches to solve both classes of problems. We start by synthesizing a controller for an approxi-mately bisimilar abstraction. Then, using a concretization procedure, we obtain a controller for our initial system that is proved “correct by design”. We provide guarantees of performance by giving estimates of the distance of the synthesized controller to the maximal (i.e the most permissive) safety controller or to the time-optimal reachability controller. Finally, we use the presented techniques combined with discrete approximately bisimilar abstractions of switched systems developed recently, for switching controller synthesis. 1.
On model based synthesis of embedded control software
- in EMSOFT 2012
"... Many Embedded Systems are indeed Software Based Control Sys-tems (SBCSs), that is control systems whose controller consists of control software running on a microcontroller device. This moti-vates investigation on Formal Model Based Design approaches for control software. Given the formal model of a ..."
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Cited by 8 (7 self)
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Many Embedded Systems are indeed Software Based Control Sys-tems (SBCSs), that is control systems whose controller consists of control software running on a microcontroller device. This moti-vates investigation on Formal Model Based Design approaches for control software. Given the formal model of a plant as a Discrete Time Linear Hybrid System and the implementation specifications (that is, number of bits in the Analog-to-Digital (AD) conversion) correct-by-construction control software can be automatically gen-erated from System Level Formal Specifications of the closed loop system (that is, safety and liveness requirements), by computing a suitable finite abstraction of the plant. With respect to given implementation specifications, the auto-matically generated code implements a time optimal control strat-egy (in terms of set-up time), has a Worst Case Execution Time lin-
A contractivity approach for probabilistic bisimulations of diffusion processes
- In Proceedings of the 48th IEEE Conference of Decision and Control
, 2009
"... Abstract — This work is concerned with the problem of characterizing and computing probabilistic bisimulations of dif-fusion processes. A probabilistic bisimulation relation between two such processes is defined through a bisimulation function, which induces an approximation metric on the expectatio ..."
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Cited by 8 (3 self)
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Abstract — This work is concerned with the problem of characterizing and computing probabilistic bisimulations of dif-fusion processes. A probabilistic bisimulation relation between two such processes is defined through a bisimulation function, which induces an approximation metric on the expectation of the (squared norm of the) distance between the two processes. We introduce sufficient conditions for the existence of a bisim-ulation function, based on the use of contractivity analysis for probabilistic systems. Furthermore, we show that the notion of stochastic contractivity is related to a probabilistic version of the concept of incremental stability. This relationship leads to a procedure that constructs a discrete approximation of a diffusion process. The procedure is based on the discretization of space and time. Given a diffusion process, we raise sufficient conditions for the existence of such an approximation, and show that it is probabilistically bisimilar to the original process, up to a certain approximation precision. I.
