The Experts below are selected from a list of 360 Experts worldwide ranked by ideXlab platform
Paulo Tabuada - One of the best experts on this subject based on the ideXlab platform.
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symbolic models for Nonlinear Control Systems without stability assumptions
IEEE Transactions on Automatic Control, 2012Co-Authors: Majid Zamani, Giordano Pola, Manuel Mazo, Paulo TabuadaAbstract:Finite-state models of Control Systems were proposed by several researchers as a convenient mechanism to synthesize Controllers enforcing complex specifications. Most techniques for the construction of such symbolic models have two main drawbacks: either they can only be applied to restrictive classes of Systems, or they require the exact computation of reachable sets. In this paper, we propose a new abstraction technique that is applicable to any Nonlinear sampled-data Control system as long as we are only interested in its behavior in a compact set. Moreover, the exact computation of reachable sets is not required. The effectiveness of the proposed results is illustrated by synthesizing a Controller to steer a vehicle.
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symbolic models for Nonlinear Control Systems without stability assumptions
arXiv: Optimization and Control, 2010Co-Authors: Majid Zamani, Giordano Pola, Manuel Mazo, Paulo TabuadaAbstract:Finite-state models of Control Systems were proposed by several researchers as a convenient mechanism to synthesize Controllers enforcing complex specifications. Most techniques for the construction of such symbolic models have two main drawbacks: either they can only be applied to restrictive classes of Systems, or they require the exact computation of reachable sets. In this paper, we propose a new abstraction technique that is applicable to any smooth Control system as long as we are only interested in its behavior in a compact set. Moreover, the exact computation of reachable sets is not required. The effectiveness of the proposed results is illustrated by synthesizing a Controller to steer a vehicle.
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symbolic models for Nonlinear Control Systems alternating approximate bisimulations
Siam Journal on Control and Optimization, 2009Co-Authors: Giordano Pola, Paulo TabuadaAbstract:Symbolic models are abstract descriptions of continuous Systems in which symbols represent aggregates of continuous states. In the last few years there has been a growing interest in the use of symbolic models as a tool for mitigating complexity in Control design. In fact, symbolic models enable the use of well-known algorithms in the context of supervisory Control and algorithmic game theory for Controller synthesis. Since the 1990s many researchers faced the problem of identifying classes of dynamical and Control Systems that admit symbolic models. In this paper we make further progress along this research line by focusing on Control Systems affected by disturbances. Our main contribution is to show that incrementally globally asymptotically stable Nonlinear Control Systems with disturbances admit symbolic models.
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to sample or not to sample self triggered Control for Nonlinear Systems
arXiv: Optimization and Control, 2008Co-Authors: Adolfo Anta, Paulo TabuadaAbstract:Feedback Control laws have been traditionally implemented in a periodic fashion on digital hardware. Although periodicity simplifies the analysis of the mismatch between the Control design and its digital implementation, it also leads to conservative usage of resources such as CPU utilization in the case of embedded Control. We present a novel technique that abandons the periodicity assumption by using the current state of the plant to decide the next time instant in which the state should be measured, the Control law computed, and the actuators updated. This technique, termed self-triggered Control, is developed for two classes of Nonlinear Control Systems, namely, state-dependent homogeneous Systems and polynomial Systems. The wide applicability of the proposed results is illustrated in two well known physical examples: a jet engine compressor and the rigid body.
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Controller synthesis for bisimulation equivalence
Systems & Control Letters, 2008Co-Authors: Paulo TabuadaAbstract:The objective of this paper is to solve the Controller synthesis problem for bisimulation equivalence in a wide variety of scenarios including discrete-event Systems, Nonlinear Control Systems, behavioral Systems, hybrid Systems and many others. This will be accomplished by showing that the arguments underlying proofs of existence and the methods for the construction of Controllers are extraneous to the particular class of Systems being considered and thus can be presented in greater generality.
Nikolaos Kazantzis - One of the best experts on this subject based on the ideXlab platform.
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Control relevant discretization of Nonlinear Systems with time delay using taylor lie series
Journal of Dynamic Systems Measurement and Control-transactions of The Asme, 2005Co-Authors: Nikolaos Kazantzis, Kilto Chong, Junyoung Park, Alexander G ParlosAbstract:A new time-discretization method for the development of a sampled-data representation of a Nonlinear continuous-time input-driven system with time delay is proposed. It is based on the Taylor-Lie series expansion method and zero-order hold assumption. The mathematical structure of the new discretization scheme is explored and characterized as useful for establishing concrete connections between numerical and system-theoretic properties. In particular, the effect of the time-discretization method on key properties of Nonlinear Control Systems, such as equilibrium properties and asymptotic stability, is examined. The resulting time-discretization provides a finite-dimensional representation for Nonlinear Control Systems with time-delay enabling the application of existing Controller design techniques. The performance of the proposed discretization procedure is evaluated using the case study of a two-degree-of-freedom mechanical system that exhibits Nonlinear behavior. Various sampling rates and time-delay values are considered.
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Control relevant discretization of Nonlinear Systems with time delay using taylor lie series
American Control Conference, 2003Co-Authors: Nikolaos Kazantzis, Kilto Chong, Junyoung Park, Alexander G ParlosAbstract:A new time-discretization method for the development of a discrete-time (sampled-data) representation of a Nonlinear continuous-time Control system with time-delay is proposed. It is based on the Taylor-Lie series expansion method and zero-order hold (ZOH) assumption. The mathematical structure of the new discretization scheme is explored and characterized as useful for establishing concrete connections between numerical and system-theoretic properties. The effect of the time-discretization method on key properties of Nonlinear Control Systems, such as equilibrium properties and asymptotic stability, is examined. The resulting time-discretization provides a finite-dimensional representation for Nonlinear Control Systems with time-delay enabling the application of existing Controller design techniques. The performance of the proposed discretization procedure is evaluated using a case study.
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time discretization of Nonlinear Control Systems via taylor methods
Computers & Chemical Engineering, 1999Co-Authors: Nikolaos Kazantzis, Costas KravarisAbstract:Abstract A new discretization method for the calculation of a sampled-data representation of a Nonlinear continuous-time system is proposed. It is based upon the well-known Taylor method and the zero-order hold (ZOH) assumption. The mathematical structure of the new discretization scheme is analyzed and characterized as being particularly useful in establishing concrete connections between numerical properties and system-theoretic properties. In particular, the effect of the Taylor discretization procedure on key properties of Nonlinear Systems, such as equilibrium properties and asymptotic stability, is examined. Within a Control context, numerical aspects of Taylor discretization are also discussed, and ‘hybrid’ discretization schemes, that result from a combination of the ‘scaling and squaring’ technique with the Taylor method, are also proposed, especially under conditions of very low sampling rates. Practical issues associated with the selection of the method’s parameters to meet CPU time and accuracy requirements, are examined as well. Finally, the performance of the proposed discretization procedure is evaluated in a chemical reactor example, that exhibits Nonlinear behavior and is subject to various sampling rates.
Giordano Pola - One of the best experts on this subject based on the ideXlab platform.
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symbolic models for Nonlinear Control Systems without stability assumptions
IEEE Transactions on Automatic Control, 2012Co-Authors: Majid Zamani, Giordano Pola, Manuel Mazo, Paulo TabuadaAbstract:Finite-state models of Control Systems were proposed by several researchers as a convenient mechanism to synthesize Controllers enforcing complex specifications. Most techniques for the construction of such symbolic models have two main drawbacks: either they can only be applied to restrictive classes of Systems, or they require the exact computation of reachable sets. In this paper, we propose a new abstraction technique that is applicable to any Nonlinear sampled-data Control system as long as we are only interested in its behavior in a compact set. Moreover, the exact computation of reachable sets is not required. The effectiveness of the proposed results is illustrated by synthesizing a Controller to steer a vehicle.
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symbolic models for Nonlinear Control Systems without stability assumptions
arXiv: Optimization and Control, 2010Co-Authors: Majid Zamani, Giordano Pola, Manuel Mazo, Paulo TabuadaAbstract:Finite-state models of Control Systems were proposed by several researchers as a convenient mechanism to synthesize Controllers enforcing complex specifications. Most techniques for the construction of such symbolic models have two main drawbacks: either they can only be applied to restrictive classes of Systems, or they require the exact computation of reachable sets. In this paper, we propose a new abstraction technique that is applicable to any smooth Control system as long as we are only interested in its behavior in a compact set. Moreover, the exact computation of reachable sets is not required. The effectiveness of the proposed results is illustrated by synthesizing a Controller to steer a vehicle.
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symbolic models for Nonlinear Control Systems alternating approximate bisimulations
Siam Journal on Control and Optimization, 2009Co-Authors: Giordano Pola, Paulo TabuadaAbstract:Symbolic models are abstract descriptions of continuous Systems in which symbols represent aggregates of continuous states. In the last few years there has been a growing interest in the use of symbolic models as a tool for mitigating complexity in Control design. In fact, symbolic models enable the use of well-known algorithms in the context of supervisory Control and algorithmic game theory for Controller synthesis. Since the 1990s many researchers faced the problem of identifying classes of dynamical and Control Systems that admit symbolic models. In this paper we make further progress along this research line by focusing on Control Systems affected by disturbances. Our main contribution is to show that incrementally globally asymptotically stable Nonlinear Control Systems with disturbances admit symbolic models.
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symbolic models for Nonlinear Control Systems using approximate bisimulation
Conference on Decision and Control, 2007Co-Authors: Giordano Pola, Antoine Girard, Paulo TabuadaAbstract: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.
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symbolic models for Nonlinear Control Systems alternating approximate bisimulations
arXiv: Optimization and Control, 2007Co-Authors: Giordano Pola, Paulo TabuadaAbstract:Symbolic models are abstract descriptions of continuous Systems in which symbols represent aggregates of continuous states. In the last few years there has been a growing interest in the use of symbolic models as a tool for mitigating complexity in Control design. In fact, symbolic models enable the use of well known algorithms in the context of supervisory Control and algorithmic game theory, for Controller synthesis. Since the 1990's many researchers faced the problem of identifying classes of dynamical and Control Systems that admit symbolic models. In this paper we make a further progress along this research line by focusing on Control Systems affected by disturbances. Our main contribution is to show that incrementally globally asymptotically stable Nonlinear Control Systems with disturbances admit symbolic models. When specializing these results to linear Systems, we show that these symbolic models can be easily constructed.
S Glavaski - One of the best experts on this subject based on the ideXlab platform.
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A subspace approach to balanced truncation for model reduction of Nonlinear Control Systems
International Journal of Robust and Nonlinear Control, 2002Co-Authors: Sanjay Lall, Jerold E. Marsden, S GlavaskiAbstract:In this paper, we introduce a new method of model reduction for Nonlinear Control Systems. Our approach is to construct an approximately balanced realization. The method requires only standard matrix computa- tions, and we show that when it is applied to linear Systems it results in the usual balanced truncation. For Nonlinear Systems, the method makes use of data from either simulation or experiment to identify the dynamics relevant to the input}output map of the system. An important feature of this approach is that the resulting reduced-order model is Nonlinear, and has inputs and outputs suitable for Control. We perform an example reduction for a Nonlinear mechanical system.
Dimos V Dimarogonas - One of the best experts on this subject based on the ideXlab platform.
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symbolic abstractions for Nonlinear Control Systems via feedback refinement relation
Automatica, 2020Co-Authors: Dimos V DimarogonasAbstract:This paper studies the construction of symbolic abstractions for Nonlinear Control Systems via feedback refinement relation. Both the delay-free and time-delay cases are addressed. For the delay-free case, to reduce the computational complexity, we propose a new approximation approach for the state and input sets based on a static quantizer, and then a novel symbolic model is constructed such that the original system and the symbolic model satisfy the feedback refinement relation. For the time-delay case, both static and dynamic quantizers are combined to approximate the state and input sets. This leads to a novel dynamic symbolic model for time-delay Control Systems, and a feedback refinement relation is established between the original system and the symbolic model. Finally, a numerical example is presented to illustrate the obtained results.
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Hierarchical Decomposition of LTL Synthesis Problem for Nonlinear Control Systems
IEEE Transactions on Automatic Control, 2019Co-Authors: Pierre-jean Meyer, Dimos V DimarogonasAbstract:This paper deals with the Control synthesis problem for a continuous Nonlinear dynamical system under a linear temporal logic (LTL) formula. The proposed solution is a top-down hierarchical decomposition of the Control problem involving three abstraction layers of the problem, iteratively solved from the coarsest to the finest. The LTL planning is first solved on a small transition system only describing the regions of interest involved in the LTL formula. For each pair of consecutive regions of interest in the resulting accepting path satisfying the LTL formula, a discrete plan is then constructed in the partitioned workspace to connect these two regions while avoiding unsafe regions. Finally, an abstraction refinement approach is applied to synthesize a Controller for the dynamical system to follow each discrete plan. The second main contribution, used in the third abstraction layer, is a new monotonicity-based method to overapproximate the finite-time reachable set of any continuously differentiable system. The proposed framework is demonstrated in simulation for a motion planning problem of a mobile robot modeled as a disturbed unicycle.
