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Majid Zamani - One of the best experts on this subject based on the ideXlab platform.
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Symbolic Models for a Class of Impulsive Systems
IEEE Control Systems Letters, 2021Co-Authors: Abdalla Swikir, Antoine Girard, Majid ZamaniAbstract:Symbolic models have been used as the basis of a systematic framework to address control design of several classes of hybrid systems with sophisticated control objectives. However, results available in the literature are not concerned with impulsive systems which are an important modeling framework of many applications. In this paper, we provide an approach for constructing symbolic models for a class of impulsive systems possessing some stability properties. We formally relate impulsive systems and their symbolic models using a notion of so-called alternating Simulation Function. We show that behaviors of the constructed symbolic models are approximately equivalent to those of the impulsive systems. Finally, we illustrate the effectiveness of our results through a case study.
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Compositional synthesis of finite abstractions for networks of systems: A small-gain approach
Automatica, 2019Co-Authors: Abdalla Swikir, Majid ZamaniAbstract:Abstract In this paper, we introduce a compositional scheme for the construction of finite abstractions (a.k.a. symbolic models) of interconnected discrete-time control systems. The compositional scheme is based on small-gain type reasoning. In particular, we use a notion of so-called alternating Simulation Functions as a relation between each subsystem and its symbolic model. Assuming some small-gain type conditions, we construct compositionally an overall alternating Simulation Function as a relation between an interconnection of symbolic models and that of original control subsystems. In such compositionality reasoning, the gains associated with the alternating Simulation Functions of the subsystems satisfy a certain “small-gain” condition. In addition, we introduce a technique to construct symbolic models together with their corresponding alternating Simulation Functions for discrete-time control subsystems under some stability property. Finally, we apply our results to the temperature regulation in a circular building by constructing compositionally a finite abstraction of a network containing N rooms for any N ≥ 3 . We use the constructed symbolic models as substitutes to synthesize controllers compositionally maintaining room temperatures in a comfort zone. We choose N = 1000 for the sake of illustrating the results. We also apply our proposed techniques to a nonlinear example of a fully connected network in which the compositionality condition still holds for any number of components. In these case studies, we show the effectiveness of the proposed results in comparison with the existing compositionality technique in the literature using a dissipativity-type reasoning.
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ECC - Compositional Synthesis of not Necessarily Stabilizable Stochastic Systems via Finite Abstractions
2019 18th European Control Conference (ECC), 2019Co-Authors: Abolfazl Lavaei, Sadegh Soudjani, Majid ZamaniAbstract:In this paper, we propose a compositional framework for the construction of finite abstractions (a.k.a. finite Markov decision processes (MDPs)) for networks of not necessarily stabilizable discrete-time stochastic control systems. The proposed scheme is based on a notion of finite-step stochastic Simulation Function, using which one can employ an abstract system as a substitution of the original one in the controller design process with guaranteed error bounds. In comparison with the existing notions of Simulation Functions, a finite-step stochastic Simulation Function needs to decay only after some finite numbers of steps instead of at each time step. In the first part of the paper, we develop a new type of small-gain conditions which are less conservative than the existing ones. The proposed condition compositionally quantifies the distance in probability between the interconnection of stochastic control subsystems and that of their (finite or infinite) abstractions. In particular, using this relaxation via finite-step stochastic Simulation Functions, it is possible to construct finite abstractions such that stabilizability of each subsystem is not necessarily required. In the second part of the paper, for the class of linear stochastic control systems, we construct finite MDPs together with their corresponding finite-step stochastic Simulation Functions. Finally, we demonstrate the effectiveness of the proposed results by compositionally constructing finite MDP of a network of four subsystems such that one of them is not stabilizable.
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ECC - Compositional Abstractions of Interconnected Discrete-Time Switched Systems
2019 18th European Control Conference (ECC), 2019Co-Authors: Abdalla Swikir, Majid ZamaniAbstract:In this paper, we introduce a compositional method for the construction of finite abstractions of interconnected discrete-time switched systems. Particularly, we use a notion of so-called alternating Simulation Function as a relation between each switched subsystem and its finite abstraction. Based on some small-gain type conditions, we use those alternating Simulation Functions to construct compositionally an overall alternating Simulation Function as a relation between an interconnection of finite abstractions and that of switched subsystems. This overall alternating Simulation Function allows one to quantify the mismatch between the output behavior of the interconnection of switched subsystems and that of their finite abstractions. Additionally, we provide an approach to construct finite abstractions together with their corresponding alternating Simulation Functions for discrete-time switched subsystems under standard assumptions ensuring incremental input-to-state stability of a switched subsystem. Finally, we apply our results to a model of road traffic by constructing compositionally a finite abstraction of the network containing 50 cells of 1000 meters each. We use the constructed finite abstractions as substitutes to design controllers compositionally keeping the density of traffic lower than 30 vehicles per cell.
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ECC - Compositional construction of abstractions via relaxed small-gain conditions Part I: continuous case
2018 European Control Conference (ECC), 2018Co-Authors: Navid Noroozi, Fabian Wirth, Majid ZamaniAbstract:In this paper, we introduce a notion of so-called finite-step Simulation Functions for discrete-time control systems. In contrast to the existing notions of Simulation Functions, a finite-step Simulation Function does not need decay at each time step but after some finite numbers of steps. We show that the existence of such a Function guarantees that the mismatch between output trajectories of the concrete and abstract systems lies within an appropriate bound. Using this relaxation, we develop a new type of small-gain conditions which are less conservative than those previously used for compositional construction of approximate abstractions of interconnected control systems. In particular, using finite-step Simulation Functions, it is possible to construct approximate abstractions, where stabilizability of each subsystem is not necessarily required. The effectiveness of our results is verified by an illustrative example.
Antoine Girard - One of the best experts on this subject based on the ideXlab platform.
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Symbolic Models for a Class of Impulsive Systems
IEEE Control Systems Letters, 2021Co-Authors: Abdalla Swikir, Antoine Girard, Majid ZamaniAbstract:Symbolic models have been used as the basis of a systematic framework to address control design of several classes of hybrid systems with sophisticated control objectives. However, results available in the literature are not concerned with impulsive systems which are an important modeling framework of many applications. In this paper, we provide an approach for constructing symbolic models for a class of impulsive systems possessing some stability properties. We formally relate impulsive systems and their symbolic models using a notion of so-called alternating Simulation Function. We show that behaviors of the constructed symbolic models are approximately equivalent to those of the impulsive systems. Finally, we illustrate the effectiveness of our results through a case study.
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From dissipativity theory to compositional synthesis of symbolic models
2018Co-Authors: Abdalla Swikir, Antoine Girard, Majid ZamaniAbstract:In this work, we introduce a compositional framework for the construction of finite abstractions (a.k.a. symbolic models) of interconnected discrete-time control systems. The compositional scheme is based on the joint dissipativity-type properties of discrete-time control subsystems and their finite abstractions. In the first part of the paper, we use a notion of so-called storage Function as a relation between each subsystem and its finite abstraction to construct compositionally a notion of so-called alternating Simulation Function as a relation between interconnected finite abstractions and that of control systems. The derived alternating Simulation Function is used to quantify the error between the output behavior of the overall interconnected concrete system and that of its finite abstraction. In the second part of the paper, we propose a technique to construct finite abstractions together with their corresponding storage Functions for a class of discrete-time control systems under some incremental passivity property. We show that if a discrete-time control system is so-called incrementally passivable, then one can construct its finite abstraction by a suitable quantization of the input and state sets together with the corresponding storage Function. Finally, the proposed results are illustrated by constructing a finite abstraction of a network of linear discrete-time control systems and its corresponding alternating Simulation Function in a compositional way without imposing any restriction on the gains or the number of the subsystems.
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brief paper hierarchical control system design using approximate Simulation
Automatica, 2009Co-Authors: Antoine Girard, George J PappasAbstract:In this paper, we present a new approach for hierarchical control based on the recent notions of approximate Simulation and Simulation Functions, a quantitative version of the Simulation relations. Given a complex system that needs to be controlled and a simpler abstraction, we show how the knowledge of a Simulation Function allows us to synthesize hierarchical control laws by first controlling the abstraction and then lifting the abstract control law to the complex system using an interface. For the class of linear control systems, we give an effective characterization of the Simulation Functions and of the associated interfaces. This characterization allows us to use algorithmic procedures for their computation. We show how to choose an abstraction for a linear control system such that our hierarchical control approach can be used. Finally, we show the effectiveness of our approach on an example.
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Hierarchical control system design using approximate Simulation
Automatica, 2009Co-Authors: Antoine Girard, George J PappasAbstract:In this paper, we present a new approach for hierarchical control based on the recent notions of approximate Simulation and Simulation Functions, a quantitative version of the Simulation relations. Given a complex system that needs to be controlled and a simpler abstraction, we show how the knowledge of a Simulation Function allows us to synthesize hierarchical control laws by first controlling the abstraction and then lifting the abstract control law to the complex system using an interface. For the class of linear control systems, we give an effective characterization of the Simulation Functions and of the associated interfaces. This characterization allows us to use algorithmic procedures for their computation. We show how to choose an abstraction for a linear control system such that our hierarchical control approach can be used. Finally, we show the effectiveness of our approach on an example.
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CDC - Hierarchical Control using Approximate Simulation Relations
Proceedings of the 45th IEEE Conference on Decision and Control, 2006Co-Authors: Antoine Girard, George J PappasAbstract:In this paper we present a new approach for hierarchical control based on the recent notions of approximate Simulation relations and Simulation Functions. Given a complex system that need to be controlled, approximate Simulation relations allow to characterize a simple approximation of the system, that can be used for the control design. The controller of this approximate system can be lifted to the complex system using an interface which is completely characterized by a Simulation Function. Then, the distance between the external trajectories of the complex system and the external trajectories of the approximation is guaranteed to remain bounded by a precision that can be evaluated from the Simulation Function. This makes our approach suitable for safety critical systems. We show an application to robot motion control.
Abdalla Swikir - One of the best experts on this subject based on the ideXlab platform.
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Symbolic Models for a Class of Impulsive Systems
IEEE Control Systems Letters, 2021Co-Authors: Abdalla Swikir, Antoine Girard, Majid ZamaniAbstract:Symbolic models have been used as the basis of a systematic framework to address control design of several classes of hybrid systems with sophisticated control objectives. However, results available in the literature are not concerned with impulsive systems which are an important modeling framework of many applications. In this paper, we provide an approach for constructing symbolic models for a class of impulsive systems possessing some stability properties. We formally relate impulsive systems and their symbolic models using a notion of so-called alternating Simulation Function. We show that behaviors of the constructed symbolic models are approximately equivalent to those of the impulsive systems. Finally, we illustrate the effectiveness of our results through a case study.
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Compositional synthesis of finite abstractions for networks of systems: A small-gain approach
Automatica, 2019Co-Authors: Abdalla Swikir, Majid ZamaniAbstract:Abstract In this paper, we introduce a compositional scheme for the construction of finite abstractions (a.k.a. symbolic models) of interconnected discrete-time control systems. The compositional scheme is based on small-gain type reasoning. In particular, we use a notion of so-called alternating Simulation Functions as a relation between each subsystem and its symbolic model. Assuming some small-gain type conditions, we construct compositionally an overall alternating Simulation Function as a relation between an interconnection of symbolic models and that of original control subsystems. In such compositionality reasoning, the gains associated with the alternating Simulation Functions of the subsystems satisfy a certain “small-gain” condition. In addition, we introduce a technique to construct symbolic models together with their corresponding alternating Simulation Functions for discrete-time control subsystems under some stability property. Finally, we apply our results to the temperature regulation in a circular building by constructing compositionally a finite abstraction of a network containing N rooms for any N ≥ 3 . We use the constructed symbolic models as substitutes to synthesize controllers compositionally maintaining room temperatures in a comfort zone. We choose N = 1000 for the sake of illustrating the results. We also apply our proposed techniques to a nonlinear example of a fully connected network in which the compositionality condition still holds for any number of components. In these case studies, we show the effectiveness of the proposed results in comparison with the existing compositionality technique in the literature using a dissipativity-type reasoning.
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ECC - Compositional Abstractions of Interconnected Discrete-Time Switched Systems
2019 18th European Control Conference (ECC), 2019Co-Authors: Abdalla Swikir, Majid ZamaniAbstract:In this paper, we introduce a compositional method for the construction of finite abstractions of interconnected discrete-time switched systems. Particularly, we use a notion of so-called alternating Simulation Function as a relation between each switched subsystem and its finite abstraction. Based on some small-gain type conditions, we use those alternating Simulation Functions to construct compositionally an overall alternating Simulation Function as a relation between an interconnection of finite abstractions and that of switched subsystems. This overall alternating Simulation Function allows one to quantify the mismatch between the output behavior of the interconnection of switched subsystems and that of their finite abstractions. Additionally, we provide an approach to construct finite abstractions together with their corresponding alternating Simulation Functions for discrete-time switched subsystems under standard assumptions ensuring incremental input-to-state stability of a switched subsystem. Finally, we apply our results to a model of road traffic by constructing compositionally a finite abstraction of the network containing 50 cells of 1000 meters each. We use the constructed finite abstractions as substitutes to design controllers compositionally keeping the density of traffic lower than 30 vehicles per cell.
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Compositional Synthesis of Finite Abstractions for Networks of Systems: A Small-Gain Approach
arXiv: Systems and Control, 2018Co-Authors: Abdalla Swikir, Majid ZamaniAbstract:In this paper, we introduce a compositional scheme for the construction of finite abstractions (a.k.a. symbolic models) of interconnected discrete-time control systems. The compositional scheme is based on small-gain type reasoning. In particular, we use a notion of so-called alternating Simulation Functions as a relation between each subsystem and its symbolic model. Assuming some small-gain type conditions, we construct compositionally an overall alternating Simulation Function as a relation between an interconnection of symbolic models and that of original control subsystems. In such compositionality reasoning, the gains associated with the alternating Simulation Functions of the subsystems satisfy a certain "small-gain" condition. In addition, we introduce a technique to construct symbolic models together with their corresponding alternating Simulation Functions for discrete-time control subsystems under some stability property. Finally, we apply our results to the temperature regulation in a circular building by constructing compositionally a finite abstraction of a network containing $N$ rooms for any $N\geq3$. We use the constructed symbolic models as substitutes to synthesize controllers compositionally maintaining room temperatures in a comfort zone. We choose $N=1000$ for the sake of illustrating the results. We also apply our proposed techniques to a nonlinear example of fully connected network in which the compositionality condition still holds for any number of components. In these case studies, we show the effectiveness of the proposed results in comparison with the existing compositionality technique in the literature using a dissipativity-type reasoning.
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From dissipativity theory to compositional synthesis of symbolic models
2018Co-Authors: Abdalla Swikir, Antoine Girard, Majid ZamaniAbstract:In this work, we introduce a compositional framework for the construction of finite abstractions (a.k.a. symbolic models) of interconnected discrete-time control systems. The compositional scheme is based on the joint dissipativity-type properties of discrete-time control subsystems and their finite abstractions. In the first part of the paper, we use a notion of so-called storage Function as a relation between each subsystem and its finite abstraction to construct compositionally a notion of so-called alternating Simulation Function as a relation between interconnected finite abstractions and that of control systems. The derived alternating Simulation Function is used to quantify the error between the output behavior of the overall interconnected concrete system and that of its finite abstraction. In the second part of the paper, we propose a technique to construct finite abstractions together with their corresponding storage Functions for a class of discrete-time control systems under some incremental passivity property. We show that if a discrete-time control system is so-called incrementally passivable, then one can construct its finite abstraction by a suitable quantization of the input and state sets together with the corresponding storage Function. Finally, the proposed results are illustrated by constructing a finite abstraction of a network of linear discrete-time control systems and its corresponding alternating Simulation Function in a compositional way without imposing any restriction on the gains or the number of the subsystems.
George J Pappas - One of the best experts on this subject based on the ideXlab platform.
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brief paper hierarchical control system design using approximate Simulation
Automatica, 2009Co-Authors: Antoine Girard, George J PappasAbstract:In this paper, we present a new approach for hierarchical control based on the recent notions of approximate Simulation and Simulation Functions, a quantitative version of the Simulation relations. Given a complex system that needs to be controlled and a simpler abstraction, we show how the knowledge of a Simulation Function allows us to synthesize hierarchical control laws by first controlling the abstraction and then lifting the abstract control law to the complex system using an interface. For the class of linear control systems, we give an effective characterization of the Simulation Functions and of the associated interfaces. This characterization allows us to use algorithmic procedures for their computation. We show how to choose an abstraction for a linear control system such that our hierarchical control approach can be used. Finally, we show the effectiveness of our approach on an example.
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Hierarchical control system design using approximate Simulation
Automatica, 2009Co-Authors: Antoine Girard, George J PappasAbstract:In this paper, we present a new approach for hierarchical control based on the recent notions of approximate Simulation and Simulation Functions, a quantitative version of the Simulation relations. Given a complex system that needs to be controlled and a simpler abstraction, we show how the knowledge of a Simulation Function allows us to synthesize hierarchical control laws by first controlling the abstraction and then lifting the abstract control law to the complex system using an interface. For the class of linear control systems, we give an effective characterization of the Simulation Functions and of the associated interfaces. This characterization allows us to use algorithmic procedures for their computation. We show how to choose an abstraction for a linear control system such that our hierarchical control approach can be used. Finally, we show the effectiveness of our approach on an example.
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CDC - Hierarchical Control using Approximate Simulation Relations
Proceedings of the 45th IEEE Conference on Decision and Control, 2006Co-Authors: Antoine Girard, George J PappasAbstract:In this paper we present a new approach for hierarchical control based on the recent notions of approximate Simulation relations and Simulation Functions. Given a complex system that need to be controlled, approximate Simulation relations allow to characterize a simple approximation of the system, that can be used for the control design. The controller of this approximate system can be lifted to the complex system using an interface which is completely characterized by a Simulation Function. Then, the distance between the external trajectories of the complex system and the external trajectories of the approximation is guaranteed to remain bounded by a precision that can be evaluated from the Simulation Function. This makes our approach suitable for safety critical systems. We show an application to robot motion control.
Peyman Mohajerin Esfahani - One of the best experts on this subject based on the ideXlab platform.
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CDC - Construction of approximations of stochastic control systems: A compositional approach
2015 54th IEEE Conference on Decision and Control (CDC), 2015Co-Authors: Majid Zamani, Matthias Rungger, Peyman Mohajerin EsfahaniAbstract:In this paper, we provide a compositional framework for the construction of infinite approximations of interconnected stochastic control systems. Our approach is based on a notion of so-called stochastic Simulation Functions that are associated with interfaces. The stochastic Simulation Functions are used to quantify the approximation error while the interfaces are used to lift the controllers synthesized for the approximation to the controllers for the original stochastic system. In the first part of the paper, we analyze interconnected stochastic control systems which consist of several stochastic control subsystems. We derive sufficient conditions that facilitate the compositional construction of stochastic Simulation Functions together with the associated interfaces. Specifically, we show how to construct a stochastic Simulation Function with the corresponding interface for the interconnected stochastic control system from the Simulation Functions and interfaces of the individual stochastic control subsystems. In the second part of the paper, we focus on linear stochastic control systems. We extend a methodology, which is known for the non-probabilistic case, to construct infinite approximations of linear stochastic control systems together with their stochastic Simulation Functions and the corresponding interfaces. Finally, we illustrate the effectiveness of the proposed results on the interconnection of four linear stochastic control subsystems.
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Approximations of Stochastic Hybrid Systems: A Compositional Approach
arXiv: Optimization and Control, 2015Co-Authors: Majid Zamani, Matthias Rungger, Peyman Mohajerin EsfahaniAbstract:In this paper we propose a compositional framework for the construction of approximations of the interconnection of a class of stochastic hybrid systems. As special cases, this class of systems includes both jump linear stochastic systems and linear stochastic hybrid automata. In the proposed framework, an approximation is itself a stochastic hybrid system, which can be used as a replacement of the original stochastic hybrid system in a controller design process. We employ a notion of so-called stochastic Simulation Function to quantify the error between the approximation and the original system. In the first part of the paper, we derive sufficient conditions which facilitate the compositional quantification of the error between the interconnection of stochastic hybrid subsystems and that of their approximations using the quantified error between the stochastic hybrid subsystems and their corresponding approximations. In particular, we show how to construct stochastic Simulation Functions for approximations of interconnected stochastic hybrid systems using the stochastic Simulation Function for the approximation of each component. In the second part of the paper, we focus on a specific class of stochastic hybrid systems, namely, jump linear stochastic systems, and propose a constructive scheme to determine approximations together with their stochastic Simulation Functions for this class of systems. Finally, we illustrate the effectiveness of the proposed results by constructing an approximation of the interconnection of four jump linear stochastic subsystems in a compositional way.
