Consistent abstractions of affine control systems

Pappas, George J.; Simić, Slobodan N.

doi:10.1109/tac.2002.1000269

Cited by 76 publications

(53 citation statements)

References 31 publications

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“…It is a concept used widely in computer science, formally described in terms of a bisimulation relation [10]. In [13]- [15], (purely) continuous systems are related to each other in terms of their vector fields: the vector field of the quotient system is the image of that of the original system under a surjective (Φ) map. The link between this form of abstraction and the notion of bisimulation is made clearly (for the linear case) in [12] and (for the nonlinear case) in [17], [20].…”

Section: Introductionmentioning

confidence: 99%

Discrete Asymptotic Abstractions of Hybrid Systems

Piovesan

Tanner

Abdallah

2006

Proceedings of the 45th IEEE Conference on Decision and Control

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Abstract-In this paper we introduce the notion of Finite Time Mode Abstraction to relate a hybrid automaton to a timed automaton that preserves the stability and reachability properties of the former. The abstraction procedure discards the continuous dynamics of each mode in the hybrid automaton completely, keeping only the information about the maximum time in which the continuous state makes a discrete jump. This information is used to construct a timed automaton, based on the original hybrid automaton, and to prove that the stability and reachability properties of the original system are retained in the abstract timed automaton. In the process of abstracting a hybrid to a timed automaton we introduce a new notion of hybrid distance metric, which provides information about both the number of discrete transitions that a system would have to make to go from one hybrid state to another, and the distance between the continuous parts of such hybrid states.

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Section: Introductionmentioning

confidence: 99%

Discrete Asymptotic Abstractions of Hybrid Systems

Piovesan

Tanner

Abdallah

2006

Proceedings of the 45th IEEE Conference on Decision and Control

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“…Assumption A.II greatly simplifies the relation between state/inputs of Σ M and state/inputs of Σ N . In particular, it reduces the construction of φ-related control systems given in [PS02] to the sequence of seven steps described in the following construction: Construction 2.7 Input: Affine distribution A M satisfying Assumptions A.I and A.II with respect to surjective submersion φ : M → N .…”

Section: Theorem 24 ([Pls00])mentioning

confidence: 99%

“…problem was addressed in [PS02] by constructing the smallest affine distribution on N containing T φ(A M ). The resulting distribution adds new directions of motion to control system Σ N allowing for trajectories that are not refinable.…”

Section: Theorem 32 (Hierarchical Trajectory Refinement)mentioning

confidence: 99%

“…A construction is provided in [PS02] which given nonlinear model Σ M and map φ, generates the abstracted model Σ N . Furthermore, given control theoretic properties such as controllability and stabilizability, we can obtain natural conditions on the map φ in order for Σ M and Σ N to have equivalent properties.…”

Section: Introductionmentioning

confidence: 99%

“…Furthermore, given control theoretic properties such as controllability and stabilizability, we can obtain natural conditions on the map φ in order for Σ M and Σ N to have equivalent properties. These include controllability for linear [PLS00], nonlinear [PS02], and Hamiltonian systems [TP03] and stabilizability of linear systems [PL01].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Hierarchical trajectory refinement for a class of nonlinear systems

Tabuada

Pappas

2005

Automatica

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Trajectory generation for nonlinear control systems is an important and difficult problem. In this paper, we provide a constructive method for hierarchical trajectory refinement. The approach is based on the recent notion of φ-related control systems. Given a control affine system satisfying certain assumptions, we construct a φ-related control system of smaller dimension. Trajectories designed for the smaller, abstracted system are guaranteed, by construction, to be feasible for the original system. Constructive procedures are provided for refining trajectories from the coarser to the more detailed system. AbstractTrajectory generation for nonlinear control systems is an important and difficult problem. In this paper, we provide a constructive method for hierarchical trajectory refinement. The approach is based on the recent notion of φ-related control systems. Given a control affine system satisfying certain assumptions, we construct a φ-related control system of smaller dimension. Trajectories designed for the smaller, abstracted system are guaranteed, by construction, to be feasible for the original system. Constructive procedures are provided for refining trajectories from the coarser to the more detailed system.

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Hierarchical Control of Linear Systems from the Abstraction Feedback Gain

Yang

2016

Asian Journal of Control

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In this paper, the problem of hierarchical control for a class of linear systems is addressed. Given a large-scale linear system, we obtain a stabilizing feedback gain for it from that of an abstract system. And then, we employ this feedback gain to design a new interface between the original system and the abstraction. Furthermore, the synthesis of the new interface can be allowed by a new simulation function characterized by a low-order matrix associated to the abstraction. Finally, an example is given to illustrate the proposed approach.

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Consistent abstractions of affine control systems

Cited by 76 publications

References 31 publications

Discrete Asymptotic Abstractions of Hybrid Systems

Discrete Asymptotic Abstractions of Hybrid Systems

Hierarchical trajectory refinement for a class of nonlinear systems

Hierarchical Control of Linear Systems from the Abstraction Feedback Gain

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