Hierarchical hybrid control systems: a lattice theoretic formulation

Caines, Peter E.; Wei, Yanjun

doi:10.1109/9.664153

Cited by 105 publications

(65 citation statements)

References 9 publications

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“…Finally, we would like to emphasize that the idea of using symbolic models for the control of continuous systems is not new and motivated much research in the area of hybrid systems [4], [12], [14], [24], [29], [32], [34], [40], [42], [47], [54]. Even though the use of symbolic models was advocated by these and many other researchers, the applicability of the proposed methods has always remained an open problem due to the lack of results ensuring existence of symbolic models for control systems.…”

Section: Related Workmentioning

confidence: 99%

Symbolic Control of Linear Systems Based on Symbolic Subsystems

Tabuada

2006

IEEE Trans. Automat. Contr.

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Abstract-This paper describes an approach to the control of continuous systems through the use of symbolic models describing the system behavior only at a finite number of points in the state space. These symbolic models can be seen as abstract representations of the continuous dynamics enabling the use of algorithmic controller design methods. We identify a class of linear control systems for which the loss of information incurred by working with symbolic subsystems can be compensated by feedback. We also show how to transform symbolic controllers designed for a symbolic subsystem into controllers for the original system. The resulting controllers combine symbolic controller dynamics with continuous feedback control laws and can thus be seen as hybrid systems. Furthermore, if the symbolic controller already accounts for software/hardware requirements, the hybrid controller is guaranteed to enforce the desired specifications by construction thereby reducing the need for formal verification.

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Section: Related Workmentioning

confidence: 99%

Symbolic Control of Linear Systems Based on Symbolic Subsystems

Tabuada

2006

IEEE Trans. Automat. Contr.

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“…Proof: The result follows by differentiating both sides of (10) with respect to time and noting that . Note that the switching function dynamics characterized by (14) defines a fixed-order dynamic compensator of the form given by (8), (9). Specifically, defining the compensator state as so that , the dynamic compensator structure is given by (15) (16) Now, it follows from Theorems 5.3 and 6.1 that for all the nonlinear feedback controlled dynamical system given by (1), (15), and (16), drives to in a finite time .…”

Section: Extensions To Nonlinear Dynamic Compensationmentioning

confidence: 99%

Nonlinear system stabilization via hierarchical switching control

Leonessa

Haddad

Chellaboina

2001

IEEE Trans. Automat. Contr.

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Abstract-In this paper, a nonlinear control-system design framework predicated on a hierarchical switching controller architecture parameterized over a set of moving system equilibria is developed. Specifically, using equilibria-dependent Lyapunov functions, a hierarchical nonlinear control strategy is developed that stabilizes a given nonlinear system by stabilizing a collection of nonlinear controlled subsystems. The switching nonlinear controller architecture is designed based on a generalized lower semicontinuous Lyapunov function obtained by minimizing a potential function over a given switching set induced by the parameterized system equilibria. The proposed framework provides a rigorous alternative to designing gain-scheduled feedback controllers and guarantees local and global closed-loop system stability for general nonlinear systems.Index Terms-Domains of attraction, dynamic compensation, equilibria-dependent Lyapunov functions, hierarchical switching control, nonlinear connective stabilization, parameterized equilibria.

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“…Abstraction is a key concept for providing ways to connect disjointed worlds together. In [4,5], the notions of abstraction, or aggregation, refer to grouping the system states into equivalence classes. Depending on the cardinality of the resulting quotient space, there may be discrete or continuous abstractions.…”

Section: Hierarchical Architecture For Multi-vehicle Multi-modal Systemsmentioning

confidence: 99%

Hierarchical Approach for Design of Multi-vehicle Multi-modal Embedded Software

Koo

Liebman

et al. 2001

Embedded Software

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Abstract. Embedded systems composed of hardware and software components are designed to interact with a physical environment in real-time in order to fulfill control objectives and system specifications. In this paper, we address the complex design challenges in embedded software by focusing on predictive and systematic hierarchical design methodologies which promote system verification and validation. First, we advocate a mix of top-down, hierarchical design and bottom-up, component-based design for complex control systems. Second, it is our point of view that at the level closest to the environment under control, the embedded software needs to be time-triggered for guaranteed safety; at the higher levels, we advocate an asynchronous hybrid controller design. We briefly illustrate our approach through an embedded software design for the control of a group of autonomous vehicles.

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Hierarchical hybrid control systems: a lattice theoretic formulation

Cited by 105 publications

References 9 publications

Symbolic Control of Linear Systems Based on Symbolic Subsystems

Symbolic Control of Linear Systems Based on Symbolic Subsystems

Nonlinear system stabilization via hierarchical switching control

Hierarchical Approach for Design of Multi-vehicle Multi-modal Embedded Software

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