Decidable and semi-decidable controller synthesis for classes of discrete time hybrid systems

Vidal, René; Schaffert, S.; Shakernia, Omid; Lygeros, John; Sastry, S. Shankar

doi:10.1109/cdc.2001.981057

Cited by 28 publications

(13 citation statements)

References 20 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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“…A more elegant approach is to use symbolic algebra software and/or quantifier elimination methods [15], [18]- [20]. The idea here is to encode the predecessor computation in an appropriate system of logic using quantifiers to capture requirements that need to hold for some control actions, all disturbance, at some or for all times, etc.…”

Section: )mentioning

confidence: 99%

“…Next, let be the set of admissible policies of length , i.e., those policies that satisfy, for all , the state and control constraints (8) over the horizon , and the terminal constraint (15) In other words, the set of admissible policies is defined as (16) The set is the set of initial states for which an admissible policy of length exists (often also called the -step controllable set) and is defined as (17)…”

Section: A Definitionsmentioning

confidence: 99%

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Reachability Analysis of Discrete-Time Systems With Disturbances

Raković

Kerrigan

Mayne

et al. 2006

IEEE Trans. Automat. Contr.

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156

108

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Abstract-This paper presents new results that allow one to compute the set of states that can be robustly steered in a finite number of steps, via state feedback control, to a given target set. The assumptions that are made in this paper are that the system is discrete-time, nonlinear and time-invariant and subject to mixed constraints on the state and input. A persistent disturbance, dependent on the current state and input, acts on the system. Existing results are not able to address state-and input-dependent disturbances and the results in this paper are, therefore, a generalization of previously published results. One of the key aims of this paper is to present results such that one can perform the relevant set computations using polyhedral algebra and computational geometry software, provided the system is piecewise affine and the constraints are polygonal. Existing methods are only applicable to piecewise affine systems that either have no control inputs or no disturbances, whereas the results in this paper remove this limitation. Some simple examples are also given that show that, even if all the relevant sets are convex and the system is linear, convexity of the set of controllable states cannot be guaranteed.

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“…The computation involves linear programming and projections (also known as FourierMotzkin eliminations). Related approaches have been used in [5], [10] for predecessor operator computations, in [3], [11] for the computation of the maximal controlled invariant set, and also in other contexts, e.g. [4], [2].…”

Section: Introductionmentioning

confidence: 99%

On a class of controlled invariant sets

Iordache

Antsaklis

2004

Proceedings of the 2004 American Control Conference

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Abstract-In this paper we introduce a new class of controlled invariant sets, called controllable invariant sets. Intuitively, a controllable invariant set has the property that from any "large enough" connected region of the set it is possible to reach any such other region of the set, regardless of disturbances. Disturbances are assumed to be bounded. The range of the control inputs is assumed to be given and is allowed to be bounded. The main result of the paper is a nonrecursive approach for the computation of controllable invariants. The other results of the paper deal with properties of the proposed method and of controllable invariance. The results of the paper assume hybrid system modes with linear discrete-time dynamics.

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Decidable and semi-decidable controller synthesis for classes of discrete time hybrid systems

Cited by 28 publications

References 20 publications

Symbolic Control of Linear Systems Based on Symbolic Subsystems

Symbolic Control of Linear Systems Based on Symbolic Subsystems

Reachability Analysis of Discrete-Time Systems With Disturbances

On a class of controlled invariant sets

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