Finite Abstractions of Discrete-time Linear Systems and Its Application to Optimal Control

Tazaki, Yuichi; Imura, Jun‐ichi

doi:10.3182/20080706-5-kr-1001.01726

Cited by 22 publications

(28 citation statements)

References 16 publications

(21 reference statements)

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“…Note that in the algorithm, it is not necessary to perform the state quantization physically, since the only purpose of the state quantization is to divide the state space into equivalence classes over which the minimum costs are compared [47]; this will be explained in Subsubsection 4.3.4. For a system with a higher state dimension, more sophisticated quantization methods should be used, see [62].…”

Section: Quantizationmentioning

confidence: 99%

Wave energy converter control by wave prediction and dynamic programming

et al. 2012

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This article appeared in a journal published by Elsevier. The attached copy is furnished to the author for internal non-commercial research and education use, including for instruction at the authors institution and sharing with colleagues.Other uses, including reproduction and distribution, or selling or licensing copies, or posting to personal, institutional or third party websites are prohibited. b s t r a c tWe demonstrate that deterministic sea wave prediction (DSWP) combined with constrained optimal control can dramatically improve the efficiency of sea wave energy converters (WECs), while maintaining their safe operation. We focus on a point absorber WEC employing a hydraulic/electric power take-off system. Maximizing energy take-off while minimizing the risk of damage is formulated as an optimal control problem with a disturbance input (the sea elevation) and with both state and input constraints. This optimal control problem is non-convex, which prevents us from using quadratic programming algorithms for the optimal solution. We demonstrate that the optimum can be achieved by bangebang control. This paves the way to adopt a dynamic programming (DP) algorithm to resolve the on-line optimization problem efficiently. Simulation results show that this approach is very effective, yielding at least a two-fold increase in energy output as compared with control schemes which do not exploit DSWP. This level of improvement is possible even using relatively low precision DSWP over short time horizons. A key finding is that only about 1 second of prediction horizon is required, however, the technical difficulties involved in obtaining good estimates necessitate a DSWP system capable of prediction over tens of seconds.

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Section: Quantizationmentioning

confidence: 99%

Wave energy converter control by wave prediction and dynamic programming

et al. 2012

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“…An approach with similar flavors has been proposed in [8,9] for hierarchical stabilization and tracking control. The hierarchical control methods presented in [45,47], based on the use of discrete abstractions, are also quite similar to the one presented here.…”

Section: Hierarchical Control Design Using Simulation Functionsmentioning

confidence: 82%

Approximate Bisimulation: A Bridge Between Computer Science and Control Theory

Girard¹,

Pappas²

2011

European Journal of Control

117

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“…Approximately bisimilar finite symbolic models have been constructed [15] based on an incremental stability property of the underlying the hybrid system. The other category of approaches to obtaining discrete abstractions is based on a priori partitioning the state space based on properties of each block which may be of interest [16][17][18][19][20][21]. Among this body of work, [18,20] make explicit use of a state quantizer.…”

Section: Introductionmentioning

confidence: 99%

Finite abstractions for hybrid systems with stable continuous dynamics

Tanner

Rawal

et al. 2011

Discrete Event Dyn Syst

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This paper outlines an abstraction process in which a particular class of hybrid automata with continuous dynamics that have parameterized positive limit sets, are being abstracted into finite transition systems. The limit sets with their corresponding attraction regions define pre-and post-conditions for the continuous dynamics, and determine the transitions in the discrete abstraction. An observable (weak) bisimulation equivalence is established between the two models. The abstraction process described can find application in verification, as well as in planning and symbolic control.

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Finite Abstractions of Discrete-time Linear Systems and Its Application to Optimal Control

Cited by 22 publications

References 16 publications

Wave energy converter control by wave prediction and dynamic programming

Wave energy converter control by wave prediction and dynamic programming

Approximate Bisimulation: A Bridge Between Computer Science and Control Theory

Finite abstractions for hybrid systems with stable continuous dynamics

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