Dynamic optimization of hybrib systems

García-Galán, S.; Barton, Paul I.

doi:10.1016/s0098-1354(98)00053-2

Cited by 42 publications

(34 citation statements)

References 4 publications

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Section: Introductionmentioning

confidence: 99%

“…Such optimization problems incorporate the system dynamic description into the constraint set [Galán and Barton, 1998;Hiskens, 2004]. As Galán and Barton [1998] and Piccoli [1998] have shown, even though hybrid system dynamics are non-smooth, the cost function is smooth away from grazing points. This statement is expressed using different terminology though, with Piccoli [1998] requiring that all flows have the same history, and Galán and Barton [1998] requiring the existence of trajectory sensitivities (discussed later).…”

Section: Introductionmentioning

confidence: 99%

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Shooting Methods for Locating Grazing Phenomena in Hybrid Systems

Donde

Hiskens

2006

Int. J. Bifurcation Chaos

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Hybrid systems are typified by strong coupling between continuous dynamics and discrete events. For such piecewise smooth systems, event triggering generally has a significant influence over subsequent system behaviour. Therefore it is important to identify situations where a small change in parameter values alters the event triggering pattern. The bounding case, which separates regions of (generally) quite different dynamic behaviour, is referred to as grazing. At a grazing point, the system trajectory makes tangential contact with an event triggering hypersurface. The paper formulates conditions governing grazing points. Both transient and periodic behaviour are considered. The resulting boundary value problems are solved using shooting methods that are applicable for general nonlinear hybrid (piecewise smooth) dynamical systems. The grazing point formulation underlies the development of a continuation process for exploring parametric dependence. It also provides the basis for an optimization technique that finds the smallest parameter change necessary to induce grazing. Examples are drawn from power electronics, power systems and robotics, all of which involve intrinsic interactions between continuous dynamics and discrete events.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Shooting Methods for Locating Grazing Phenomena in Hybrid Systems

Donde

Hiskens

2006

Int. J. Bifurcation Chaos

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“…However those complications largely disappear under the assumption that the order of events does not change as θ and t f vary, i.e., no grazing situations occur. This assumption is common throughout the literature, though it is expressed in various ways: transversal crossings of triggering hypersurfaces are assumed in [18], existence of trajectory sensitivities is assumed in [19], and [20] assumes all flows have the same history. All statements are equivalent.…”

Section: Dynamic Embedded Optimizationmentioning

confidence: 99%

“…Furthermore, [19] shows that if J is a smooth function of its arguments, then it is continuously differentiable with respect to θ and t f . The minimization can therefore be solved using gradient-based methods.…”

Section: Dynamic Embedded Optimizationmentioning

confidence: 99%

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Dynamic Embedded Optimization and Shooting Methods for Power System Performance Assessment

Hiskens

Park

Donde

Power Electronics and Power Systems

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Power system dynamic performance enhancement can often be formulated as a dynamic embedded optimization problem. The associated cost function quantifies performance and involves dynamically evolving state variables. The dynamic model is embedded within the constraints. Power systems form an important example of hybrid systems, with interactions between continuous dynamics and discrete events playing a fundamental role in behavior. However, it is shown that for a large class of problems, the cost function is smooth even though the underlying dynamic response is non-smooth. Complementing this design-oriented optimization framework, techniques for assessing power system performance and vulnerability can often be expressed as boundary value problems, and solved using shooting methods. It is shown that performance limitations are closely related to grazing phenomena. Techniques are presented for determining parameter values that induce limit cycles and grazing.179 I.A. Hiskens, J-W. Park and V. Donde, "Dynamic embedded optimization and shooting methods for power system performance assessment", in Applied Mathematics for Deregulated

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Design of Hybrid Electrochemical Devices

Stamps

Gatzke

2009

Microfabricated Power Generation Devices

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Dynamic optimization of hybrib systems

Cited by 42 publications

References 4 publications

Shooting Methods for Locating Grazing Phenomena in Hybrid Systems

Shooting Methods for Locating Grazing Phenomena in Hybrid Systems

Dynamic Embedded Optimization and Shooting Methods for Power System Performance Assessment

Design of Hybrid Electrochemical Devices

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