Viscosity solutions for an optimal control problem with Preisach hysteresis nonlinearities

Bagagiolo, Fabio

doi:10.1051/cocv:2004007

Cited by 14 publications

(12 citation statements)

References 18 publications

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“…is the input to the Duhem hysteresis model in (10). Hence, we see the shaft torsion θ as the stress input σ to (4).…”

Section: B Linearized and Discretized Plant Dynamicsmentioning

confidence: 99%

“…In [7], the notion of dissipated energy as lifetime parameter was suggested, and in [5], [6] both the total dissipated energy and the accumulated damage in the rainflow counting sense are equated to the total variations of certain hysteresis operator. Optimal control problems with Preisach hysteresis have been investigated in works such as [8]- [10]. However, it is not straightforward to include the Preisach hysteresis into the optimal control problem, due to the lack of computational tractability of this infinite-dimensional operator.…”

Section: Introductionmentioning

confidence: 99%

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Wind turbine control with active damage reduction through energy dissipation

Barradas-Berglind

Jayawardhana

Wisniewski

2016

2016 American Control Conference (ACC)

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Abstract-In this paper we propose an active damage reduction control strategy for wind turbines based on dissipated energy. To this end we rely on the equivalences relating both damage in the rainflow counting sense and dissipated energy to the variations of Preisach hysteresis operators. Since dissipation theory is well suited for control systems, we adopt the dissipated energy of a Duhem hysteresis model that is described by a differential equation. Accordingly, we incorporate the dissipated energy into the optimal control problem formulation as a proxy to the damage. Lastly, the proposed strategy is evaluated with NREL's FAST high-fidelity non-linear wind turbine.

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“…is the input to the Duhem hysteresis model in (10). Hence, we see the shaft torsion θ as the stress input σ to (4).…”

Section: B Linearized and Discretized Plant Dynamicsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Wind turbine control with active damage reduction through energy dissipation

Barradas-Berglind

Jayawardhana

Wisniewski

2016

2016 American Control Conference (ACC)

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“…Yanhua Ma * and Jianqin Mao S [9]. But little work has considered the stress-dependent hysteresis and its application.…”

Section: Modeling and Optimal Control For A Smart Structure With Strementioning

confidence: 99%

Modeling and optimal control for a smart structure with stress-dependent hysteresis

Mao

2009

2009 IEEE International Conference on Control and Automation

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The stress-dependent hysteresis existing in giant magnetostrictive materials impeded applications of magnetostrictive smart structures (MSS) under different mechanical loads. In this paper we propose a stress-dependent model for the hysteresis in a giant magnetostrictive actuator (GMA). Based on the proposed model, a finite horizon optimal control problem is studied for the system taking account of stress-dependent hysteresis without constructing the inverse operator extensively used. By dynamic programming method and the viscosity solutions theory, we derive the first order discontinuous Hamilton-Jacobi-Bellman (HJB) equation, and further prove that the value function is the unique viscosity solution of the HJB equation. Moreover, a discrete approximation scheme is adopted for the application of the control method. Simulation results verify the effectiveness of both the modeling and the control method.

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“…without explicit dependence on time, as instead the Mayer problem is. In the last decade, control and optimal control problems for ODEs with hysteresis have been the subject of an increasing number of articles, see for instance Gudovich-Quincampoix [9], Ilchmann-Logemann-Ryan [10], Bagagiolo [2] and the references therein. Finally, the literature concerning the Traveling Salesman Problem is of course very huge, and also several versions of suitable dynamic programming algorithms are intensively studied via optimization techniques.…”

Section: Introductionmentioning

confidence: 99%

About an Optimal Visiting Problem

Bagagiolo

Benetton

2011

Appl Math Optim

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In this paper we are concerned with the optimal control problem consisting in minimizing the time for reaching (visiting) a xed number of target sets, in particular more than one target. Such a problem is of course reminiscent of the famous Traveling Salesman Problem and brings all its computational di culties. Our aim is to apply the dynamic programming technique in order to characterize the value function of the problem as the unique viscosity solution of a suitable Hamilton-Jacobi equation. We introduce some external variables, one per target, which keep in memory whether the corresponding target is already visited or not, and we transform the visiting problem in a suitable Mayer problem. This fact allows us to overcome the lacking of the Dynamic Programming Principle for the originary problem. The external variables evolve with a hysteresis law and the Hamilton-Jacobi equation turns out to be discontinuous.

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Viscosity solutions for an optimal control problem with Preisach hysteresis nonlinearities

Cited by 14 publications

References 18 publications

Wind turbine control with active damage reduction through energy dissipation

Wind turbine control with active damage reduction through energy dissipation

Modeling and optimal control for a smart structure with stress-dependent hysteresis

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