Control and optimal control theories with applications

Burghes, David; Graham, Alexander

doi:10.1533/9780857099495

Cited by 8 publications

(8 citation statements)

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“…In the ACP method, there is no need to specify the exact number of switching points by the initial guess, and we can obtain the solution with an initial guess which contains more switching points. For example, we apply the ACP method on problem (4.1), with switching points s = [2,4,6,8]. With this initial guess, we consider three switching points, but we know that the optimal control has only one switching point.…”

Section: Illustration Of the Acp Methods On A Test Examplementioning

confidence: 99%

A Combined Adaptive Control Parametrization and Homotopy Continuation Technique for the Numerical Solution of Bang–bang Optimal Control Problems

2014

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We present an efficient computational procedure for the solution of bang-bang optimal control problems. The method is based on a well-known adaptive control parametrization method, which is one of the direct methods for numerical solution of optimal control problems. First, the adaptive control parametrization method is reviewed and then its advantages and disadvantages are illustrated. In order to resolve the need for a priori knowledge about the structure of optimal control and for resolving the sensitivity to an initial guess, a homotopy continuation technique is combined with the adaptive control parametrization method. The present combined method does not require any assumptions on the control structure and the number of switching points. In addition, the switching points are captured accurately; also, efficiency of the method is reported through illustrative examples.2010 Mathematics subject classification: primary 49J30; secondary 65H20, 49M37.

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Section: Illustration Of the Acp Methods On A Test Examplementioning

confidence: 99%

A Combined Adaptive Control Parametrization and Homotopy Continuation Technique for the Numerical Solution of Bang–bang Optimal Control Problems

2014

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“…The so-called Bang-Bang model originates from control literature theory with an introduction of its basics concepts in [19,Chapter 11]. The original version of the model enables to switch between two states and as far as we are concerned between the main adsorption Ω a and desorption Ω d curves.…”

Section: Hysteresis Effects On Water Content and Sorption Capacity: Tmentioning

confidence: 99%

“…Recently, the so-called Bang-Bang model, inspired by the control literature [17][18][19], has been introduced to take into account the hysteresis effects on moisture sorption capacity in a model of heat and mass transfer [5]. In [20], the model is coupled with a moisture transport equation to determine the optimal experiment design to estimate the coefficients of the moisture sorption curves.…”

Section: Introductionmentioning

confidence: 99%

Critical assessment of a new mathematical model for hysteresis effects on heat and mass transfer in porous building material

Berger

Busser

Colinart

et al. 2020

International Journal of Thermal Sciences

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The reliability of mathematical models for heat and mass transfer in building porous material is of capital importance. A reliable model permits to carry predictions of the physical phenomenon with sufficient confidence in the results. Among the physical phenomena, the hysteresis effects on moisture sorption and moisture capacity need to be integrated in the mathematical model of transfer. This article proposes to explore the use of an smooth Bang-Bang model to simulate the hysteresis effects coupled with heat and mass transfer in porous material. This model adds two supplementary differential equations to the two classical ones for heat and mass transfer. The solution of these equations ensures smooth transitions between the main sorption and desorption curves. Two parameters are required to control the speed of transition through the intermediary curves. After the mathematical description of the model, an efficient numerical model is proposed to compute the fields with accuracy and reduced computational efforts. It is based on the Du Fort-Frankel scheme for the heat and mass balance equations. For the hysteresis numerical model, an innovative implicit-explicit approach is proposed. Then, the predictions of the numerical model are compared with experimental observations from literature for two case studies. The first one corresponds to a slow cycle of adsorption and desorption while the second is based on a fast cycling case with alternative increase and decrease of moisture content. The comparisons highlight a very satisfactory agreement between the numerical predictions and the observations. In the last Section, the reliability and efficiency of the proposed model is investigated for long term simulation cases. The importance of considering hysteresis effects in the reliability of the predictions are enhanced by comparison with classical approaches from literature.

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“…The well-known Chebyshev polynomials are defined on the interval −1,1 and can be determined by the followingrecurrence formula [11]:…”

Section: The Definition and Properties Of The Shifted Chebyshev Polmentioning

confidence: 99%

Solution a Class of Riemann-Liouville Derivative-Composition Fractional Order Optimal Control Problems

Holel¹

2018

IJAST

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This paper introduces a new direction to approximately solving a class of multi between Riemann-Liouville fractional derivative of ∈ (0,1), and the composition of the Caputo fractional derivative of , ∈ (0,1) with the control variable ().In this technique; we approximate FOCPs with boundary conditions. The method is based on a spectral method using Chebyshev polynomials approximation and Clenshaw and Curtis scheme for the numerical integration of non-singular functions to evaluate both the state and control variables. Illustrative examples are included to demonstrate the validity and applicability of the suggested approaches.

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Control and optimal control theories with applications

Cited by 8 publications

References 0 publications

A Combined Adaptive Control Parametrization and Homotopy Continuation Technique for the Numerical Solution of Bang–bang Optimal Control Problems

A Combined Adaptive Control Parametrization and Homotopy Continuation Technique for the Numerical Solution of Bang–bang Optimal Control Problems

Critical assessment of a new mathematical model for hysteresis effects on heat and mass transfer in porous building material

Solution a Class of Riemann-Liouville Derivative-Composition Fractional Order Optimal Control Problems

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