Explicit state and output feedback boundary controllers for partial differential equations

Smyshlyaev, Andrey; Krstić, Miroslav

doi:10.2298/jac0302001s

Cited by 25 publications

(17 citation statements)

References 15 publications

(17 reference statements)

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“…To find roots of a characteristic transcendent equation, containing only Fourier transform of equation kernel (see (12)), Step 2. Using those roots to separate real and imaginary parts of a system of equalities with respect to unknown function Fourier transform (see (11)) and to obtain the corresponding system of moments problem (see (15)), Step 3. Applying control formulae for corresponding optimality criterion (see (18) and (22) or (25)), to determine desired function of optimal control, Step 4.…”

Section: Discussionmentioning

confidence: 99%

“…Taking into consideration the uncertainty type of those equations, one may easily see, that control algorithm to be developed should be based on some integral transform. Optimal control problems for integro-differential equations are considered also in [8,9,10,11].…”

Section: ·) and Difference Or Convolution Type If K (X S ·) = Kmentioning

confidence: 99%

“…However, here we will proceed in a different way [1,12,13]. Taking into account that function φ 1 (t) is compactly supported, one may separate real and imaginary parts of equalities (11) and as a result get the following countable system of equalities:…”

Section: Remark 1 Separating Real and Imaginary Parts Of Expressionmentioning

confidence: 99%

“…From expressions (A2) extended for all z ∈ C it is easy to see, that they are entire or not simultaneously. Thus, for example, a + = a + (z) is an entire analytical function if and only if conditions (11) and (12) are satisfied.…”

Section: Appendixmentioning

confidence: 99%

See 3 more Smart Citations

On optimal boundary and distributed control of partial integro–differential equations

Khurshudyan¹

2014

Archives of Control Sciences

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To memoriam of my father Zhora M. Khurshudyan is dedicated.A method of optimal control problems investigation for linear partial integro-differential equations of convolution type is proposed, when control process is carried out by boundary functions and right hand side of equation. Using Fourier real generalized integral transform control problem solution is reduced to minimization procedure of chosen optimality criterion under constraints of equality type on desired control function. Optimality of control impacts is obtained for two criteria, evaluating their linear momentum and total energy. Necessary and sufficient conditions of control problem solvability are obtained for both criteria. Numerical calculations are done and control functions are plotted for both cases of control process realization.

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Section: Discussionmentioning

confidence: 99%

Section: ·) and Difference Or Convolution Type If K (X S ·) = Kmentioning

confidence: 99%

Section: Remark 1 Separating Real and Imaginary Parts Of Expressionmentioning

confidence: 99%

Section: Appendixmentioning

confidence: 99%

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On optimal boundary and distributed control of partial integro–differential equations

Khurshudyan¹

2014

Archives of Control Sciences

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“…The key approach is that of transforming the body input problem into a standard boundary control problem for which solutions readily exist ( [2], [11][12]). In our particular transformation, we imbed free parameters in the desired stable target systems that allows us to tune the performance of the resulting compensator.…”

Section: Feedback Compensation Of the In-domain Attenuation Of Inputsmentioning

confidence: 99%

Feedback compensation of the in-domain attenuation of inputs in diffusion processes

Yebi

Ayalew

2013

2013 American Control Conference

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This paper addresses the problem of compensating for the in-domain attenuation of inputs for a class of process control applications. Specific examples include the challenge of maintaining uniform temperatures or through-cure during thickfilm radiative drying and curing processes in the face of the effective input's variation with film depth due to the so-called Beer-Lambert effect. These distributed parameter control problems are modeled with parabolic PDEs for the diffusion processes along with an in-domain input with a spatial attenuation function. The approach presented in this paper involves transforming the original model to an equivalent boundary input problem to which existing output feedback backstepping boundary control design methods can be applied. The resulting compensation scheme includes a mechanism for tuning the closed-loop performance. The performance of this scheme is compared with a controller designed via modal approximation of the PDE.

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Local stabilization of semilinear parabolic system by boundary control

Xie

2019

Asian Journal of Control

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This paper addresses local stabilization of a semilinear parabolic system by boundary control. Under a certain assumption on the nonlinearity of the parabolic equation, a linear boundary feedback control law is applied to control the semilinear system. Based on the operator theories and relations of different norms, locally exponential stabilization of the closed loop system is established. Simulations support the established stability result.

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Explicit state and output feedback boundary controllers for partial differential equations

Cited by 25 publications

References 15 publications

On optimal boundary and distributed control of partial integro–differential equations

On optimal boundary and distributed control of partial integro–differential equations

Feedback compensation of the in-domain attenuation of inputs in diffusion processes

Local stabilization of semilinear parabolic system by boundary control

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