Optimal Control of a Bilinear System with a Quadratic Cost Functional

Körpeoğlu, Seda Göktepe; Küçük, İsmail

doi:10.1109/iccubea.2018.8697554

Cited by 3 publications

(6 citation statements)

References 11 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Now assume that we construct model reduction bases W and V , and compute the reduced-order model by projection as in (10). This leads to the reduced-order bilinear system…”

Section: Bilinear Second-order Systemsmentioning

confidence: 99%

“…We want to construct the model reduction bases W and V , and the corresponding reduced structured-bilinear system via projection as in (10) such that its leading regular subsystem transfer functions interpolate those of the original one; i.e., G k (σ 1 , . .…”

Section: Structured Transfer Function Interpolationmentioning

confidence: 99%

“…Let G be a bilinear system, as described by (9), and G the reduced-order bilinear system, constructed by (10). Given sets of (a) If V is constructed as…”

Section: Theorem 8 (Matrix Interpolation)mentioning

confidence: 99%

“…Corollary 2 (Two-sided matrix interpolation with identical point sets) Let G be a bilinear system, described by (9), and G the reduced-order bilinear system, constructed by (10). Given a set of interpolation points σ 1 , .…”

Section: Theorem 8 (Matrix Interpolation)mentioning

confidence: 99%

“…Bilinear systems can also result from approximation of general nonlinear systems employing the Carleman linearization process [7,8]. Moreover, bilinear systems are nowadays often used in the parameter control of partial differential equations (PDEs) [9,10]. Looking back to the linear case, bilinear systems can be used as a generalizing framework in the modeling of linear stochastic [11] and parametervarying systems [12][13][14], allowing the application of established system-theoretic tools such as model order reduction for those system classes.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Structure-preserving interpolation of bilinear control systems

2021

View full text Add to dashboard Cite

In this paper, we extendthe structure-preserving interpolatory model reduction framework, originally developed for linear systems, to structured bilinear control systems. Specifically, we give explicit construction formulae for the model reduction bases to satisfy different types of interpolation conditions. First, we establish the analysis for transfer function interpolation for single-input single-output structured bilinear systems. Then, we extend these results to the case of multi-input multi-output structured bilinear systems by matrix interpolation. The effectiveness of our structure-preserving approach is illustrated by means of various numerical examples.

show abstract

“…Now assume that we construct model reduction bases W and V , and compute the reduced-order model by projection as in (10). This leads to the reduced-order bilinear system…”

Section: Bilinear Second-order Systemsmentioning

confidence: 99%

Section: Structured Transfer Function Interpolationmentioning

confidence: 99%

“…Let G be a bilinear system, as described by (9), and G the reduced-order bilinear system, constructed by (10). Given sets of (a) If V is constructed as…”

Section: Theorem 8 (Matrix Interpolation)mentioning

confidence: 99%

Section: Theorem 8 (Matrix Interpolation)mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Structure-preserving interpolation of bilinear control systems

2021

View full text Add to dashboard Cite

show abstract

Diffusivity Control of Heat Transfer Process Using Optimality Conditions

Göktepe¹

2021

European Journal of Science and Technology

View full text Add to dashboard Cite

In this paper, a distributed parameter system expressed as a parabolic partial differential equation governed by a diffusivity control is considered. A modal space expansion approach is used to convert the distributed parameter system into a lumped parameter system. Thereafter, Pontryagin's maximum principle is used to compute the optimal control function that leads to a nonlinear two-point boundary value problem (TPBVP). An iterative numerical technique, variation of extremals is used to solve the nonlinear TPBVP. The feasibility and applicability of the proposed solution is demonstrated by numerical simulations generated in MATLAB.

show abstract

Structure-Preserving Interpolation of Bilinear Control Systems

Benner,

Gugercin,

Werner

2020

Preprint

View full text Add to dashboard Cite

In this paper, we extend the structure-preserving interpolatory model reduction framework, originally developed for linear systems, to structured bilinear control systems. Specifically, we give explicit construction formulae for the model reduction bases to satisfy different types of interpolation conditions. First, we establish the analysis for transfer function interpolation for single-input single-output structured bilinear systems. Then, we extend these results to the case of multi-input multi-output structured bilinear systems by matrix interpolation. The effectiveness of our structure-preserving approach is illustrated by means of various numerical examples.

show abstract

Optimal Control of a Bilinear System with a Quadratic Cost Functional

Cited by 3 publications

References 11 publications

Structure-preserving interpolation of bilinear control systems

Structure-preserving interpolation of bilinear control systems

Diffusivity Control of Heat Transfer Process Using Optimality Conditions

Structure-Preserving Interpolation of Bilinear Control Systems

Contact Info

Product

Resources

About