The design of optimal observers via shifted Chebyshev polynomials

Horng, Ing-Rong; Chou, Jyh–Horng

doi:10.1080/0020718508961146

Cited by 29 publications

(20 citation statements)

References 10 publications

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“…The constant matrix W depends on the particular choice of the orthogonal function vector T (t). For example, if the shift Chebyshev function is employed, the constant matrices W are given as [32] Integrating Equation (4) …”

Section: Optimal Controller Design Using the Ofamentioning

confidence: 99%

Design of robust quadratic‐optimal controllers for uncertain singular systems using orthogonal function approach and genetic algorithm

Chen¹,

Ho²,

Chou³

2008

Optim Control Appl Methods

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This paper discusses the robust-optimal state feedback controller design problems of linear singular systems under the structured (elemental) parameter uncertainties by using the orthogonal function approach (OFA) and the hybrid Taguchi genetic algorithm (HTGA). A sufficient condition is proposed to ensure that the linear singular systems with the structured parameter uncertainties are regular, impulse free, and asymptotically stable. Based on the OFA, an algorithm only involving algebraic computation is derived in this paper and then is integrated with the HTGA to design the robust-optimal state feedback controller of linear uncertain singular systems subject to robust stability constraint and the minimization of a quadratic performance index. A design example of a two degree of freedom mass-spring-damper system is given to demonstrate the applicability of the proposed approach. Detailed steps: HTGAStep 1: Setting parameters. Input: population size G, crossover rate p c , mutation rate p m , and number of generations.Output: the state feedback gain K in Equation (2) and the value of J in Equation (8).Using the proposed approach with m = 4, |k i j | 15 in which i = 1, 2 and j = 1, 2, . . . , 6 are the elements of the state feedback gain matrix K , and the 2-norm-based matrix measure, we can

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Section: Optimal Controller Design Using the Ofamentioning

confidence: 99%

Design of robust quadratic‐optimal controllers for uncertain singular systems using orthogonal function approach and genetic algorithm

Chen¹,

Ho²,

Chou³

2008

Optim Control Appl Methods

Self Cite

View full text Add to dashboard Cite

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“…Although the asymptotic principle can be applied to improve the convergence of the estimated states by choosing the eigenvalues of the observer with a sufficiently negative real part, the design result is not satisfactory due to the fact that a large estimation error may occur during the transient period of observation. [13][14][15] Several previous studies have been devoted to coping with the design issue of reducing the large estimation error occurring during the transient period of observation. [12][13][14][15][16][17] The reduced-order observer reduces the order of the observer by using the sensed outputs.…”

Section: Introductionmentioning

confidence: 99%

“…[13][14][15] Several previous studies have been devoted to coping with the design issue of reducing the large estimation error occurring during the transient period of observation. [12][13][14][15][16][17] The reduced-order observer reduces the order of the observer by using the sensed outputs. To the authors' best knowledge, to date, only Kung and Yeh 13 as well as Horng and Chou 14,15 have studied the problem of transient estimation performance improvement for "reduced-order observers.…”

Section: Introductionmentioning

confidence: 99%

“…18,19 One design method requires the dynamical equation in an observable form, while the other design approach does not require so. Based on the dynamical system in an observable form, Kung and Yeh 13 as well as Horng and Chou 14,15 studied the problem of transient estimation performance improvement for the "reduced-order observer of an Observable-Form-Based dynamical system (OFB-reduced-order observer)." However, the methods proposed by Kung and Yeh 13 as well as Horng and Chou 14,15 cannot be applied to deal with the design issue of the "reduced-order observer of a Non-Observable-Form-Based dynamical system (NOFB-reduced-order observer)."…”

Section: Introductionmentioning

confidence: 99%

“…On the other hand, it merits attention that when the number of outputs is greater than the number of unmeasurable states, the approaches presented by Kung and Yeh 13 as well as Horng and Chou 14,15 cannot be utilized to uniquely determine the observer gain matrix of a linear optimal OFB-reduced-order observer. The reason is that after the eigenvalues are assigned, in the works of Kung and Yeh 13 as well as Horng and Chou, 14,15 the degree of design freedom remaining is not fully utilized.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Optimal design of reduced-order observers with specified eigenvalues and performance measurement of minimizing estimation errors using evolutionary optimization

Chou

Cheng

2019

Journal of Low Frequency Noise, Vibration and Active Control

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A new method is proposed in this paper which designs a reduced-order observer of a non-observable-form-based dynamical system such that: (i) the eigenvalues are specified to satisfy desired convergence performance, (ii) a full-rank condition is satisfied, and (iii) a quadratic performance measurement of the deviation of the estimates from the actual states is minimized so as to reduce the large error occurring during the transient period of observation. The proposed approach combines the merits of both the orthogonal functions approach and evolutionary optimization. By solving a Sylvester equation, the proposed optimal design method can not only be used to design the reduced-order observer of a non-observable-form-based dynamical system, but also can avoid the shortcomings of approaches already existing in relevant literatures. Two examples are given to demonstrate the effectiveness and efficiency of the proposed new optimization method on the performance of state estimations. From the demonstrative examples, it can be seen that the estimated state errors asymptotically converge quickly to zero. In addition, the performance measurement values based on the proposed optimal design approach are apparently much lower than those based on the existing nonoptimal design method.

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Approximate solution of integral equations and convolution integrals using Legendre polynomials

Bokhari

Chaudhry

Qadir

1997

Approx. Theory & its Appl.

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The design of optimal observers via shifted Chebyshev polynomials

Cited by 29 publications

References 10 publications

Design of robust quadratic‐optimal controllers for uncertain singular systems using orthogonal function approach and genetic algorithm

Design of robust quadratic‐optimal controllers for uncertain singular systems using orthogonal function approach and genetic algorithm

Optimal design of reduced-order observers with specified eigenvalues and performance measurement of minimizing estimation errors using evolutionary optimization

Approximate solution of integral equations and convolution integrals using Legendre polynomials

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