Control, Identification, and Input Optimization

Kalaba, Robert E.; Spingarn, K.

doi:10.1007/978-1-4684-7662-0

Cited by 94 publications

(52 citation statements)

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“…The case where µ = 0 has been solved in literature [4]. The multi-objective optimisation problem, corresponding to µ ≠ 0, can be solved by the Euler-Lagrange method which results in the following two-point boundary-value problem: …”

Section: Single Weighted Cost Function Methods For a Time Domain Inputmentioning

confidence: 99%

“…It is a common practice to perturb the system of interest and use the resulting data to build the model [1][2][3]. The accuracy of parameter estimates is increased by the use of optimal excitation signals [4,5]. The pertinence of a model is the critical factor for proper tuning of a controller, usually performed as a model-based optimisation task.…”

Section: Open Accessmentioning

confidence: 99%

“…The principle of the design of optimal input signals for system identification is to maximise the sensitivity of the state variable or the observation to the unknown parameter [4]. The justification for this approach is the Cramer-Rao lower bound, which provides a lower bound for the estimation error covariance.…”

Section: Plant-friendly Identification With Respect To the Cost Functmentioning

confidence: 99%

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Plant Friendly Input Design for Parameter Estimation in an Inertial System with Respect to D-Efficiency Constraints

Jakowluk

2014

Entropy

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System identification, in practice, is carried out by perturbing processes or plants under operation. That is why in many industrial applications a plant-friendly input signal would be preferred for system identification. The goal of the study is to design the optimal input signal which is then employed in the identification experiment and to examine the relationships between the index of friendliness of this input signal and the accuracy of parameter estimation when the measured output signal is significantly affected by noise. In this case, the objective function was formulated through maximisation of the Fisher information matrix determinant (D-optimality) expressed in conventional Bolza form. As setting such conditions of the identification experiment we can only talk about the D-suboptimality, we quantify the plant trajectories using the D-efficiency measure. An additional constraint, imposed on D-efficiency of the solution, should allow one to attain the most adequate information content from the plant which operating point is perturbed in the least invasive (most friendly) way. A simple numerical example, which clearly demonstrates the idea presented in the paper, is included and discussed.

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Section: Single Weighted Cost Function Methods For a Time Domain Inputmentioning

confidence: 99%

Section: Open Accessmentioning

confidence: 99%

Section: Plant-friendly Identification With Respect To the Cost Functmentioning

confidence: 99%

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Plant Friendly Input Design for Parameter Estimation in an Inertial System with Respect to D-Efficiency Constraints

Jakowluk

2014

Entropy

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“…3. The alternative way of calculating sensitivities is based on the so called adjoint equations (see, e.g., Kalaba and Spingarn 1982;Schittkowski 2002). However, this way requires solving ODE's backward in time.…”

Section: Sensitivity Equations: No Feedbackmentioning

confidence: 99%

Control of linear extended nD systems with minimized sensitivity to parameter uncertainties

Rafajłowicz

2013

Multidim Syst Sign Process

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A new view on uncertain system parameters is presented considering them in the same way as other independent variables, e.g., time or space variables. After re-interpreting the well known equations for the sensitivities of a system to parameter changes, we consider the problem of optimal control that takes into account not only the quality of control itself, but also a reduction in the influence of parameter changes. Firstly, we re-derive and elucidate known results for systems described by linear ordinary differential equations in the statespace form. Then, it is shown how to extend the well known theory of designing optimal controllers with quadratic criterion so as to cover the reduction of uncertainties in systems described by a class of linear partial differential equations. As a result, we obtain a controller that has a new modal structure in space. Furthermore, the controller incorporates additional sensitivity signals for each mode.

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“…Later, in the late 60s, Nahi and Wallis (1969) made a significant step by using an optimality criterion to design inputs in the time domain. Since then the use of optimality criteria was a great deal of interest and was investigated by, e.g., Fedorov (1972), Kalaba and Springarn (1982) or Goodwin and Payne (1997). At first, designed inputs were used for manoeuvres in which only one flight control was deflected.…”

Section: Introductionmentioning

confidence: 99%

Power spectrum optimization in the design of multisine manoeuvre for identification purposes

Lichota

Szulczyk

Agudelo

et al. 2017

jtam

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In this paper, two sets of multisine signals are designed for system identification purposes. The first one is obtained without any information about system dynamics. In the second case, the a priori information is given in terms of dimensional stability and control derivatives. Magnitude Bode plots are obtained to design the multisine power spectrum that is optimized afterwards. A genetic algorithm with linear ranking, uniform crossover and mutation operator has been employed for that purpose. Both designed manoeuvres are used to excite the aircraft model, and then system identification is performed. The estimated parameters are obtained by applying two methods: Equation Error and Output Error. The comparison of both investigated cases in terms of accuracy and manoeuvre time is presented afterwards.

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Control, Identification, and Input Optimization

Cited by 94 publications

References 0 publications

Plant Friendly Input Design for Parameter Estimation in an Inertial System with Respect to D-Efficiency Constraints

Plant Friendly Input Design for Parameter Estimation in an Inertial System with Respect to D-Efficiency Constraints

Control of linear extended nD systems with minimized sensitivity to parameter uncertainties

Power spectrum optimization in the design of multisine manoeuvre for identification purposes

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