Sensitivity and inverse analysis methods for parameter intervals

Shao, Guojian; Su, Jingbo

doi:10.3724/sp.j.1235.2010.00274

Cited by 8 publications

(6 citation statements)

References 14 publications

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“…Theorem 1. The asymptotical stability of the input-free system (22) (ie, with u k = 0) is guaranteed if there exists matrices P = P T > 0 and G such that the LMI (24) holds.…”

Section: Stability Criteriamentioning

confidence: 99%

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State estimation of system with bounded uncertain parameters: Interval multimodel approach

Ichalal

Marx

Maquin

et al. 2018

Adaptive Control & Signal

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The objective of this study is the analysis of dynamic systems represented by a multimodel expression with variable parameters. Changes in these parameters are unknown but bounded. Since it is not possible to estimate these parameters over time, the simulation of such systems requires the consideration of all possible values taken by these parameters. More precisely, the goal is to determine, at any moment, the smallest set containing all the possible values of the state vector simultaneously compatible with the state equations and with a priori known bounds of the uncertain parameters. This set will be characterized by two trajectories corresponding to the lower and upper limits of the state at every moment.This characterization can be realized by a direct simulation of the system, given the bounds of its parameters. It can also be implemented with a Luenberger-type observer, fed with the system measurements. KEYWORDSbounded uncertainties, interval observers, multimodel technique, uncertain systems INTRODUCTIONAs widely known, one of the main difficulties in system simulation, control, or estimation is dealing with uncertainties. These uncertainties may affect the input or output signals of the system (eg, unknown input, disturbance, measurement noises, etc) as well as the system model itself (eg, nonmodeled dynamics, unknown parameter, etc). The uncertainties may also be of different natures: total lack of information (unknown value of a parameter) or partial knowledge (upper and lower bounds, statistical properties, etc). This paper deals with systems with uncertain parameters.Even a low magnitude change in some parameters may have a significant impact on the system behavior and, namely, on the system state trajectory. Uncertain parameters can be considered from two main points of view: the stochastic and the deterministic ones. In the first approach, the uncertain parameters are assumed to be the results of random process realizations. It then needs to choose the probability density functions and their parameters describing the system's uncertain parameters. In the deterministic approach, no statistical models of the parameters are assumed to be available, and only the upper and lower bounds of the parameter values are known. This approach, also known as the interval approach, is adopted in this paper.The search for trajectories, which are solutions of differential inclusions, 1 were the starting point of the large amount of works on stability, stabilization, and state estimation. In the latter topic, our communication follows the pioneering work of Gouzé et al, 2 which proposed the synthesis of the interval-type observer to reconstruct the system state 480 ;32:480-493. ICHALAL ET AL. 481from measurements of inputs and outputs. Since then, many results were published on designing observers adapted to nonlinear systems with uncertain but bounded parameters. [3][4][5][6] The model-based state estimation techniques in the context of bounded uncertainties can be classified into two categories. The first one is ba...

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“…Theorem 1. The asymptotical stability of the input-free system (22) (ie, with u k = 0) is guaranteed if there exists matrices P = P T > 0 and G such that the LMI (24) holds.…”

Section: Stability Criteriamentioning

confidence: 99%

“…The positivity of the functions j ensures that (24) are sufficient conditions to (26) and thus to ΔV k < 0 and to the input-free asymptotical stability of (22). (22) is asymptotically stable if there exists matrices P i = P T i > 0 and G such that…”

Section: Stability Criteriamentioning

confidence: 99%

State estimation of system with bounded uncertain parameters: Interval multimodel approach

Ichalal

Marx

Maquin

et al. 2018

Adaptive Control & Signal

View full text Add to dashboard Cite

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“…Truss and frame structures were used as examples to demonstrate the validity and feasibility of the presented methods. Shao and Su [17] proposed a sensitivity analysis method for engineering parameters. In this context, parameter intervals and decision-making target intervals were determined using the IA method.…”

Section: Introductionmentioning

confidence: 99%

Uncertainty Definition on the Constitutive Models for RC Columns Wrapped with FRP

et al. 2014

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This paper aims to explore the effectiveness of the fiber-reinforced polymer (FRP)-confining mechanism in concrete in which parameters are uncertain. The confinement effect of high stiffness FRP jackets results an increase in the compressive strength of reinforced concrete columns and should be clearly defined. Various constitutive models have been constructed to predict the mechanical behavior of FRP-wrapped columns by considering this effect. However, the mechanical response of confined concrete columns due to FRP jackets under concentric compression has still been a challenging issue, and there are still some uncertainties in mechanical and also geometrical properties in the analysis and design procedure. These uncertainties can be studied with interval analysis (IA) to determine sharp bounds of the mechanical parameters such as effective lateral confining stress, Young's modulus of concrete and FRP, and geometrical parameters. For this purpose, an IA has been performed using deterministic values of compressive strength for significant number (163) of experimental data being reported by several researchers on FRP-confined square/rectangular columns. The results indicate that uncertainties in material parameters and compressive strengths play an important role in determining the lateral stresses of FRP-confined columns.

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“…Interval SA methods explore the full range of parameter uncertainties and the interval sensitivities represent a measure for the individual effect of each interval parameter. Such methods require a linear variation of parameter values within their intervals [16,17] and the sensitivity calculation is relatively easy to implement.…”

Section: Introductionmentioning

confidence: 99%

Probabilistic and Nonprobabilistic Sensitivity Analyses of Uncertain Parameters

Fang

Zhang

Bao

et al. 2014

Mathematical Problems in Engineering

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Parameter sensitivity analyses have been widely applied to industrial problems for evaluating parameter significance, effects on responses, uncertainty influence, and so forth. In the interest of simple implementation and computational efficiency, this study has developed two sensitivity analysis methods corresponding to the situations with or without sufficient probability information. The probabilistic method is established with the aid of the stochastic response surface and the mathematical derivation proves that the coefficients of first-order items embody the parameter main effects on the response. Simultaneously, a nonprobabilistic interval analysis based method is brought forward for the circumstance when the parameter probability distributions are unknown. The two methods have been verified against a numerical beam example with their accuracy compared to that of a traditional variance-based method. The analysis results have demonstrated the reliability and accuracy of the developed methods. And their suitability for different situations has also been discussed.

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Sensitivity and inverse analysis methods for parameter intervals

Cited by 8 publications

References 14 publications

State estimation of system with bounded uncertain parameters: Interval multimodel approach

State estimation of system with bounded uncertain parameters: Interval multimodel approach

Uncertainty Definition on the Constitutive Models for RC Columns Wrapped with FRP

Probabilistic and Nonprobabilistic Sensitivity Analyses of Uncertain Parameters

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