A new approach to handle additive and multiplicative uncertainties in the measurement for LPV filtering

Lacerda, Márcio J.; Tognetti, Eduardo S.; Oliveira, Ricardo C. L. F.; Peres, Pedro L. D.

doi:10.1080/00207721.2014.911389

Cited by 51 publications

(46 citation statements)

References 36 publications

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“…The proposed approach tried to balance between the computational efficiency and the reduction of conservatism, presenting a trade‐off solution between the quadratic LF and approaches based on PDLF for LPV systems. In this way, strategies that already rely on the convex representation given by , as in other works, besides many others, may benefit from the proposed approach in terms of computational performance.…”

Section: Discussionmentioning

confidence: 96%

“…Notice that (27) provides a simple way to generate the vertices of the simplex that bounds (22), not requiring any complex algorithm. These vertices coordinates can be stored as columns of a matrix, analogously to (23), resulting in…”

Section: A Possible Solutionmentioning

confidence: 99%

“…The same 600 configurations tested for the standard LF and PDLF are analyzed a third time in this turn by the proposed approach. Toward this end, theorem 1 in the work of Geromel and Colaneri 7 has been modified usingH given by (28) instead of H given by (23). The results are listed in Tables 7 and 8, in which the feasibility ratio and average computational time are presented, respectively.…”

Section: Illustrating the Computational Effortmentioning

confidence: 99%

See 2 more Smart Citations

On computational issues for stability analysis of LPV systems using parameter‐dependent Lyapunov functions and LMIs

Mozelli

Adriano

2019

Intl J Robust & Nonlinear

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Summary Robust stability analysis of linear systems subject to time‐varying parameters is investigated. The objective is to discuss some computational issues associated with solving stability conditions based on parameter‐dependent Lyapunov functions by means of linear matrix inequalities (LMIs), which are exacerbated as the quantity of time‐varying parameters increases. A new solution related to the inclusion of the time derivatives of the parameters is proposed, improving the computational cost without resulting in much conservatism. The time complexity to solve the LMIs reduces from factorial to linear. Numerical examples are provide to illustrate the advantages of the proposed methodology.

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Section: Discussionmentioning

confidence: 96%

Section: A Possible Solutionmentioning

confidence: 99%

Section: Illustrating the Computational Effortmentioning

confidence: 99%

See 1 more Smart Citation

On computational issues for stability analysis of LPV systems using parameter‐dependent Lyapunov functions and LMIs

Mozelli

Adriano

2019

Intl J Robust & Nonlinear

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“…Following the pioneer work of Peaucelle et al and de Oliveira et al , in the papers , through reciprocal application of Elimination lemma, some degrees of freedom are provided by slack variables in the LMI setting or the so‐called dilated LMIs are introduced for the filter design. By imposing special structures on the slack variables in and employing completely parameter‐dependent Lyapunov matrices, the filtering problem for time‐varying systems is formulated in a less conservative manner.…”

Section: Introductionmentioning

confidence: 99%

“…The state reconstruction for LPV discrete‐time systems is considered in using the estimated parameters that they are available with only some degrees of accuracy. The H ∞ LPV filter design subject to additive and multiplicative uncertainties in the scheduling parameters by imposing a special structure on the auxiliary variables is addressed in . The problem of gain‐scheduled H ∞ filtering using inexact scheduling parameters is investigated in , as well as in for the filtering in the H 2 sense.…”

Section: Introductionmentioning

confidence: 99%

Gain‐scheduled filtering for linear parameter‐varying systems using inexact scheduling parameters with bounded variation rates

Sadeghzadeh

2015

Intl J Robust & Nonlinear

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SUMMARYThis paper is concerned with the problem of full-order H 2 linear parameter-varying filter design for continuous-time systems with bounded rate of variations under the condition that the scheduling parameters do not exactly fit the real ones. The scheduling parameters and their derivatives are supposed to belong to polytopes with known vertices. The synthesis conditions are formulated in terms of parameter-dependent bilinear matrix inequalities by means of parameter-dependent Lyapunov function and introducing some extra variables for the filter design. An iterative procedure is presented to cast the bilinear matrix inequalities problem into a linear matrix inequality optimization problem. The design of robust filters for both timevarying and time-invariant systems can be viewed as particular cases of the proposed method. The merit of the method presented in this paper lies in two fields. The first pertains to dealing with the measurement uncertainty in a less conservative manner than available approaches in the gain-scheduled filtering problem. The second is to provide more efficient methods than the existing ones in the literature for the robust filter design.

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Robust real‐time parameter estimation for linear systems affected by external noises and uncertainties

Agulhari

Neto

Lacerda

et al. 2020

Adaptive Control & Signal

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Summary A robust adaptive parameter estimation method, based on the application of a full‐order filter capable of rejecting exogenous disturbances, is proposed in this article. A linear matrix inequality condition is proposed to synthesize the desired robust filter, assuming the presence of a known input control with constraints. The filter uses the output of the system to estimate the desired signal that will be employed in the adaptive estimation procedure and, to assure robustness to exogenous noise and unstructured uncertainties, the ℋ∞ guaranteed cost is minimized in the synthesis condition. The filtered signals are then applied to an adaptive procedure to estimate the unknown system's internal parameters, which is also proposed in this article. It is shown that lower values for the ℋ∞ guaranteed cost from the disturbance input to the error output of the filter imply more accurate estimations of the parameters. The efficiency of the proposed estimation technique is illustrated through a simulated model and a physical system has been considered to validate real‐time estimation.

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A new approach to handle additive and multiplicative uncertainties in the measurement for LPV filtering

Cited by 51 publications

References 36 publications

On computational issues for stability analysis of LPV systems using parameter‐dependent Lyapunov functions and LMIs

On computational issues for stability analysis of LPV systems using parameter‐dependent Lyapunov functions and LMIs

Gain‐scheduled filtering for linear parameter‐varying systems using inexact scheduling parameters with bounded variation rates

Robust real‐time parameter estimation for linear systems affected by external noises and uncertainties

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