Robust LPV control with bounded parameter rates

Bennani, Samir; Willemsen, Dehlia; Scherer, Carsten W.

doi:10.2514/6.1997-3641

Cited by 8 publications

(7 citation statements)

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“…One need to solve some Riccati functions based on linear fractional transform. In reference [10], this method was used whose disadvantages were too many restricts and time consumed when the scheduling parameters' number was big, sometimes, there was no solution for this method. The other defined a parameter box based on scheduling parameters' work region and get system model using models at parameter box corners.…”

Section: A Controller Design Based On Polytopicmentioning

confidence: 99%

Robust gain-scheduling controller to LPV system using gap metric

Zhang

2008

2008 International Conference on Information and Automation

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The gain-scheduling was a good choice for dynamic systems whose operation range were very large, when the dynamic systems were turned into linear parameter varying systems (LPV) through appropriate states transform. The method of designing robust gain-scheduling to LPV system based on polytopic was studied, and a new scheduling strategy was proposed because of the conservatism of the scheduling strategy based on varying parameter's position. The new scheduling strategy was based on gap metric. From simulation result, we can see that the new strategy can reduce overshoot by about 10%, and can reduce the controller maximal output by about 30%, and can restrain states' oscillation compared with the old strategy.

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Section: A Controller Design Based On Polytopicmentioning

confidence: 99%

Robust gain-scheduling controller to LPV system using gap metric

Zhang

2008

2008 International Conference on Information and Automation

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“…We consider a rocket autopilot problem perturbed by stochastic disturbances as in [15], the unperturbed dynamics of which is depicted in Fig. 5 and given as follows, assuming that the pitch rate q and specific normal force are available as a measurement via rate gyros and accelerometers [164,165]: [165], and the notations are defined in Table 4. Since this example explicitly takes into account stochastic perturbation, the spectrally-normalized DNN of Definition 6.3 is used to guarantee the Lipschitz condition of Theorem 2.5 by Lemma 6.2.…”

Section: Lipschitz Condition and Spectral Normalizationmentioning

confidence: 99%

“…where e = x − x d , and V = ξ1 ξ0 Θδq is defined in Theorem 2.3 with M = Θ Θ replaced by diag(M, Γ −1 ) for ξ 0 = [x d , ϑ ] and ξ 1 = [x , θ ] . Furthermore, if the learning error = 0 (CV-STEM control), (165) with σ = 0 guarantees asymptotic stability of x to x d in (163).…”

Section: Adaptive Control With Cv-stem and Ncmmentioning

confidence: 99%

Contraction Theory for Nonlinear Stability Analysis and Learning-based Control: A Tutorial Overview

Tsukamoto,

Chung,

Slotine

2021

Preprint

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Contraction theory is an analytical tool to study differential dynamics of a non-autonomous (i.e., time-varying) nonlinear system under a contraction metric defined with a uniformly positive definite matrix, the existence of which results in a necessary and sufficient characterization of incremental exponential stability of multiple solution trajectories with respect to each other. By using a squared differential length as a Lyapunov-like function, its nonlinear stability analysis boils down to finding a suitable contraction metric that satisfies a stability condition expressed as a linear matrix inequality, indicating that many parallels can be drawn between well-known linear systems theory and contraction theory for nonlinear systems. Furthermore, contraction theory takes advantage of a superior robustness property of exponential stability used in conjunction with the comparison lemma. This yields much-needed safety and stability guarantees for neural network-based control and estimation schemes, without resorting to a more involved method of using uniform asymptotic stability for input-to-state stability. Such distinctive features permit systematic construction of a contraction metric via convex optimization, thereby obtaining an explicit exponential bound on the distance between a time-varying target trajectory and solution trajectories perturbed externally due to disturbances and learning errors. The objective of this paper is therefore to present a tutorial overview of contraction theory and its advantages in nonlinear stability analysis of deterministic and stochastic systems, with an emphasis on deriving formal robustness and stability guarantees for various learning-based and data-driven automatic control methods. In particular, we provide a detailed review of techniques for finding contraction metrics and associated control and estimation laws using deep neural networks.

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“…, δ k ; this boils down to solving a standard linear matrix inequality (LMI) problem. By a well-known controller parameter elimination procedure, we arrive at the following LMI conditions that guarantee the existence of a polytopic LPV controller [14], [15]…”

Section: Lpv Controller Synthesismentioning

confidence: 99%