Gain Scheduled Control of Bounded Multilinear Discrete Time Systems with Uncertanties: An Iterative LMI Approach

Grunert, Tim; Dehnert, Robert; Kummert, Anton; Tibken, Bernd; Fielsch, Sven

doi:10.1109/cdc40024.2019.9029623

Cited by 5 publications

(1 citation statement)

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“…To find a solution of these BMIs, an iterative algorithm is designed, in which LMIs are solved in each iteration stage. Such iterative LMI algorithms for discrete-time systems have already been published for example in Dehnert et al (2015); Grunert et al (2019); Dehnert (2020); Dehnert et al (2020); Lerch et al (2021b); Lerch et al (2021a) in various other contexts. The use of LMIs provides an efficient and numerically stable design method and allows to account for bounded parameter uncertainty or nonlinearities by means of a convex combination of extremal system realizations.…”

Section: Introductionmentioning

confidence: 99%

Robust Feedback Control for Discrete-Time Systems Based on Iterative LMIs with Polytopic Uncertainty Representations Subject to Stochastic Noise

Dehnert¹,

Damaszek²,

Lerch³

et al. 2022

Front. Control Eng.

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This paper deals with the design of linear observer-based state feedback controllers with constant gains for a class of nonlinear discrete-time systems in the form of a quasi-linear representation in presence of stochastic noise. For taking into account nonlinearities in the design of linear observer-based state feedback controllers, a polytopic modeling approach is investigated. An optimization problem is formulated to reduce the sensitivity of the controlled system towards stochastic input, state, and output noise with a predefined covariance. Due to the nonlinearities, the separation principle does not hold, thus, the controller and the observer have to be designed simultaneously. For this purpose, a Lyapunov-based method is used, which provides, in addition to the controller and observer gains, a stability proof for the nonlinear closed loop in a predefined polytopic domain. In general, this leads to nonlinear matrix inequalities. To solve these nonlinear matrix inequalities efficiently, we propose an approach based on linear matrix inequalities (LMIs) with a superposed iteration rule. When using this iterative LMI approach, a minimization task can be solved additionally, which desensitizes the closed loop to stochastic noise. The proposed method additionally enables the consideration of different linear closed loop structures by a unified Lyapunov-based framework. The efficiency of the proposed approach is demonstrated and compared with a classical LQG approach for a nonlinear overhead traveling crane.

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