Model reduction of a class of discrete-time nonlinear systems

Ibrir, Salim; Bettayeb, Maâmar

doi:10.1016/j.amc.2014.10.063

Cited by 8 publications

(1 citation statement)

References 33 publications

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“…A typical example among such systems is the one-link rigid robot under gravitation field. 35 Furthermore, both the control analysis and model reduction problems of this class of systems have been intensively studied (see, for instance, Ibrir et al., 27,29 Ibrir and Diopt, 30 and Ibrir and Bettayeb 36 ).…”

Section: Problem Formulationmentioning

confidence: 99%

Observer-based trajectory tracking control with preview action for a class of discrete-time Lipschitz nonlinear systems and its applications

Liao

2014

Advances in Mechanical Engineering

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In this article, the observer-based preview tracking control problem is investigated for a class of discrete-time Lipschitz nonlinear systems. To convert the observer-based trajectory tracking problem into a regulation problem, the classical difference technique is used to construct an augmented error system containing tracking error signal and previewable reference knowledge. Then, a state feedback controller with specific structures is taken into consideration. Sufficient design condition is established, based on the Lyapunov function approach, to guarantee the asymptotic stability of the closed-loop system. By means of some special mathematical derivations, the bilinear matrix inequality condition is successfully transformed into a tractable linear matrix inequality. Meanwhile, the gains of both observer and tracking controller can be computed simultaneously only in one step. As for the original system, the developed tracking control law is composed of an integrator, an observer-based state feedback controller, and a preview action term related to the reference signal. Finally, two numerical examples are provided to demonstrate the effectiveness of the theoretical method.

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Section: Problem Formulationmentioning

confidence: 99%

Observer-based trajectory tracking control with preview action for a class of discrete-time Lipschitz nonlinear systems and its applications

Liao

2014

Advances in Mechanical Engineering

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A projection-based algorithm for model-order reduction with H2 performance: A convex-optimization setting

Ibrir

2018

Automatica

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Optimal projection methods for model order reduction of discrete-time systems

Ibrir

2018

IMA Journal of Mathematical Control and Information

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Numerical algorithms are developed for model order reduction of discrete-time systems using both optimal projection and $H_2$-norm minimization. The state-space matrices of the reduced-order system are obtained via the solution of a convex optimization problem. Subsequently, the results are exploited for the design of non-linear reduced-order systems verifying the input-to-state stability property. Proofs of stability and error approximation bounds are provided along with numerical simulations to highlight the strengths and the validity of the theoretical results.

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Model reduction of a class of discrete-time nonlinear systems

Cited by 8 publications

References 33 publications

Observer-based trajectory tracking control with preview action for a class of discrete-time Lipschitz nonlinear systems and its applications

Observer-based trajectory tracking control with preview action for a class of discrete-time Lipschitz nonlinear systems and its applications

A projection-based algorithm for model-order reduction with H2 performance: A convex-optimization setting

Optimal projection methods for model order reduction of discrete-time systems

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