Stable inversion for nonlinear systems

Hunt, L. R.; Meyer, George E.

doi:10.1016/s0005-1098(97)00064-2

Cited by 185 publications

(90 citation statements)

References 5 publications

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“…These analytical approaches to model inversion have been further developed by a number of researchers including Isidori [9], Hunt and Meyer [10] and Zou and Devasia [11], especially for applications involving the design of control systems. Some of these approaches are applied to nonlinear models through methods involving transformation of the nonlinear descriptions to linear and controllable models using a nonlinear state feedback control law.…”

Section: Model Inversion and The Inverse Simulation Approachmentioning

confidence: 99%

Feedback methods for inverse simulation of dynamic models for engineering systems applications

Murray-Smith

2011

Mathematical and Computer Modelling of Dynamical Systems

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Inverse simulation is a form of inverse modelling in which computer simulation methods are used to find the time histories of input variables that, for a given model, match a set of required output responses. Conventional inverse simulation methods for dynamic models are computationally intensive and can present difficulties for high-speed applications. This paper includes a review of established methods of inverse simulation, giving some emphasis to iterative techniques that were first developed for aeronautical applications. It goes on to discuss the application of a different approach which is based on feedback principles. This feedback method is suitable for a wide range of linear and nonlinear dynamic models and involves two distinct stages. The first stage involves design of a feedback loop around the given simulation model and, in the second stage, that closed-loop system is used for inversion of the model. Issues of robustness within closed-loop systems used in inverse simulation are not significant as there are no plant uncertainties or external disturbances. Thus the process is simpler than that required for the development of a control system of equivalent complexity. Engineering applications of this feedback approach to inverse simulation are described through case studies that put particular emphasis on nonlinear and multi-input multi-output models.

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Section: Model Inversion and The Inverse Simulation Approachmentioning

confidence: 99%

Feedback methods for inverse simulation of dynamic models for engineering systems applications

Murray-Smith

2011

Mathematical and Computer Modelling of Dynamical Systems

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“…Among different nonlinear systems, pure-feedback systems can represent more practical processes such as biochemical processes [11], aircraft flight control systems [2], or mechanical systems [12]. To design a control for the pure-feedback systems, the backstepping control technique provides a systematic framework [13].…”

Section: Introductionmentioning

confidence: 99%

Adaptive control of pure-feedback systems in the presence of parametric uncertainties

Asadi¹,

Shandiz²

2017

Turk J Elec Eng & Comp Sci

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Abstract:The purpose of this study is to investigate an adaptive control approach for completely nonaffine pure-feedback systems with linear/nonlinear parameterization. In this approach, the parameter separation technique and the idea of the positive function of linearly connected parameters are coupled effectively with the combination of backstepping and time-scale separation. Subsequently, a fast dynamical equation is derived from the original subsystem, where the solution is sought to approximate the corresponding ideal virtual/actual control inputs. Furthermore, the adaptation law of unknown parameters can be derived based on Lyapunov theory in the backstepping technique and there is no need to design a state predictor for this purpose. Therefore, it results in higher accuracy and avoids complexity. The closed-loop stability and the state regulation of these systems are proved. Finally, the simulation results are provided to demonstrate the effectiveness of the proposed approach.

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“…The exact inversion of square, nonminimum phase nonlinear systems was presented in, amongst others, [1] and [2] for the continuous-time case, and in [3] for the discrete-time case. The procedure is accomplished in three steps, namely (1) the transformation of the nonlinear system to a special form, called the normal form, (2) the inversion of the normal form, and (3) the structuring of the resulting inverse system's state equation as a linear system and partitioning the linear dynamics into stable and unstable parts via an equivalence transformation.…”

Section: Introductionmentioning

confidence: 99%

Improvements in stable inversion of NARX models by using Mann iteration

Eksteen

Heyns

2015

Inverse Problems in Science and Engineering

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The use of Mann iteration in the stable inversion of NARX models that have been converted to state space form is investigated to either recover the convergence or improve the accuracy of the best approximate solution under conditions when Picard iteration fails to converge. Attention is given to the use of filtering and time-varying iteration gains. The results are potentially of use in response reconstruction for fatigue testing purposes where the inverse of a NARX model, obtained by system identification, may be used to achieve the reconstruction.

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Stable inversion for nonlinear systems

Cited by 185 publications

References 5 publications

Feedback methods for inverse simulation of dynamic models for engineering systems applications

Feedback methods for inverse simulation of dynamic models for engineering systems applications

Adaptive control of pure-feedback systems in the presence of parametric uncertainties

Improvements in stable inversion of NARX models by using Mann iteration

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