Intersection-based piecewise affine approximation of nonlinear systems

Zavieh, Amin Hossein; Rodrigues, Luís

doi:10.1109/med.2013.6608790

Cited by 10 publications

(16 citation statements)

References 28 publications

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“…Different from the well-known system form with constant unknown parameters studied in [5], [8], [11], system (1) depicts systems with switched unknown parameters. It is of practical interest as it can model many engineering applications operating in multiple modes such as aircraft wing [19], mechanical systems with friction [20] and backlash [21].…”

Section: Problem Formulation and Preliminariesmentioning

confidence: 99%

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Adaptive Observer for a Class of Systems with Switched Unknown Parameters Using DREM

Liu¹,

Zhang²,

Liu³

et al. 2022

Preprint

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In this note, we develop an adaptive observer for a class of nonlinear systems with switched unknown parameters to estimate the states and parameters simultaneously. The main challenge lies in how to eliminate the disturbance effect of zero-input responses caused by the switching on the parameter estimation. These responses depend on the unknown states at switching instants (SASI) and constitute an additive disturbance to the parameter estimation, which obstructs parameter convergence to zero. Our solution is to treat the zero-input responses as excitations instead of disturbances. This is realized by first augmenting the system parameter with the SASI and then developing an estimator for the augmented parameter using the dynamic regression extension and mixing (DREM) technique. Thanks to its property of element-wise parameter adaptation, the system parameter estimation is decoupled from the SASI. As a result, the estimation errors of system states and parameters converge to zero asymptotically. Furthermore, the robustness of the proposed adaptive observer is guaranteed in the presence of disturbances and noise. A numerical example validates the effectiveness of the proposed approach.

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Section: Problem Formulation and Preliminariesmentioning

confidence: 99%

“…for θji being the j-th element of θi with θi = θi − θ * i . The indicator function χ i in the adaptation law (19) indicates that the value of θi remains constant when subsystem i is inactive and θi is adapted during the active phase of subsystem i.…”

Section: B Drem-based Parameter Estimatormentioning

confidence: 99%

Adaptive Observer for a Class of Systems with Switched Unknown Parameters Using DREM

Liu¹,

Zhang²,

Liu³

et al. 2022

Preprint

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show abstract

“…explored a uniform triangular‐shape partition for the domain and approximated a nonlinear function by adjusting the grid size of the partition. Zavieh and Rodrigues used heuristic selection of linearization points where a new linearization point is determined by the intersection of tangential lines associated with the old linearization points. Casselman and Rodrigues used a set of linearization points and Voronoi partitions in the approximation.…”

Section: Integration Of Scheduling and Control Based On Pwa Modelmentioning

confidence: 99%

An integrated framework for scheduling and control using fast model predictive control

Zhuge

Ierapetritou

2015

AIChE Journal

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in Wiley Online Library (wileyonlinelibrary.com) Integration of scheduling and control involves extensive information exchange and simultaneous decision making in industrial practice (Engell and Harjunkoski, Comput Chem Eng. 2012;47:121-133; Baldea and Harjunkoski I, Comput Chem Eng. 2014;71:377-390). Modeling the integration of scheduling and dynamic optimization (DO) at control level using mathematical programming results in a Mixed Integer Dynamic Optimization which is computationally expensive (Flores-Tlacuahuac and Grossmann, Ind Eng Chem Res. 2006;45(20):6698-6712). In this study, we propose a framework for the integration of scheduling and control to reduce the model complexity and computation time. We identify a piece-wise affine model from the first principle model and integrate it with the scheduling level leading to a new integration. At the control level, we use fast Model Predictive Control (fast MPC) to track a dynamic reference. Fast MPC also overcomes the increasing dimensionality of multiparametric MPC in our previous study (Zhuge and Ierapetritou, AIChE J. 2014;60(9):3169-3183). Results of CSTR case studies prove that the proposed approach reduces the computing time by at least two orders of magnitude compared to the integrated solution using mp-MPC. V C 2015 American Institute of Chemical Engineers AIChE J, 61: 3304-3319, 2015 Keywords: integration of scheduling and control, piece-wise affine approximation, fast model predictive control, Multiparametric model predictive control, mixed integer nonlinear programming

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“…In fact, as accuracy increases, so does the number of regions, increasing also with the domain of approximation. 32…”

Section: Introductionmentioning

confidence: 99%

Deterministic robust control design for an iron core linear drive including second-order electrical dynamics

Villegas

Hecker

Peña

2018

Proceedings of the Institution of Mechanical Engineers, Part I:

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This work proposes a deterministic robust controller to improve tracking performance for a linear motor, taking into account the electrical dynamics imposed by a commercial current controller. The design is split in two parts by means of the backstepping technique, in which the first part corresponds to a typical deterministic robust controller, neglecting the electrical dynamics. In the second part, a second-order electrical dynamics is considered using a particular state transformation. There, the proposed control law is composed of a term to compensate the known part of the model and a robust control term to impose a bound on the effect of uncertainties on tracking error. Stability and boundedness results for the complete controller are given. To this effect, a general result on boundedness and stability of nonlinear systems with conditionally bounded state variables is derived first. Finally, experimental results for the complete controller show an improvement on tracking error of up to 31.7% when compared with the results from the typical controller that neglects the electrical dynamics.

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Intersection-based piecewise affine approximation of nonlinear systems

Cited by 10 publications

References 28 publications

Adaptive Observer for a Class of Systems with Switched Unknown Parameters Using DREM

Adaptive Observer for a Class of Systems with Switched Unknown Parameters Using DREM

An integrated framework for scheduling and control using fast model predictive control

Deterministic robust control design for an iron core linear drive including second-order electrical dynamics

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