Identifiability of affine linear parameter-varying models

Alkhoury, Ziad; Petreczky, Mihály; Mercère, Guillaume

doi:10.1016/j.automatica.2017.01.029

Cited by 12 publications

(17 citation statements)

References 21 publications

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“…This would require the formulation of a different cost function, which measures the predictive power of the model, to determine future actuation inputs. Rapid learning is also related to the question of quantity versus quality of data and identifiability [ 48 , 49 ]; more data is usually better, although it is possible to work with less data if it is representative of the system. Further, similar methods could be used to optimize sensors and exploit partial measurements within the SINDY-MPC framework.…”

Section: Discussionmentioning

confidence: 99%

“…More recently, convergence and recovery has been explored in a generalized framework for sparse relaxed regularized regression [ 47 ], for which SINDy constitutes a special case. Conditions under which a model structure can be recovered from input–output data have also been examined in the context of identifiability [ 48 , 49 ].…”

Section: Sindy-mpc Frameworkmentioning

confidence: 99%

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Sparse identification of nonlinear dynamics for model predictive control in the low-data limit

2018

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Data-driven discovery of dynamics via machine learning is pushing the frontiers of modelling and control efforts, providing a tremendous opportunity to extend the reach of model predictive control (MPC). However, many leading methods in machine learning, such as neural networks (NN), require large volumes of training data, may not be interpretable, do not easily include known constraints and symmetries, and may not generalize beyond the attractor where models are trained. These factors limit their use for the online identification of a model in the low-data limit, for example following an abrupt change to the system dynamics. In this work, we extend the recent sparse identification of nonlinear dynamics (SINDY) modelling procedure to include the effects of actuation and demonstrate the ability of these models to enhance the performance of MPC, based on limited, noisy data. SINDY models are parsimonious, identifying the fewest terms in the model needed to explain the data, making them interpretable and generalizable. We show that the resulting SINDY-MPC framework has higher performance, requires significantly less data, and is more computationally efficient and robust to noise than NN models, making it viable for online training and execution in response to rapid system changes. SINDY-MPC also shows improved performance over linear data-driven models, although linear models may provide a stopgap until enough data is available for SINDY. SINDY-MPC is demonstrated on a variety of dynamical systems with different challenges, including the chaotic Lorenz system, a simple model for flight control of an F8 aircraft, and an HIV model incorporating drug treatment.

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Section: Discussionmentioning

confidence: 99%

Section: Sindy-mpc Frameworkmentioning

confidence: 99%

Sparse identification of nonlinear dynamics for model predictive control in the low-data limit

2018

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“…In particular, in order to identify LPV-LFR models, it is enough to test them for uncertainty blocks of the form (5) which come from scheduling variables. Theorem 7 allows us to use the recent results of [1] to investigate identifiability of LPV-LFRs.…”

Section: Equivalence Between Alpv and Lfr-lpv: Preservation Of Imentioning

confidence: 99%

“…This enables us to show in a second step that the input-output behavior of an ALPV model uniquely determines the input-output behavior of the corresponding LFR. Indeed, from [1], it follows that minimal ALPV models with the same inputoutput behavior are related by a constant state isomor-phism. We then show that that the classical transformation from ALPV models to LFR models preserves isomorphism.…”

Section: Introductionmentioning

confidence: 99%

Structural properties of affine LPV to LFR transformation: Minimality, input-output behavior and identifiability

Alkhoury

Petreczky

Mercère

2016

2016 IEEE 55th Conference on Decision and Control (CDC)

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In this paper, we introduce and study important properties of the transformation of Affine Linear Parameter-Varying (ALPV) state-space representations into Linear Fractional Representations (LFR). More precisely, we show that (i) state minimal ALPV representations yield minimal LFRs, and vice versa, (ii) the input-output behavior of the ALPV represention determines uniquely the input-output behavior of the resulting LFR, (iii) structurally identifiable ALPVs yield structurally identifiable LFRs, and vice versa. We then characterize LFR models which correspond to equivalent ALPV models based on their input-output maps. As illustrated all along the paper, these results have important consequences for identification and control of systems described by LFRs.

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“…The linear parameter varying (LPV) model, which consists of a series of linear time invariant (LTI) models, has developed rapidly due to its adaptability in the past 30 years [13][14][15][16]. The LTI models only guarantee the performance around given operating points, and the obtained linear model can only work near the given operating point.…”

Section: Introductionmentioning

confidence: 99%

A Novel Real-Time Mechanism Modeling Approach for Turbofan Engine

et al. 2019

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Nonlinear component level model (NCLM) is a widely used model for aeroengines. However, it requires iterative calculation and is, therefore, time-consuming, which restricts its real-time application. This study aims at developing a simplified real-time modeling approach for turbofan engines. A mechanism modeling approach is proposed based on linear models to avoid the iterative calculation in NCLM so as to effectively reduce the computational complexity. Linear local models, of which the outputs are the solution of the balance equations in NCLM, are established at the ground operating points and are combined into a linear parameter varying (LPV) state-space model. Then, the model is extended throughout the full flight envelope in a polytopic expression and is integrated with the flow path calculation to obtain satisfactory real-time performance. In order to ensure the accuracy of the integrated model, the upper bound of convergence residual of the iteration is strictly set and consideration on the interpolation method is taken. The simulation results demonstrate that the integrated model requires much less computational resources than the NCLM does. Meanwhile, it maintains an acceptable accuracy performance and, therefore, is suitable for real-time application.

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Identifiability of affine linear parameter-varying models

Cited by 12 publications

References 21 publications

Sparse identification of nonlinear dynamics for model predictive control in the low-data limit

Sparse identification of nonlinear dynamics for model predictive control in the low-data limit

Structural properties of affine LPV to LFR transformation: Minimality, input-output behavior and identifiability

A Novel Real-Time Mechanism Modeling Approach for Turbofan Engine

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