Tensor Product Model Transformation in Control Systems

Tensor Product (TP) model transformation is a systematic framework for converting nonlinear or parameter-dependent dynamical systems into a convex combination of fixed linear subsystems. By employing higher-order singular value decomposition (HOSVD) on multidimensional data arrays, the method identifies principal components that capture the dominant behaviour of the original model. Truncation of smaller singular values yields a reduced-order representation, trading off complexity against fidelity. The resulting polytopic form comprises a finite set of vertex models and associated weighting functions, enabling controller synthesis via linear matrix inequalities. This approach unifies Takagi–Sugeno fuzzy modelling and linear parameter-varying (LPV) techniques, offering rigorous guarantees on stability and performance. It has found applications in aerospace flutter suppression, robotic manipulator control, automotive powertrain management and renewable-energy systems, where varying operating conditions demand both robustness and real-time implementability.

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Tensor Product Model Transformation in Control Systems publication trend

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Technical terms

Tensor Product Model Transformation: A technique that converts a parameter-dependent or nonlinear system into a convex combination of linear subsystems by using tensor decompositions.

Higher-Order Singular Value Decomposition (HOSVD): A generalisation of matrix SVD to multidimensional arrays, extracting principal factors across multiple modes.

Linear Parameter-Varying (LPV) System: A class of control models whose parameters change over time or operating conditions within known bounds.

Takagi–Sugeno (T-S) Fuzzy Model: A modelling paradigm that represents nonlinear dynamics as weighted sums of linear submodels using fuzzy-logic rules.

Convex Hull: The smallest convex set that contains all weighting combinations of vertex models, defining the feasible operating envelope of a TP representation.

References

1. Transition Between TS Fuzzy Models and the Associated Convex Hulls by TS Fuzzy Model Transformation. IEEE Transactions on Fuzzy Systems (2023).
2. Relaxed TS Fuzzy Model Transformation to Improve the Approximation Accuracy/Complexity Tradeoff and Relax the Computation Complexity. IEEE Transactions on Fuzzy Systems (2024).
3. Tensor Product Model-based Robust Flutter Control Design for the FLEXOP Aircraft. IFAC-PapersOnLine (2019).