Improved Embedding of Nonlinear Systems in Linear Parameter-Varying Models With Polynomial Dependence

Abstract

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Functional observability and subspace reconstruction in nonlinear systems

“…Third, our theory fosters data-driven methods for the automated construction of the embedding space, and its map Φ to the original system's attractor, in applications where analytical analysis of the model is untractable (e.g., due to unknown parameters or high dimensionality). This would thus extend previous works on automated embedding construction [80] and full system identification from embedding coordinates [81]. Although our application examples focus on univariate measurements and functionals, the theory is formalized for multivariate cases (q, r ≥ 1) and can be directly applied to determine the existence and conditioning of such map, assessing how good the reconstruction is expected to be (locally).…”

On the State-Feedback Controller Design for Polynomial Linear Parameter-Varying Systems with Pole Placement within Linear Matrix Inequality Regions

“…Within the affine representation, in turn, if the time-varying parameter is defined in polynomial functions of two or greater degrees, a polynomial LPV (PLPV) system should be addressed [19][20][21][22]. As an insight into polynomial LPV systems, let us point out that this particular representation for dynamical systems has been considered, over the years, to approximate real systems such as turbofan engines [23], electrostatically actuated microgrippers [24], 3DOF gyroscopes [25], jet engine compressors [26], flexible robot end-effectors [27], and riderless bicycles [22], among others. Additional important aspects on LPV methodology, in general, can be found in [28,29], presenting data-driven modeling and H ∞ control, respectively.…”