Data-Driven Predictive Control for Linear Parameter-Varying Systems

Based on the extension of the behavioral theory and the Fundamental Lemma for Linear Parameter-Varying (LPV) systems, this paper introduces a Data-driven Predictive Control (DPC) scheme capable to ensure reference tracking and satisfaction of Input-Output (IO) constraints for an unknown system under the conditions that (i) the system can be represented in an LPV form and (ii) an informative data-set containing measured IO and scheduling trajectories of the system is available. It is shown that if the data set satisfies a persistence of excitation condition, then a data-driven LPV predictor of future trajectories of the system can be constructed from the IO data set and online measured data. The approach represents the first step towards a DPC solution for nonlinear and time-varying systems due to the potential of the LPV framework to represent them. Two illustrative examples, including reference tracking control of a nonlinear system, are provided to demonstrate that the data-based LPV-DPC scheme, achieves similar performance as LPV model-based predictive control.Comment: Accepted to 4th IFAC Workshop on Linear Parameter-Varying System

Realization Theory for LPV State-Space Representations with Affine Dependence

In this paper we present a Kalman-style realization theory for linear parameter-varying state-space representations whose matrices depend on the scheduling variables in an affine way (abbreviated as LPV-SSA representations). We deal both with the discrete-time and the continuous-time cases. We show that such a LPV-SSA representation is a minimal (in the sense of having the least number of state-variables) representation of its input-output function, if and only if it is observable and span-reachable. We show that any two minimal LPV-SSA representations of the same input-output function are related by a linear isomorphism, and the isomorphism does not depend on the scheduling variable.We show that an input-output function can be represented by a LPV-SSA representation if and only if the Hankel-matrix of the input-output function has a finite rank. In fact, the rank of the Hankel-matrix gives the dimension of a minimal LPV-SSA representation. Moreover, we can formulate a counterpart of partial realization theory for LPV-SSA representation and prove correctness of the Kalman-Ho algorithm. These results thus represent the basis of systems theory for LPV-SSA representation.Comment: The main difference with respect to the previous version is as follows: typos have been fixe

M[pi]log, Macromodeling via parametric identification of logic gates

This paper addresses the development of computational models of digital integrated circuit input and output buffers via the identification of nonlinear parametric models. The obtained models run in standard circuit simulation environments, offer improved accuracy and good numerical efficiency, and do not disclose information on the structure of the modeled devices. The paper reviews the basics of the parametric identification approach and illustrates its most recent extensions to handle temperature and supply voltage variations as well as power supply ports and tristate devices