Control of Nonlinear and LPV Systems: Interval Observer-Based Framework

Abstract

The problem of output stabilization of a class of nonlinear systems subject to parametric and signal uncertainties is studied. First, an interval observer is designed estimating the set of admissible values for the state. Next, it is proposed to design a control algorithm for the interval observer providing convergence of interval variables to zero, that implies a similar convergence of the state for the original nonlinear system. An application of the proposed technique shows that a robust stabilization can be performed for linear time-varying and Linear-Parameter-Varying (LPV) systems without assumption that the vector of scheduling parameters is available for measurements. Efficiency of the proposed approach is demonstrated through two examples.

Metzler Matrix Transform Determination using a Nonsmooth Optimization Technique with an Application to Interval Observers

“…More recent works like [14] and [6] interestingly propose techniques to find a static state coordinate transform P and an observer gain L so that M = P (A − LC)P −1 is Metzler even for a non-Metzler matrix A. Methods based on the numerical resolution of a Sylvester equation were proposed.…”

On design of interval observers for parabolic PDEs

“…For future developments, the proposed interval observer can be used for control design of an uncertain PDE system in the spirit of Efimov et al (2013), and a more complex uncertainty of PDE equation can also be incorporated in the design procedure.…”

Zonotopes and Kalman observers: Gain optimality under distinct uncertainty paradigms and robust convergence

“…Explicitly characterizing how the model and measurement uncertainties can influence the possible state values is also useful, not only when an automated decision-making is further required (e.g. fault diagnosis Ding, 2008), but also in some control frameworks (Efimov, Raïssi, & Zolghadri, 2013). Two paradigms can be used to model uncertainties: The stochastic one relies on probability theory and mainly deals with random variables.…”