A Novel Dissipativity-Based Control for Inexact Nonlinearity Cancellation Problems

Giacomo Innocenti,Paolo Paoletti

doi:10.1155/2015/319761

Abstract

When dealing with linear systems feedback interconnected with memoryless nonlinearities, a natural control strategy is making the overall dynamics linear at first and then designing a linear controller for the remaining linear dynamics. By canceling the original nonlinearity via a first feedback loop, global linearization can be achieved. However, when the controller is not capable of exactly canceling the nonlinearity, such control strategy may provide unsatisfactory performance or even induce instability. Here, the interplay between accuracy of nonlinearity approximation, quality of state estimation, and robustness of linear controller is investigated and explicit conditions for stability are derived. An alternative controller design based on such conditions is proposed and its effectiveness is compared with standard methods on a benchmark system.

Highlights

Introduction and MotivationsOne of the most prolific areas of interest in the nonlinear control theory deals with the existence of coordinate changes and nonlinear inputs which are capable of making the complete system linear, so that the mathematical tools of the linear control framework can be successfully exploited
When dealing with linear systems feedback interconnected with memoryless nonlinearities, a natural control strategy is making the overall dynamics linear at first and designing a linear controller for the remaining linear dynamics
The extension to generic systems, for which only an output y = g(x) is measurable, is known as output feedback linearization and it exploits a linearizing control input of the form u = a(x) + b(x)w to make the relationship between the output y and the new input w linear

Summary

Introduction and Motivations

One of the most prolific areas of interest in the nonlinear control theory deals with the existence of coordinate changes and nonlinear inputs which are capable of making the complete system linear, so that the mathematical tools of the linear control framework can be successfully exploited. These techniques analyze the equilibrium stability by exploiting the closed loop form that features the feedback interconnection between a linear subsystem and a static nonlinearity satisfying a sector condition. The originating method of this family is the circle criterion Since these techniques explicitly take into account the nonlinearity ε, that is, the cancellation residual, their results are partially based on the knowledge of the interplay between controller and observer. This advantage vanishes by the very complicated dependence of the linear subsystem properties from K and L that prevents their explicit computation. The induced norm ‖H‖2,2 is referred to as the H∞-norm of H

An Alternative Control Strategy

Example

Conclusions