A method is proposed for designing controllers with arbitrarily small tracking error for uncertain, mismatched nonlinear systems in the strict feedback form. This method is another "synthetic input technique," similar to backstepping and multiple surface control methods, but with an important addition, /spl tau/-1 low pass filters are included in the design where /spl tau/ is the relative degree of the output to be controlled. It is shown that these low pass filters allow a design where the model is not differentiated, thus ending the complexity arising due to the "explosion of terms" that has made other methods difficult to implement in practice. The backstepping approach, while suffering from the problem of "explosion of terms" guarantees boundedness of tracking errors globally; however, the proposed approach, while being simpler to implement, can only guarantee boundedness of tracking error semiglobally, when the nonlinearities in the system are non-Lipschitz.

Dynamic surface control for a class of nonlinear systems

Implementation of backstepping becomes increasingly complex as the order of the system increases. This increasing complexity is mainly driven by the need to compute command derivatives at each step of the design, with the ultimate step requiring derivatives of the same order as the plant. This article addresses a modification that obviates the need to compute analytic derivatives by introducing command filters in the backstepping design. While the concept of the command filter has previously been introduced in the literature, the main contribution of this technical note is the rigorous analysis of the effect of the command filter on closed-loop stability and performance, and a proof of stability based on Tikhonov's theorem. The implementation approach includes a compensated tracking error that retains the standard stability properties of backstepping approaches.

Command Filtered Backstepping

Survey Constructive nonlinear control: a historical perspective

On the convergence of an extended state observer for nonlinear systems with uncertainty

In this document, we present the main ideas and results concerning high-gain observers and some of their applications in control. The introduction gives a brief history of the topic. Then, a motivating second-order example is used to illustrate the key features of high-gain observers and their use in feedback control. This is followed by a general presentation of high-gain-observer theory in a unified framework that accounts for modeling uncertainty, as well as measurement noise. The paper concludes by discussing the use of high-gain observers in the robust control of minimum-phase nonlinear systems.

https://onlinelibrary.wiley.com/doi/pdf/10.1002/rnc.3156

High-gain observers in nonlinear feedback control

An observer-based controller is designed to stabilize a fully linearizable nonlinear system. The system is assumed to be left-invertible and minimum-phase. The controller is robust to uncertainties in modelling the nonlinearities of the system. The design of the controller and the stability analysis employs the techniques of singular perturbations. A new ‘Tikhonov-like’ theorem is presented and used to analyse the system when the control is globally bounded.

Farzad Esfandiari

Papers

Output feedback stabilization of fully linearizable systems