Funnel control -- a survey

TL;DR

This survey reviews the development and application of funnel control, a method ensuring prescribed transient and steady-state behavior for a broad class of dynamical systems using a simple, structurally based control strategy.

Contribution

It provides a comprehensive overview of funnel control's theoretical foundations, system classes it applies to, and recent advancements including PDE systems and input constraints.

Findings

Funnel control guarantees boundedness and error funnel adherence for various systems.

It applies to systems with arbitrary relative degree and PDE descriptions.

The survey discusses practical applications and input constraints.

Abstract

The methodology of funnel control was introduced in the early 2000s, and it has developed since then in many respects achieving a level of mathematical maturity balanced by practical applications. Its fundamental tenet is the attainment of prescribed transient and asymptotic behaviour for continuous-time controlled dynamical processes encompassing linear and nonlinear systems described by functional differential equations, differential-algebraic systems, and partial differential equations. Considered are classes of systems specified by structural properties - such as relative degree and stable internal dynamics - of the systems only, the precise systems' data are in general unknown; the latter reflects the property that in general any model of a dynamical process is not precise. Prespecified are: a funnel shaped through the choice of a smooth function and freely chosen by the designer, a fairly large class of smooth reference signals, and a system class satisfying certain structural properties. The aim is to design, based on the structural assumptions and the input and output information only, a single `simple' control strategy -- called the funnel controller -- so that its application to any system of the given class and to any reference signal results in feasibility of the funnel control objective: that is solutions of the closed-loop system do not exhibit blow-up in finite time, all variables are bounded, and -- most importantly -- the evolution of the error between the system's output and the reference signal remains within the prespecified funnel. In the Introduction, we describe the genesis of funnel control. After that, we investigate diverse system classes amenable to funnel control. Funnel control is shown for systems with arbitrary relative degree and systems described by partial differential equations. Finally, we discuss input constraints and applications.