Abstract
Tracking of reference signals is addressed in the context of a class of nonlinear controlled systems modelled by r-th-order functional differential equations, encompassing inter alia systems with unknown “control direction” and dead-zone input effects. A control structure is developed which ensures that, for every member of the underlying system class and every admissible reference signal, the tracking error evolves in a prescribed funnel chosen to reflect transient and asymptotic accuracy objectives. Two fundamental properties underpin the system class: bounded-input bounded-output stable internal dynamics, and a high-gain property (an antecedent of which is the concept of sign-definite high-frequency gain in the context of linear systems).
Highlights
Since its inception in 2002, the concept of funnel control has been widely investigated
An asymptotic and non-asymptotic tracking control objective has been achieved for a large class of nonlinear systems with “higher relative degree” described by functional differential equations that satisfy a high-gain property
A feedback strategy has been developed which is simple in the sense of funnel control and as “simple” as one may expect for higher relative degree
Summary
Since its inception in 2002, the concept of funnel control has been widely investigated. The approach considers the following basic question: for a given class of dynamical systems, with input u and output y, and a given class of reference signals yref , does there exist a single control strategy (generating u) which ensures that, for every member of the system class and every admissible reference signal, the output y approaches the reference yref with prescribed transient behaviour and prescribed asymptotic accuracy? The twofold objective of “prescribed transient behaviour and asymptotic accuracy” is encompassed by the adoption of a so-called “performance funnel” in which the error function t → e(t) := y(t) − yref (t) is required to evolve; see Fig. 1. A feedback strategy is developed which assures attainment of the above twofold performance objective: this is the core of the main result, Theorem 1.9. We proceed to highlight the features and distinguishing novelties of this result vis à vis the existing literature
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