Sufficient Conditions for Output Reference Tracking for Nonlinear Systems: a Contractive Approach

Abstract

This paper deals with a tracking problem for nonlinear systems. We present sufficient conditions for the state-feedback output tracking problem, in case of arbitrarily large constant references and arbitrarily large domain of attraction. We present an extension of forwarding-based control techniques applied in an incremental framework. Simulations of an academic example are presented to validate the results.

Sufficient Conditions for Global Integral Action via Incremental Forwarding for Input-Affine Nonlinear Systems

“…First, we provide a new extension of the forwarding design with exact change of coordinates [27, Section IV] in the incremental context. This extends our preliminary results published in [14] for the SISO case. Then, in Section IV, we propose an incremental version of the forwarding mod{L g V } approach first appeared in [33].…”

“…Definition 1 mainly states that any two trajectories of system (54) converge (exponentially) one to each other. Since we focused on time-invariant systems, a direct consequence of the δGES property is stated in the following lemma (see [14,Lemma 1]).…”

Harmonic internal models for structurally robust periodic output regulation

“…We conjecture that in order to achieve global results, incremental stability properties may need to be ensured. Preliminary results in this direction for the simple case of integral action have been investigated in [37].…”

About Robustness of Control Systems Embedding an Internal Model

“…In addition to uniform ultimate boundedness of the closed-loop system, Assumption 3 requires the perturbed controlled plant to satisfy a non-local incremental input-to-state stability property with respect to the exogenous signals w [33]. We remark that the same property can be also characterized in terms of convergent systems [34], and we refer the reader to [33]- [36] and the references therein for control design techniques ensuring that such property holds.…”