Further Results on Output Regulation by Pure Error Feedback

Abstract

This work addresses the design of internal model-based regulators for nonlinear systems by error feedback in the general "non-equilibrium" framework proposed in (Byrnes and Isidori, 2003). The material presented here is specifically meant to complement the work in (Byrnes and Isidori, 2004) where a procedure for designing nonlinear internal model-based regulators was presented for systems having relative degree 1.

Remote tracking via encoded information for nonlinear systems

“…If this is the case and if the initial conditions of the plant are allowed to vary on a fixed (though arbitrarily large) compact set, there is no loss of generality in considering the case in which the controlled plant has relative degree 1 (see for instance [1]). We henceforth suppose that system (1) is expressed in the formż…”

Bifurcations caused by non-affinity of singularly perturbed control systems

“…The numerous research efforts on solution of nonlinear system stabilization problem have been done during the last few decades. Various methodologies are available for controller design of affine-incontrol systems, for instance, [1]- [3].…”

Output Stabilization via Nonlinear Luenberger Observers

“…This assumption has been substantially weakened in [5] (see also [6] and [4]) by simply asking that the positive orbit of the set of initial conditions under the flow of (15) be bounded (which is, in turn, equivalent to the existence of a compact set A, having the properties indicated above, which is the graph of a set-valued map π). Of course, it is apparent that all these cases fit into the framework presented in section 2.1.…”

“…In this context, it is important to note that the proposed framework encompasses a number of problems which have been recently addressed (see, among others, [25,31,11,5,4,12]), all relying upon various versions of the so-called "minimum-phase" and "immersion" assumptions.…”

“…Standard backstepping arguments (see, e.g., [4] and also [11]) show the existence of matrix K such that, in the systeṁ…”