Dynamic scaling and observer design with application to adaptive control

Immersion and invariance observers with time-delayed output measurements

“…However, as shown in the examples, in many cases of practical interest these equations turn out to be solvable. In [14] and [15], for the delay-free case, the authors present methodologies for selecting the functions β(·) and φ(·) for some classes of systems. These methods may be extended to the time-delayed case.…”

“…These methods may be extended to the time-delayed case. However, we remark that the aim of this manuscript is not to extend the methods presented in [14] or [15], but to show how the general I&I ideas introduced in [7] for designing observers may be extended when the output measurements are corrupted with time-delays.…”

“…which is negative definite for any κ > − 1 σ , and therefore the origin of the estimation error dynamics (14) with function β(·) as above is globally uniformly asymptotically stable. Then, the retarded observer (2) with l(·) as in (6) takes the following form 1.…”

Dynamic vs static scaling: an existence result

“…Preliminary results using this idea have been reported in Karagianis et al (2009);Ortner and Astolfi (2009), for the case of observer design and adaptive control and in Carnevale and Astolfi (2009), for the stabilization of simple cascades.…”

Constructive Interconnection and Damping Assignment for Port-Controlled Hamiltonian Systems

“…A similar approach has been exploited in [28] and [29] to solve optimal control/robust problems for nonlinear input-affine systems, in [14] for adaptive control problems and in [30] and [31] for the analysis of some properties of nonlinear control systems. This notion is instrumental for the construction of an auxiliary energy function defined in the extended state-space.…”