Adaptive immersion and invariance control for a class of electromechanical systems

Abstract

This paper proposes a control approach for a class of electromechanical systems based on immersion and invariance method. Two cases are considered: full information system and unknown parameters existence. Thereafter, two controllers are, respectively, proposed: stabilization control and adaptive control. The effectiveness of the obtained control schemes is illustrated via simulation of an example.

Sampled-data stabilisation of a class of state-delayed nonlinear dynamics

“…Several extensions and applicatisve results have been developed which identify a recognized control approach ( [2], [3], [4]). It was extended to the discrete-time domain in [5] in relation with adaptive control in presence of parameter uncertainties.…”

Adaptive interconnection and damping assignment passivity‐based control for linearly parameterized discrete‐time port controlled Hamiltonian systems via I&I approach

“…Recently in the literature, a new tool for designing asymptotically stabilizing and adaptive control laws for nonlinear systems called the Immersion and Invariance control method “I&I" has been proposed 19 . Indeed, in several papers, the I&I approach is used to design stabilizing controllers, 20‐22 while in some other works it is used to design adaptive controllers through establishing I&I parameter estimators 19,23‐36 . Nevertheless, there is not any adaptive I&I control study applied to the Hamiltonian systems.…”

“…More precisely, the I&I stabilization and the I&I adaptive control. Some studies use the I&I approach as a stabilizing controller [36][37][38] and some other studies use it as an adaptive controller by establishing I&I parameter estimation [39][40][41][42][43][44][45][46][47][48][49][50][51][52].…”

Immersion and invariance stabilization of strict-feedback dynamics under sampling

“…It relies on the idea of driving the trajectories of a nonlinear system towards the ones of an a-priori defined stable target dynamics while preserving their boundedness. Such an approach qualifies for its robustness with respect to higher order dynamics, applicability to real cases and simplicity, as illustrated in several practical domains (Mannarino & Mantegazza, 2014;Rabai, Mnasri, Khaled, & Gasmi, 2013). A first extension to nonlinear discrete-time systems in strict-feedback form was provided by Yalcin and Astolfi (2011).…”