Stable concurrent learning and control of dynamical systems is the subject adaptive control. Despite being an established field with many practical applications a rich theory, much development in for nonlinear revolves around few key algorithms. By exploiting strong connections between classical techniques recent progress optimization machine learning, we show that there exists considerable unt...

This paper presents a nonlinearly parameterized controller for the adaptive control of base-isolated buildings subjected to a set of near-fault earthquakes. The control scheme is based on discrete direct adaptive control, wherein the system response is minimized under parameter uncertainties. Stable tuning laws for the controller parameters are derived using the Lyapunov approach. The controlle...

Recently, through the use of parameterized fuzzy approximators, various adaptive fuzzy control schemes have been developed to deal with nonlinear systems whose dynamics are poorly understood. An important class of parameterized fuzzy approximators is constructed using radial basis function (RBF) as a membership function. However, some tuneable parameters in RBF appear nonlinearly and the determ...

A novel adaptive backstepping design for a class of nonlinearly parameterized systems with a triangular structure is proposed. Under the Lipschitz condition with respect to unknown parameters of the system, an effective adaptive controller is designed without the requirement on the compactness of the unknown parametric set. Especially, the proposed adaptive control enables the advantage of “tun...

A new framework to design immersion and invariance adaptive controllers for nonlinearly parameterized, nonlinear systems was recently proposed by the authors. The key step is the construction of a monotone mapping, via a suitable selection of a controller tuning function, which has to satisfy some integrability conditions—this translates into the need to solve a partial differential equation (P...

We present a framework for estimating states and parameters in systems that can be described by a detectable linear system perturbed by a nonlinear function of the states, exogenous signals, and a vector of unknown, constant parameters. The estimators designed in this framework consist of two interconnected modules: a parameter estimator that is constructed as though the states and the nonlinea...

The nonlinear Schrödinger equation with a third-order dispersive term is considered. Infinite families of embedded solitons, parameterized by the propagation velocity, are found through a gauge transformation. By applying this transformation, an embedded soliton can acquire any velocity above a certain threshold value. It is also shown that these families of embedded solitons are linearly stabl...