In this article we consider the sequences of sample and population covariance operators for a sequence of arrays of Hilbertian random elements. Then under the assumptions that sequences of the covariance operators norm are uniformly bounded and the sequences of the principal component scores are uniformly sumable, we prove that the convergence of the sequences of covariance operators would impl...

This letter proposes an adaptive neural network-based backstepping controller that uses rigid graph theory to address the distance-based formation control problem and target tracking for nonlinear multi-agent systems with bounded time-delay disturbance. The radial basis function network (RBFNN) is used overcome compensate unknown nonlinearity disturbance in system dynamics. effect of state agen...

We show that any collection of n-dimensional orbifolds with sectional curvature and volume uniformly bounded below, diameter bounded above, and with only isolated singular points contains orbifolds of only finitely many orbifold homeomorphism types. This is a generalization to the orbifold category of a similar result for manifolds proven by Grove, Petersen, and Wu. It follows that any Laplace ...

In this paper, an Adaptive Backstepping Neural Network control approach is used for a class of affine nonlinear systems which describe the pump model in the strict feedback form. The close loop signals are semi globally uniformly ultimately bounded and the output of the system is proven to follow a desired trajectory. Simulation results are presented to show the effectiveness of the approach pr...

This paper presents an adaptive fuzzy controller for a class of completely pure-feedback nonlinear systems. Takagi-Sugeno type fuzzy logic systems are used to approximate the unknown nonlinear functions. The controller synthesis is developed by the backstepping technique and the small gain approach. The closed-loop control system is proved to be semi-globally uniformly ultimately bounded (SGUUB...

This paper proposes a robust sliding mode observer for a class of linear uncertain systems to generate a reconstruction of faults. The state estimation error of the proposed observer is shown to be uniformly ultimately bounded with respect to a ball whose radius is a function of design parameters. An exact fault reconstruction scheme that is decoupled from the uncertainty is presented. In simul...

We consider a delayed Holling type II predator-prey system with birth pulse and impulsive harvesting on predator population at different moments. Firstly, we prove that all solutions of the investigated system are uniformly ultimately bounded. Secondly, the conditions of the globally attractive prey-extinction boundary periodic solution of the investigated system are obtained. Finally, the perm...