Because of inaccuracy of modeling and parameters measurement, the controlled systems are subjected by the inaccuracy inevitably and the control of uncertain systems is studied by many researchers. Uncertain nonlinear systems partial state variables control technique is developed, and applied to single pendulum systems. In order to make a certain state variable asymptotically stable and adaptive...

We consider the asymptotic behavior of the solution of the non-local parabolic equation ut = (κ (u))rr + (κ (u))r r + f (u) (a+2πb ∫ 1 0 f (u)r dr) 2 , for 0 < r < 1, t > 0, with a homogeneous Dirichlet boundary condition. The equation is the so-called Ohmic-heating model, which comes from thermal electricity in this paper, u and f (u) represent the temperature of the conductor and the electric...

We present a results about convergence of products of row-stochastic matrices which are infinite to the left and all have positive diagonals. This is regarded as in inhomogeneous consensus process where confidence weights may change in every time step but where each agent has a little bit of self confidence. The positive diagonal leads to a fixed zero pattern in certain subproducts of the infin...

In this note, adaptive neural control is presented for a class of strict-feedback nonlinear systems with unknown time delays. Using appropriate Lyapunov–Krasovskii functionals, the uncertainties of unknown time delays are compensated for such that iterative backstepping design can be carried out. In addition, controller singularity problems are solved by using the integral Lyapunov function and...

This paper addresses the problem of global output feedback, link position tracking control of robot manipulators. Specifically, a robust, Lyapunov-based controller is designed to ensure that the link position tracking error is globally uniformly ultimately bounded despite the fact that only link position measurements are available in the presence of incomplete model information (i.e., parametri...

Let p ∈ (0, 1]. In this paper, the authors prove that a sublinear operator T (which is originally defined on smooth functions with compact support) can be extended as a bounded sublinear operator from product Hardy spacesH(R × R) to some quasi-Banach space B if and only if T maps all (p, 2, s1, s2)-atoms into uniformly bounded elements of B. Here s1 ≥ ⌊n(1/p− 1)⌋ and s2 ≥ ⌊m(1/p− 1)⌋. As usual,...

In this paperwepropose novel distributed adaptive controllers for leaderless synchronization in networks of identical discrete-time dynamical systems. Separate algorithms are developed for the cases of known and unknown control directions. Assuming that the directed network graph is strongly connected, it is proved that all agent outputs converge toward an emerging, unknown in advance, synchron...

The propose of this paper is to present a modified block iterative algorithm for finding a common element between the set of solutions of the fixed points of two countable families of asymptotically relatively nonexpansive mappings and the set of solution of the system of generalized mixed equilibrium problems in a uniformly smooth and uniformly convex Banach space. Our results extend many know...

A Liapunov theorem is introduced guaranteeing uniform boundedness and uniform ultimate boundedness for a timevarying nonlinear system _ x(t) = f(x(t); t). The study of uniform boundedness and uniform ultimate boundedness of particular classes of time-varying nonlinear systems _ x(t) = f(x(t); t) is reduced to the study of the corresponding timeinvariant frozen systems _ x(t) = f(x(t); ) for all...

This note describes the pleasant features that accrue in weighted settings when the partial sums of the operator-valued Fourier series corresponding to a multiplier function ψ : T → C are uniformly bounded in operator norm. This circle of ideas also includes a Tauberiantype condition on the multiplier function ψ sufficient to insure such uniform boundedness of partial sums. These considerations...