Search

In this paper, two adaptive output feedback control schemes are proposed for a class of nonlinear systems with unmodeled dynamics and unmeasured states as well as unknown high-frequency gain. Radial basis function (RBF) neural networks (NNs) are used to approximate the unknown nonlinear functions. K-filters are designed to estimate the unmeasured states. An available dynamic signal is introduced to dominate the unmodeled dynamics. By introducing the dynamic surface control (DSC) method, the bounded condition of the approximation error is removed, and the tracking control is achieved. Moreover, the number of adjustable parameters and the complexity of the design are both reduced. By theoretical analysis, the closed-loop system is shown to be semi-globally uniformly ultimately bounded (SGUUB). Simulation results are provided to illustrate the effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]

In this study, a robust adaptive control is proposed for a class of strict-feedback state delayed non-linear systems with unmodelled dynamics and distributed time-varying delays using radial basis function neural networks. Dynamic uncertainties are dealt with using separation technique and introducing a dynamic signal. The terms including state time-varying delay and distributed time-varying delay uncertainties are compensated for by constructing appropriate Lyapunov-Krasovskii functionals. Using Young's inequality, only one learning parameter need to be tuned online at each step of recursion. It is proved that the proposed design method is able to guarantee semi-global uniform ultimate boundedness of all signals in the closed-loop system. Simulation results demonstrate the effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]

The high-dimensional D. H. Lehmer problem over quarter intervals is studied. By using the properties of character sum and the estimates of Dirichlet L-function, the previous result is improved to be the best possible in the case of q = p, an odd prime with p = 1(mod 4), which is shown by studying the mean square value of the error term. [ABSTRACT FROM AUTHOR]

In this paper we study the relationship between the generalized Lucas polynomials and the Euler numbers and give several interesting identities involving them. [ABSTRACT FROM AUTHOR]

In this paper, adaptive neural network (NN) tracking control is investigated for a class of uncertain multiple-input-multiple-output (MIMO) nonlinear systems in triangular control structure with unknown nonsymmetric dead zones and control directions. The design is based on the principle of sliding mode control and the use of Nussbaum-type functions in solving the problem of the completely unknown control directions. It is shown that the dead-zone output can be represented as a simple linear system with a static time-varying gain and bounded disturbance by introducing characteristic function. By utilizing the integral-type Lyapunov function and introducing an adaptive compensation term for the upper bound of the optimal approximation error and the dead-zone disturbance, the closed-loop control system is proved to be semiglobally uniformly ultimately bounded, with tracking errors converging to zero under the condition that the slopes of unknown dead zones are equal. Simulation results demonstrate the effectiveness of the approach. [ABSTRACT FROM AUTHOR]