Summary An adaptive prescribed performance control design procedure for a class of nonlinear pure‐feedback systems with both unknown vector parameters and unmodeled dynamics is presented. The unmodeled dynamics lie within some bounded functions, which are assumed to be partially known. A state transformation and an auxiliary system are proposed to avoid using the cumbersome formula to handle the nonaffine structure. Simultaneously, a parameter‐type Lyapunov function and L function are designed to ensure the prescribed performance of the pure‐feedback system. As illustrated by examples, the proposed adaptive prescribed performance control scheme is shown to guarantee global uniform ultimate boundedness. At the same time, this method not only guarantees the prescribed performance of the system but also makes the tracking error asymptotically close to a certain value or stable.

In this paper, the existence of solutions of fractional differential equations with integral boundary conditions is investigated. The upper and lower solutions combined with monotone iterative technique is applied. Problems of existence and unique solutions are discussed.

SummaryThis article investigates the finite‐time output feedback stabilization problem for a class of nonlinear time‐varying delay systems in the p‐normal form. First, a reduced‐order state observer is designed to estimate the unmeasurable state. Then, an output feedback controller is constructed, with the help of the finite‐time Lyapunov stability theorem, it is proved that the state of the resulting closed‐loop system converges to the origin in finite time. Two simulation examples are given to verify the effectiveness of the proposed scheme.

In this paper, we study boundary value problems of nonlinear fractional differential equations in a Banach Space E of the following form:where D 0 + denotes the Caputo fractional derivative, 0 < p, q ≤ 1. Some new results on the solutions are obtained, by the concept of measures of noncompactness and the fixed point theorem of Mönch type.MSC 2010 : 34B37, 34K10, 34L15, 34L30, 34A45

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In this paper, we consider the problem of Mittag-Leffler stabilization of fractional-order nonlinear systems with unknown control coefficients. With the help of backstepping design method, the stabilizing functions and tuning functions are constructed. The controller is designed to ensure that the pseudo-state of the fractional-order nonlinear system converges to the equilibrium. The effectiveness of the proposed method has been verified by some simulation examples.