Search

The paper studies the prescribed performance output regulation problem for a class of nonlinear uncertain strict-feedback systems which are driven by nonlinear exosystems. Fuzzy logic systems (FLSs) are used to approximate the unknown functions. A fuzzy adaptive observer is designed to estimate the system state. A fuzzy internal model is designed to reject disturbance. Simultaneously, a parameter-type Lyapunov function and L function are designed to ensure the prescribed performance of the system. As illustrated by example, the proposed prescribed performance fuzzy adaptive output feedback control scheme is shown to guarantee semi-globally uniformly ultimately bounded, and the dynamic performance and steady-state performance of the tracking error are dependent on the prescribed performance functions.

This paper considers the finite time state estimation problem of complex-valued bidirectional associative memory (BAM) neutral-type neural networks with time-varying delays. By resorting to the Lyapunov function approach, the Wirtinger inequality and the reciprocally convex approach, a delay-dependent criterion in terms of LMIs is established to guarantee the finite-time boundedness of the error-state system for the addressed system. Meanwhile, an effective state estimator is designed to estimate the network states through the available output measurements. Finally, a numerical example is presented to demonstrate the effectiveness of the proposed results.

The predictor-based control is known as an effective method to compensate input delays. Yet the traditional predictors, like Smith predictor, have poor robustness with respect to system disturbances. In this paper, with the consideration of future disturbances, a novel robust predictive scheme is developed for input delay systems subject to nonlinear disturbances. The Artstein reduction method is used to provide performance analysis of different predictor-based controllers, which shows that the proposed predictor-based controller can provide better disturbance attenuation than previous approaches in the literature for a wide range of disturbances.

In this paper, the mixed H 2/H ∞ control problem is investigated for a class of nonlinear discrete-time networked control systems with random network-induced delays, stochastic packet dropouts and probabilistic sensor faults. The packet dropouts process is modeled as a homogeneous Markov chains taking values in a finite state space. Network-induced delays occur in a random way with known upper bound. A set of stochastic variables are exploited to describe sensor faults with different probabilistic density functions. By using a delay-dependent Lyapunov functional, a mode-dependent mixed H 2/H ∞ controller is designed to guarantee both stochastic stability of the closed-loop system and the prescribed H2, H¥ control performances. Sufficient conditions for the existence of the mixed H 2/H ∞ controller are presented in terms of a series of LMIs. If these LMIs are feasible, then the modedependent mixed H 2/H ∞ controller can be obtained. A numerical example is given to demonstrate the effectiveness of the developed method.

We study the quotient of hypergeometric functions $\mu _a^* (r) = \frac{\pi } {{2\sin (\pi a)}}\frac{{F(a,1 - a;1;1 - r^3 )}} {{F(a,1 - a;1;r^3 )}},r \in (0,1) $ in the theory of Ramanujan’s generalized modular equation for a ∈ (0, 1/2], find an infinite product formula for µ1/3*(r) by use of the properties of µ a * and Ramanujan’s cubic transformation. Besides, a new cubic transformation formula of hypergeometric function is given, which complements the Ramanujan’s cubic transformation.

we study the monotonicity of certain combinations of the Gaussian hypergeometric functions F(−1/2, 1/2; 1; 1 − x c ) and F(−1/2 − δ, 1/2 + δ; 1;1 − x d ) on (0, 1) for given 0 < c ⩽ 5d/6 < ∞ and δ ∈ (−1/2, 1/2), and find the largest value δ 1 = δ 1(c, d) such that inequality F(−1/2, 1/2; 1; 1 − x c ) < F(−1/2 − δ, 1/2 + δ; 1; 1 − x d ) holds for all x ∈ (0, 1). Besides, we also consider the Gaussian hypergeometric functions F(a−1 −δ, 1-a+δ; 1;1 −x 3) and F(a−1, 1 −a; 1; 1−x 2) for given a ∈ [1/29, 1) and δ ∈ (a−1, a), and obtain the analogous results.

This paper investigates the problem of adaptive neural control for a class of strict-feedback stochastic nonlinear systems with multiple time-varying delays, which is subject to input saturation. Via the backstepping technique and the minimal learning parameters algorithm, the problem is solved. Based on the Razumikhin lemma and neural networks' approximation capability, a new adaptive neural control scheme is developed. The proposed control scheme can ensure that the error variables are semi-globally uniformly ultimately bounded in the sense of four-moment, while all the signals in the closed-loop system are bounded in probability. Two simulation examples are provided to demonstrate the effectiveness of the proposed control approach.

For x = (x 1, x 2, ..., x n ) ∈ ℝ + , the symmetric function ψ n (x, r) is defined by $$\psi _n (x,r) = \psi _n \left( {x_1 ,x_2 , \cdots ,x_n ;r} \right) = \sum\limits_{1 \leqslant i_1 < i_2 \cdots < i_r \leqslant n} {\prod\limits_{j = 1}^r {\frac{{1 + x_{i_j } }} {{x_{i_j } }}} } ,$$ , where r = 1, 2, ..., n and i 1, i 2, ..., i n are positive integers. In this article, the Schur convexity, Schur multiplicative convexity and Schur harmoni convexity of ψ n (x, r) are discussed. As applications, some inequalities are established by use of the theory of majorization.

In the article, we establish several Lazarevic and Cusa type inequalities involving the hyperbolic sine and cosine functions with two parameters. As applications, we find some new bounds for certain bivariate means.

This paper deals with the problem of decentralized \(\mathcal{L}_{2}\)–\(\mathcal{L}_{\infty}\) filtering for a class of interconnected (or large-scale) Markovian jump systems with constant time delays. The purpose is to present delay-dependent conditions for the existence of mode-dependent decentralized filters, which guarantees that the filtering error system is stochastically stable with a prescribed \(\mathcal{L}_{2}\)–\(\mathcal{L}_{\infty}\) disturbance attenuation level. Such a purpose is achieved by using a mode-dependent centralized Lyapunov functional together with the so-called Jensen’s inequality. The obtained synthesis conditions are expressed in terms of linear matrix inequalities (LMIs), which leads to a convex design method for the concerned filters. An example including numerical and simulation results is provided finally to illustrate the effectiveness of the proposed design method.

This paper addresses the H ∞ control problem for jumping delayed systems with two separable Markov processes. The objective is to design a controller such that the resulting closed-loop system is exponentially mean-square stable with a given decay rate and satisfies a prescribed H ∞ performance level. A decay-rate-dependent condition is obtained for the existence of admissible controllers in term of linear matrix inequalities. Two numerical examples are presented to demonstrate the effectiveness of the proposed method.

The problem of nonfragile robust H∞ filtering for a class of Takagi–Sugeno fuzzy time-delay systems is investigated in the paper. We design a fuzzy filter which can tolerate some level of the filter gain variations while ensuring both the robust stability and a prescribed H∞ performance level of the filtering error system. Delay-dependent sufficient conditions for the existence of such filters are obtained in terms of linear matrix inequalities, and an explicit expression of a desired filter is given.

The Schur convexity or concavity problem of the Gini mean values S(a, b; x, y) with respect to (x, y) ∈ (0, ∞) × (0, ∞) for fixed (a, b) ∈ ℝ × ℝ is still open. In this paper, we prove that S(a, b; x, y) is Schur convex with respect to (x, y) ∈ (0, ∞) × (0, ∞) if and only if (a, b) ∈ {(a, b): a ⩾ 0, b ⩾ 0, a + b ⩾ 1}, and Schur concave with respect to (x, y) ∈ (0, ∞) × (0, ∞) if and only if (a, b) ∈ {(a, b): b ⩽ 0, b ⩽ a, a + b ⩽ 1} ∩ {(a, b): a ⩽ 0, a ⩽ b, a + b ⩽ 1}.

In this note, we prove the partial regularity of stationary weak solutions for the Landau-Lifshitz system with general potential in four or three dimensional space. As well known, in general, since the constraint of the methods, in order to get the partial regularity of stationary weak solution of the Landau-Lifshitz system with potential, we need to add some very strongly conditions on the potential. The main difficulty caused by potential is how to find the equation satisfied by the scaling function, which breaks down the blow-up processing. We estimate directly Morrey’s energy to avoid the difficulties by blowing up.

The aim of this work is to prove the partial regularity of the harmonic maps with potential. The main difficulty caused by the potential is how to find the equation satisfied by the scaling function. Under the assumption on the potential we can obtain the equation, however, for a general potential, even if it is smooth, the partial regularity is still open.

Using the Alzer integral inequality and the elementary properties of the gamma function, a double inequality for gamma function is established, which is an improvement of Merkle's inequality.