Iterative learning fault-tolerant control for discrete-time nonlinear systems subject to stochastic actuator faults

This paper is concerned with an iterative learning fault-tolerant control strategy for discrete-time nonlinear systems where actuator faults arbitrarily occur. First, the stochastic faults occurring in multiplicative and additive manner are considered. Then, statistical behaviors of both faults-corrupted control signals from the actuator to the plant and faults-free ones from the iterative learning controller to the actuator are analyzed. Meanwhile, sufficient conditions of convergence for the proposed strategy are established by resorting to the time-weighted norm technique. Finally, two numerical examples are provided to illustrate the effectiveness and reliability of the proposed results. Both theoretical analysis and simulations indicate that the developed strategy is satisfactory in preserving decent tracking accuracy of the addressed systems subject to actuator faults.

Approximation Properties of Chebyshev Polynomials in the Legendre Norm

In this paper, we present some important approximation properties of Chebyshev polynomials in the Legendre norm. We mainly discuss the Chebyshev interpolation operator at the Chebyshev–Gauss–Lobatto points. The cases of single domain and multidomain for both one dimension and multi-dimensions are considered, respectively. The approximation results in Legendre norm rather than in the Chebyshev weighted norm are given, which play a fundamental role in numerical analysis of the Legendre–Chebyshev spectral method. These results are also useful in Clenshaw–Curtis quadrature which is based on sampling the integrand at Chebyshev points.

Weighted Norm Inequalities for Multilinear Fourier Multipliers with Mixed Norm

In this paper, weighted norm inequalities for multilinear Fourier multipliers satisfying Sobolev regularity with mixed norm are discussed. Our result can be understood as a generalization of the result by Fujita and Tomita by using the L r -based Sobolev space, 1 < r ≤ 2 with mixed norm.

Baskakov-Kantorovich operators reproducing affine functions

We present a new Kantorovich modi cation of Baskakov operators which reproduce a ne functions. We present an upper estimate for the rate of convergence of the new operators in polynomial weighted spaces and characterize all functions for which there is convergence in the weighted norm.

Accurate Reconstruction of the Radiation of Sparse Sources from a Small Set of Near-Field Measurements by Means of a Smooth-Weighted Norm for Cluster-Sparsity Problems

The aim of this contribution is to present an approach that allows to improve the quality of the reconstruction of the far-field from a small number of measured samples by means of sparse recovery using a relatively coarse grid for source positions (with sample spacing of the order of λ/8) compared to the grid usually required. In particular, the iterative method proposed employs a smooth-weighted constrained minimization, that guarantees a better probability of correct estimate of the sparse sources and an improved quality in the reconstruction, with a similar computational effort respect to the standard ℓ1 re-weighted minimization approach.

On the Approximation by Balázs–Szabados Operators

We present three new approximation properties of the Balázs–Szabados operators. Firstly, we prove that, in certain cases, these operators approximate some super-exponential functions on compact intervals. Next, we provide a new estimate of the error of approximation using a suitable modulus of continuity. Finally, we characterize the functions which can be uniformly approximated in the weighted norm of polynomial weight spaces.