Search Results (21)

This paper addresses the critical multiple-uncertainty challenge in laser link acquisition for space gravitational wave detection missions—a key bottleneck where spacecraft attitude alignment for laser link establishment is perturbed by inherent random disturbances in such missions, while also needing to balance ultra-high attitude precision, fuel efficiency, and compliance with engineering constraints. To tackle this, a convex optimization-based attitude control strategy integrating covariance control and free terminal time optimization is proposed. Specifically, a stochastic attitude dynamics model is first established to explicitly incorporate the aforementioned random disturbances. Subsequently, an objective function is designed to simultaneously minimize terminal state error and fuel consumption, with three key constraints (covariance constraints, pointing constraints, and torque saturation constraints) integrated into the convex optimization framework. Furthermore, to resolve non-convex terms in chance constraints, this study employs a hierarchical convexification method that combines Schur’s complementary theorem, second-order cone relaxation, and Taylor expansion techniques. This approach ensures lossless relaxation, renders the optimization problem computationally tractable without sacrificing solution accuracy, and overcomes the shortcomings of traditional convexification methods in handling chance constraints. Finally, numerical simulations demonstrate that the proposed method adheres to engineering constraints while maintaining spacecraft attitude errors below 1 μrad under environmental uncertainties. This study provides a convex optimization solution for laser link acquisition in space gravitational wave detection missions considering uncertainty conditions, and its framework can be extended to the optimal design of other stochastically uncertain systems. Full article

The generalization of strongly convex and strongly m-convex functions is presented in this paper. We began by proving the properties of a strongly modified $(h,m)$-convex function. The Schur inequality and the Hermite–Hadamard (H-H) inequalities are proved for the proposed class. Moreover, H-H inequalities are also proved in the context of Riemann–Liouville (R-L) integrals. Some examples and graphs are also presented in order to show the existence of this newly defined class. Full article

This paper investigates the decentralized fuzzy control problems for nonlinear-state-unmeasured interconnected descriptor systems (IDSs) that utilize the observer-based-feedback approach and the proportional–derivative feedback control (PDFC) method. First of all, the IDS is represented as interconnected Takagi–Sugeno (T–S) fuzzy subsystems. These subsystems can effectively capture the dynamic behavior of the system through fuzzy rules. For the stability analysis of the system, this paper uses the free-weighing Lyapunov function (FWLF), which allows the designer to set the weight matrix, to achieve the desired control performance and design the controller more easily. Furthermore, the control problem can be transformed into a set of linear matrix inequalities (LMIs) through the Schur complement, which can be solved using convex optimization methods. Simulation results confirm the effectiveness of the proposed method in achieving the desired control objectives and ensuring system stability. Full article

In this paper, with the use of newly defined class up and down log–convex fuzzy-number valued mappings, we offer a few new and original mappings defined by applying some mild restrictions over the definition of up and down log–convex fuzzy-number valued mapping. With the use of these mappings, we are able to develop partners of Fejér-type inequalities for up and down log–convexity, which improve upon certain previously established findings. The discussion also includes these mappings’ characteristics. Moreover, some nontrivial examples are also provided to prove the validation of our main results. Full article

This paper discusses an observer-based control problem for uncertain Takagi–Sugeno Fuzzy Singular Systems (T-SFSS) subject to passivity performance constraints. Through the Parallel Distributed Compensation (PDC) approach and the Proportional Derivative (PD) control scheme, an observer-based fuzzy controller is constructed to achieve the stability of the considered system. An unlimited positive definite matrix is utilized to construct the Lyapunov function and derive sufficient stability conditions to develop a relaxed design method. Moreover, some technologies, such as the Schur complement, projection lemma, and Singular Value Decomposition (SVD), are applied to convert the conditions to Linear Matrix Inequality (LMI) form. Therefore, the convex optimization algorithm is used to solve the LMI conditions to find feasible solutions. The observer-based fuzzy controller is established with the obtained solutions to guarantee stability and passivity performance for the uncertain nonlinear singular systems. Finally, two examples are provided to verify the availability of the proposed fuzzy control approach. Full article

For an abelian topological group G, the sequence group ${\ell }^1\left(G\right)$ of all absolutely summable sequences in G is studied. It is shown that ${\ell }^1\left(G\right)$ is a Pontryagin reflexive group in case G is a reflexive metrizable group or an LCA group. Further, ${\ell }^1\left(G\right)$ has the Schur property if and only if G has it and ${\ell }^1\left(G\right)$ is a Schwartz group if and only if G is linearly topologized. Full article

The theory of symmetry has a significant influence in many research areas of mathematics. The class of symmetric functions has wide connections with other classes of functions. Among these, one is the class of convex functions, which has deep relations with the concept of symmetry. In recent years, the Schur convexity, convex geometry, probability theory on convex sets, and Schur geometric and harmonic convexities of various symmetric functions have been extensively studied topics of research in inequalities. The present attempt provides novel portmanteauHermite–Hadamard–Jensen–Mercer-type inequalities for convex functions that unify continuous and discrete versions into single forms. They come as a result of using Riemann–Liouville fractional operators with the joint implementations of the notions of majorization theory and convex functions. The obtained inequalities are in compact forms, containing both weighted and unweighted results, where by fixing the parameters, new and old versions of the discrete and continuous inequalities are obtained. Moreover, some new identities are discovered, upon employing which, the bounds for the absolute difference of the two left-most and right-most sides of the main results are established. Full article

Convexity is crucial in obtaining many forms of inequalities. As a result, there is a significant link between convexity and integral inequality. Due to the significance of these concepts, the purpose of this study is to introduce a new class of generalized convex interval-valued functions called $\left(p,s\right)$-convex fuzzy interval-valued functions ($\left(p,s\right)$-convex F-I-V-Fs) in the second sense and to establish Hermite–Hadamard (H–H) type inequalities for $\left(p,s\right)$-convex F-I-V-Fs using fuzzy order relation. In addition, we demonstrate that our results include a large class of new and known inequalities for $\left(p,s\right)$-convex F-I-V-Fs and their variant forms as special instances. Furthermore, we give useful examples that demonstrate usefulness of the theory produced in this study. These findings and diverse approaches may pave the way for future research in fuzzy optimization, modeling, and interval-valued functions. Full article

Jensen-type inequalities for the recently introduced new class of $(h,g;m)$-convex functions are obtained, and certain special results are indicated. These results generalize and extend corresponding inequalities for the classes of convex functions that already exist in the literature. Schur-type inequalities are given. Full article

We solve the Pauli tomography problem for Gaussian signals using the notion of Schur complement. We relate our results and method to a notion from convex geometry, polar duality. In our context polar duality can be seen as a sort of geometric Fourier transform and allows a geometric interpretation of the uncertainty principle and allows to apprehend the Pauli problem in a rather simple way. Full article

It is a familiar fact that inequalities have become a very popular method using fractional integrals, and that this method has been the driving force behind many studies in recent years. Many forms of inequality have been studied, resulting in the introduction of new trend in inequality theory. The aim of this paper is to use a fuzzy order relation to introduce various types of inequalities. On the fuzzy interval space, this fuzzy order relation is defined level by level. With the help of this relation, firstly, we derive some discrete Jensen and Schur inequalities for convex fuzzy interval-valued functions (convex fuzzy-IVF), and then, we present Hermite–Hadamard inequalities ($HH$-inequalities) for convex fuzzy-IVF via fuzzy interval Riemann–Liouville fractional integrals. These outcomes are a generalization of a number of previously known results, and many new outcomes can be deduced as a result of appropriate parameter “$\gamma$” and real valued function “$\Omega$” selections. We hope that our fuzzy order relations results can be used to evaluate a number of mathematical problems related to real-world applications. Full article

The matrix eigenvalue is very important in matrix analysis, and it has been applied to matrix trace inequalities, such as the Lieb–Thirring–Araki theorem and Thompson–Golden theorem. In this manuscript, we obtain a matrix eigenvalue inequality by using the Stein–Hirschman operator interpolation inequality; then, according to the properties of exterior algebra and the Schur-convex function, we provide a new proof for the generalization of the Lieb–Thirring–Araki theorem and Furuta theorem. Full article