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A combined hybrid mixed and hybridizable discontinuous Galerkin method is formulated for the flow and transport equations. Convergence of the method is obtained by deriving optimal a priori error bounds in the L 2 norm in space. Since the velocity in the transport equation depends on the flow problem, the stabilization parameter in the HDG method is a function of the discrete velocity. In addition, a key ingredient in the convergence proof is the construction of a projection that is shown to satisfy optimal approximation bounds. Numerical examples confirm the theoretical convergence rates and show the efficiency of high order discontinuous elements. [ABSTRACT FROM AUTHOR]

In this paper, an alternative version of the quantum phase estimation is proposed, in which the Hadamard gates at the beginning are substituted by a quantum Fourier transform. This new circuit coincides with the original one, when the ancilla is initialized with 0 . With the help of a projection-based tensor decomposition and closed-form expressions of its exponential, this new method can be interpreted as a multiplier coupled to the Hamiltonian of the corresponding target unitary operator. Based on this observation, a recursive decomposition is derived. [ABSTRACT FROM AUTHOR]

A convergent numerical method for α -dissipative solutions of the Hunter–Saxton equation is derived. The method is based on applying a tailor-made projection operator to the initial data, and then solving exactly using the generalized method of characteristics. The projection step is the only step that introduces any approximation error. It is therefore crucial that its design ensures not only a good approximation of the initial data, but also that errors due to the energy dissipation at later times remain small. Furthermore, it is shown that the main quantity of interest, the wave profile, converges in L ∞ for all t ≥ 0 , while a subsequence of the energy density converges weakly for almost every time. [ABSTRACT FROM AUTHOR]

In this study, we establish a new inertial generalized viscosity approximation method and prove that the resulting sequence strongly converges to a common solution of a split generalized mixed equilibrium problem, fixed point problem for a finite family of nonexpansive mappings and hierarchical fixed point problem in real Hilbert spaces. As an application, we demonstrate the use of our main finding in compressed sensing in signal processing. Additionally, we include numerical examples to evaluate the efficiency of the suggested method and then conduct a comparative analysis of its efficiency with different methods. Our findings can be used in a variety of contexts to improve results.

In our previous works, using an exactly solvable model as an example, we demonstrated the validity of the reaction operator in the basic equation of spin chemistry. However, in those works, only recombination from the singlet state was considered, although the general relations allowed us to consider the general case. In this paper, such a general case is analyzed. The radical pair comes into contact in a mixed singlet-triplet state, and recombination proceeds from both the singlet and triplet states. The result obtained fully corresponds to the basic equation of spin chemistry. [ABSTRACT FROM AUTHOR]

Here, we consider a stationary inclusion in a real Hilbert space X, governed by a set of constraints K, a nonlinear operator A, and an element f ∈ X . Under appropriate assumptions on the data, the inclusion has a unique solution, denoted by u. We state and prove a covergence criterion, i.e., we provide necessary and sufficient conditions on a sequence { u n } ⊂ X , which guarantee its convergence to the solution u. We then present several applications that provide the continuous dependence of the solution with respect to the data K, A and f on the one hand, and the convergence of an associate penalty problem on the other hand. We use these abstract results in the study of a frictional contact problem with elastic materials that, in a weak formulation, leads to a stationary inclusion for the deformation field. Finally, we apply the abstract penalty method in the analysis of two nonlinear elastic constitutive laws. [ABSTRACT FROM AUTHOR]

In this article, we will investigate the boundedness of the Cauchy singular integral operator under Hölder norm. This boundedness can be obtained by improving the method used in the early proof of the famous 2P theorems (Plemelj-Sokhotski formula and Privalov-Muskhelishvili theorem) by Jinyuan Du, which deepens the 2P theorems. Then, various Cauchy singular integral operators on the system of curves or open arcs are also proved to be bounded. [ABSTRACT FROM AUTHOR]

In this study, we establish a new inertial generalized viscosity approximation method and prove that the resulting sequence strongly converges to a common solution of a split generalized mixed equilibrium problem, fixed point problem for a finite family of nonexpansive mappings and hierarchical fixed point problem in real Hilbert spaces. As an application, we demonstrate the use of our main finding in compressed sensing in signal processing. Additionally, we include numerical examples to evaluate the efficiency of the suggested method and then conduct a comparative analysis of its efficiency with different methods. Our findings can be used in a variety of contexts to improve results. [ABSTRACT FROM AUTHOR]

The flight control system for reusable launch vehicles has to work for an extensive flight envelope ranging from hypersonic to subsonic Mach numbers. Since the plant dynamics are highly nonlinear, time-varying, and coupled, classical controllers are designed for large stability margins about the linearised points. This limits the performance of the classical controller, and the design process is iterative and time-consuming. Hence adaptive controllers are designed to handle such complex systems using a standard quadratic Lyapunov function. The existing parameter update laws of the model reference adaptive control system are not robust to bounded disturbances and unmodelled dynamics. Hence this paper proposes modified controller parameter update laws using a rectangular projection operator and barrier Lyapunov function, ensuring robustness to structured and unstructured uncertainties. The rectangular projection-based control law provides that the controller parameters remain within the specified upper and lower limits, whereas the barrier Lyapunov-based controller maintains the trajectory also within the specified error limit. The effectiveness of the proposed update laws is demonstrated for the automatic landing phase of a reusable launch vehicle. [ABSTRACT FROM AUTHOR]

In this paper, we propose a self-adaptive derivative-free projection method for solving large-scale nonlinear monotone equations with convex constraints. The search direction satisfies the sufficient descent property, which is independent of any line search. Based on the Lipschitz continuity and monotonicity property, the proposed method is shown to be globally convergent. Moreover, the numerical results are reported to show the effectiveness of the proposed method by comparing with the existing current methods. [ABSTRACT FROM AUTHOR]

This article, published in Mathematical Notes, explores the minimal norm of a projection operator for linear interpolation on an n-dimensional ball. The author proves that the interpolation projection operator, with nodes coinciding with the vertices of a regular simplex inscribed in the boundary sphere, has the least norm. The article provides mathematical formulas and proofs to support this claim. The author also examines the relationship between the simplex and the minimal ellipsoid containing it. The article is written in a technical and mathematical language, aimed at researchers and mathematicians. The author acknowledges A. V. Akopyan for their assistance in proving Theorem 1. [Extracted from the article]

This paper investigates adaptive flight control design strategies which are robust to a wide range of both parametric and non-parametric uncertainties for a highly non-linear, time-varying and under-actuated launch vehicle system. In general, scheduled PID controllers are designed for the rigid body dynamics of the launch vehicle and structural filters/compensators are used to stabilize underactuated dynamics such as slosh and flexibility. In this work, two stable Lyapunov-based adaptive controllers are designed with full-state feedback. In the first controller, adapted gains are constrained to be within the limits defined by the user using a rectangular projection operator. In the second controller, tracking error is also constrained using a barrier Lyapunov function. States of the under-actuated dynamics and rigid body dynamics are estimated from the noisy attitude and attitude rate measurements using an extended Kalman filter. Tracking and regulation control studies are conducted to show the efficiency of the proposed controller update laws using different command signals. [ABSTRACT FROM AUTHOR]

In this paper, we propose a general framework that provides a unified convergence analysis of the derivative-free projection-based method (DFPM) for solving large-scale constrained nonlinear monotone equations. The new results provide a complete picture on the convergence guarantees of DFPM and cover the existing relevant convergence results as special cases. Preliminary numerical experiment results are also reported to show the numerical performance of six line search schemes used in the existing DFPM. [ABSTRACT FROM AUTHOR]

The conditional probability interpretation of quantum gravity has been criticized for violating the constraints of the theory and also not giving the correct expression for the propagator. We have shown that following Page’s proposal of constructing an appropriate projector for the stationary state of a closed system, we can arrive at the correct expression for the propagator by using conditional probability rule. Also, it is shown that a unitary evolution of states of a subsystem at local level may be a consequence of non-unitary projection of appropriate states at global level. [ABSTRACT FROM AUTHOR]

This paper describes a quadcopter manipulator system, an aerial robot with an extended workspace, its controller design, and experimental validation. The aerial robot is based on a quadcopter with a three degree of freedom robotic arm connected to the base of the vehicle. The work aims to create a stable airborne robot with a robotic arm that can work above and below the airframe, regardless of where the arm is attached. Integrating a robotic arm into an underactuated, unstable system like a quadcopter can enhance the vehicle's functionality while increasing instability. To execute a mission with accuracy and reliability during a real‐time task, the system must overcome the inter‐coupling effects and external disturbances. This work presents a novel design for a robust adaptive feedback linearization controller with a model reference adaptive controller and hardware implementation of the quadcopter manipulator system with plant uncertainties. The closed‐loop stability of the aerial robot and the tracking error convergence with the robust controller is analyzed using Lyapunov stability analysis. The quadcopter manipulator system is custom developed in the lab with an off‐the‐shelf quadcopter and a 3D‐printed robotic arm. The robotic system architecture is implemented using a Jetson Nano companion computer for autonomous onboard flight. Experiments were conducted on quadcopter manipulator system to evaluate the autonomous aerial robot's stability and trajectory tracking with the proposed controller. [ABSTRACT FROM AUTHOR]

Let { X n : n ∈ N } be a linear process with density function f (x) ∈ L 2 (R) . We study wavelet density estimation of f(x). Under some regular conditions on the characteristic function of innovations, we achieve, based on the number of nonzero coefficients in the linear process, the minimax optimal convergence rate of the integrated mean squared error of density estimation. Considered wavelets have compact support and are twice continuously differentiable. The number of vanishing moments of mother wavelet is proportional to the number of nonzero coefficients in the linear process and to the rate of decay of characteristic function of innovations. Theoretical results are illustrated by simulation studies with innovations following Gaussian, Cauchy and chi-squared distributions. [ABSTRACT FROM AUTHOR]

This paper presents a rapidly direct algorithm (RDA) to calculate explicit Fréchet derivatives (EFD) for marine controlled-source electromagnetic measurement (MCSEM) in a three-dimensional (1-D) transversely isotropic (TI) formation. By discretizing the Helmholtz equations about coupled potentials on Yee’s staggered grids by the 3-D finite volume method (FVM), we obtain a complex linear system about the unknown potentials excited by a mass of moving electric current sources. To efficiently determine electromagnetic (EM) fields, we introduce an interpolation operator and projection operator per receiver by using the direct solver PARDISO and 3-D Newtown interpolation. Based on this, the perturbation in goal conductivity is expressed as a piece-wise constant function according to block or pixel model. The spatial scattered electric currents will be decomposed into a series of electric current elements distributed on Yee’s grids due to the conductivity perturbation. We then discretize the scattered electric currents by 3-D FVM and obtain the new right-hand terms about the unknown scattered potentials. This allows for fast production of the linear relationship between the changes in the EM fields and the relative conductivity perturbation per block or pixel, ultimately resulting in the EFD of MCSEM responses. Numerical results demonstrate the efficiency and accuracy of this method. The 3-D pixel sensitivities are presented to further investigate the response characteristics of MCSEM in several cases.

Here, we consider a stationary inclusion in a real Hilbert space X, governed by a set of constraints K, a nonlinear operator A, and an element f∈X. Under appropriate assumptions on the data, the inclusion has a unique solution, denoted by u. We state and prove a covergence criterion, i.e., we provide necessary and sufficient conditions on a sequence {un}⊂X, which guarantee its convergence to the solution u. We then present several applications that provide the continuous dependence of the solution with respect to the data K, A and f on the one hand, and the convergence of an associate penalty problem on the other hand. We use these abstract results in the study of a frictional contact problem with elastic materials that, in a weak formulation, leads to a stationary inclusion for the deformation field. Finally, we apply the abstract penalty method in the analysis of two nonlinear elastic constitutive laws.

Copyright of Journal of Fuzhou University is the property of Journal of Fuzhou University, Editorial Department and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

A high-order Kalman filter for full-dimensional variables is proposed for a class of dynamic systems whose state model and measurement model are both nonlinear. The filter requires Taylor expansion of the system equations, and then performs Kronecker product operation on the linear part in the Taylor expansion. Finally, a linear dynamic model is achieved based on the full-dimensional vector formed by the state variables and the high-order dimension expansion variables. After designing the filter, the Kalman filter for the original state variables estimation was selected through the projection operator. The excellent performance of the novel filter is analyzed from the aspects of the information utilization of the state estimation value and the size of the state estimation error covariance matrix. The numerical verification is carried out by computer simulation. [ABSTRACT FROM AUTHOR]

We consider an abstract problem P in a metric space X which has a unique solution u ∈ X. Our aim in this current paper is two folds: first, to provide a convergence criterion to the solution of Problem P, that is, to give necessary and sufficient conditions on a sequence {un} ⊂ X which guarantee the convergence un → u in the space X; second, to find a Tyknonov triple T such that a sequence {un} ⊂ X is a T-approximating sequence if and only if it converges to u. The two problems stated above, associated to the original Problem P, are closely related. We illustrate how they can be solved in three particular cases of Problem P: a variational inequality in a Hilbert space, a fixed point problem in a metric space and a minimization problem in a reflexive Banach space. For each of these problems we state and prove a convergence criterion that we use to define a convenient Tykhonov triple T which requires the condition stated above. We also show how the convergence criterion and the corresponding T -well posedness concept can be used to deduce convergence and classical well-posedness results, respectively. [ABSTRACT FROM AUTHOR]

The aim of this paper is to propose a robust adaptive control for a quadrotor equipped with two manipulators constrained along a high voltage line (HVL). Due to the urgent need of the HVL to inspect, the quadrotor compared to humans has many advantages such as cost and less time, higher accuracy, access to impassable points, and most importantly, reducing human victims. In this paper, two manipulators are used to hang the quadrotor from the HVL and move along it such that the quadrotor can perform monitoring operations more accurately. The motion equations are derived for the constrained quadrotor by the Lagrangian method. A control law is derived based on inverse dynamics of reduced-form equations. A robust adaptive controller is proposed for control of the constrained quadrotor in the presence of dynamic uncertainties and external disturbances. The nonlinear terms in the dynamic model are approximated by radial basis function neural network (RBFNN) and adaptive laws based on the projection operator. Moreover, saturation functions are considered for inputs in the controller by an auxiliary system. Stability analysis of the closed-loop system is performed by the Lyapunov theory. In order to confirm the effectiveness of the proposed method, some numerical simulations are carried out. The simulation results show the quadrotor can move along the HVL in the presence of the dynamic model uncertainties and the external disturbances and satisfy the considered constraints. [ABSTRACT FROM AUTHOR]

The Dai-Kou method Dai and Kou (2013), [12] is efficient for solving unconstrained optimization problems. However, its modified variants are quite rare for constrained nonlinear monotone equations. In an attempt to address this, two adaptive versions of the scheme with new and efficient parameter choices are presented in this paper. The schemes are obtained by analyzing eigenvalues of a modified Dai-Kou iteration matrix and constructing two new directions, which are used in the scheme's algorithms. The new methods are derivative-free, which is an attribute required for handling problems with very large dimensions. Both methods also satisfy the required condition for analyzing global convergence in the literature. By applying mild conditions, it is shown that the schemes are globally convergent and description of their effectiveness is achieved through experiments with four effective schemes for solving constrained nonlinear monotone equations. Furthermore, the methods are applied to recover images that are contaminated by impulse noise in compressed sensing.

Psomopoulou defined and studied the Invariant submanifolds of a manifold with f(2ν + 3, −1)-structure. In this paper fa(2ν + 3, −1) structure has been defined and submanifolds, of a manifold with such a structure have been studied. Some interesting results have been stated and proved in this paper. [ABSTRACT FROM AUTHOR]

In this paper, neurodynamic approaches are proposed for solving nonsmooth distributed optimization problems under inequality and set constraints, that is to find the solution that minimizes the sum of local cost functions. A continuous-time neurodynamic approach is designed and its state solution exists globally and converges to an optimal solution of the corresponding distributed optimization problem. Then, a neurodynamic approach with event-triggered mechanism is considered for the purpose of saving communication costs, and then, the convergence and its Zeno-free property are proved. Moreover, to realize the practical application of the neurodynamic approach, a discrete-time neurodynamic approach is proposed to solve nonsmooth distributed optimization problems under inequality and set constraints. It is rigorously proved that the iterative sequence generated by the discrete-time neurodynamic approach converges to the optimal solution set of the distributed optimization problem. Finally, numerical examples are solved to demonstrate the effectiveness of the proposed neurodynamic approaches, and the neurodynamic approach is further applied to solve the ill-conditioned Least Absolute Deviation problem and the load sharing optimization problem. [ABSTRACT FROM AUTHOR]

In this paper, we consider a new class of quasi-variational inequalities, which is called the general quasi-variational inequality. Using the projection operator technique, we establish the equivalence between the general quasi-variational inequalities and the fixed point problems. We use this alternate formulation to propose some new inertial iterative schemes for solving the general quasi-variational inequalities. The convergence criteria of the new inertial projection methods under some appropriate conditions is investigated. Since the general quasi-variational inequalities include the quasi-variational inequalities, variational inequalities, complementarity problems and the related optimization problems as special cases, our results continue to hold for these problems. It is an interesting problem to compare the efficiency of the proposed methods with other known methods.

Nonlinear Dynamic Inversion(NDI) control has excellent rapidity and decoupling ability, unfortunately it lacks the essential robustness to disturbance. From the perspective of enhancing the robustness, an adaptive NDI method based on L1 adaptive structure is proposed. The L1 adaptive structure is introduced into the NDI control to enhance its robustness, which also guarantees the stability and expected dynamic performance of the system suffering from the disturbance influence. Secondly, the flight control law of the advanced aircraft is designed based on the present method to improve the robustness and fault tolerance of the flight control system. Finally, the effectiveness of the flight control law based on the present approach is verified under the fault disturbance. The results showed that the flight control law based on L1 adaptive NDI has excellent dynamic performance and strong robustness to parameter uncertainties and disturbances.

In this paper, we develop a control law for Functional Electrical Stimulation (FES) application fields. This work aims to command the knee joint movement of patients in the seated position suffering from neurological disorders that lead to a partial or total paralysis of the limb. For this purpose, we propose the synthesis of an adaptive continuous control that permits to the knee joint the tracking of a time-varying desired angle. The knee movement is represented by the dynamical model of the lower limb. The designed control ensures an asymptotic stability while considering constraints such as unknown model parameters, unknown perturbation effects and unknown spasticity and fatigue parameters. The applicability and the effectiveness of the designed control law are shown through the simulation results. [ABSTRACT FROM AUTHOR]

Let Xp be a modulated convergence space, that is, a modular space equipped with a sequential convergence structure. Given an element x of Xp, we consider the minimisation problem of finding x0 € K such that r(x-xo) = inffr(x-y): y € Kg, where r is a modular, and K is a subset of Xp. Such an element x0 is called a best approximant. We prove an existence of best approximants in a large class of modulated convergence spaces. We also investigate semicontinuity of the related modular projection which in general is a nonlinear multi-valued operator. Problems of finding best approximants are important in approximation theory and probability theory. In particular, we show how our results can be applied to the approximation of functions in variable Lebesgue spaces by rational functions. [ABSTRACT FROM AUTHOR]

The classical Dai–Kou scheme (SIAM J Optim 23(1):296–320, 2013), which is popularly referred to as CGOPT, represents one of the most numerically efficient methods for unconstrained optimization. This article exploits nice properties of the scheme together with the projection method to present an adaptive Dai–Kou type method for solving constrained system of nonlinear monotone equations. The new scheme utilizes the backtracking line search strategy by Zhang and Zhou (J Comput Appl Math 196:478–484, 2006) to determine the step-size in the algorithm. In addition, the scheme requires less memory to implement as it avoids computing Jacobian matrix. This attribute makes it an ideal choice for large-scale problems. Other attributes of the scheme include its ability to generate search directions that satisfy the vital condition for global convergence and its applications to signal and image reconstruction problems in compressive sensing. The global convergence of the new scheme is proved using basic assumptions and numerical experiments conducted suggests that the new approach has a clear edge over four iterative schemes in the literature. [ABSTRACT FROM AUTHOR]

In this article, an adaptive dynamic surface control approach is proposed for uncertain strict‐feedback systems (SFSs) to guarantee both the prescribed transient tracking performance and the asymptotic tracking while realizing the accurate parameter estimation. It is assumed that SFSs are subject to linearly parametric uncertainties in both the drift terms and the control coefficients. A new inequality on the arctangent function, which can be widely used in the robust or the adaptive control designs, is established. Owing to this inequality, nonlinear robust filters with arctangent functions are designed and embedded into the backstepping control algorithm to avoid the "differential explosion" problem. Moreover, an improved forgetting‐factor‐based parameter estimation error reconstruction mechanism is proposed. And the obtained parameter estimation errors are integrated into the adaptive laws to achieve the accurate parameter estimation. Furthermore, the projection operator is applied to avoid the singularity problem of the control law. Besides, an asymmetric error transformation is introduced to restrict the tracking error within the prescribed performance envelope. It is proved that the tracking error and the parameter estimation errors asymptotically converge to zero and the tracking error satisfies the prescribed transient performance. Finally, the effectiveness of the proposed control approach is validated in terms of the single‐link manipulator actuated by a brush DC motor. [ABSTRACT FROM AUTHOR]

A new design of a non-parametric adaptive approximate model based on Differential Neural Networks (DNNs) applied for a class of non-negative environmental systems with an uncertain mathematical model is the primary outcome of this study. The approximate model uses an extended state formulation that gathers the dynamics of the DNN and a state projector (pDNN). Implementing a non-differentiable projection operator ensures the positiveness of the identifier states. The extended form allows producing continuous dynamics for the projected model. The design of the learning laws for the weight adjustment of the continuous projected DNN considered the application of a controlled Lyapunov-like function. The stability analysis based on the proposed Lyapunov-like function leads to the characterization of the ultimate boundedness property for the identification error. Applying the Attractive Ellipsoid Method (AEM) yields to analyze the convergence quality of the designed approximate model. The solution to the specific optimization problem using the AEM with matrix inequalities constraints allows us to find the parameters of the considered DNN that minimizes the ultimate bound. The evaluation of two numerical examples confirmed the ability of the proposed pDNN to approximate the positive model in the presence of bounded noises and perturbations in the measured data. The first example corresponds to a catalytic ozonation system that can be used to decompose toxic and recalcitrant contaminants. The second one describes the bacteria growth in aerobic batch regime biodegrading simple organic matter mixture. • A non-parametric observer is realized on Differential Neural Networks (DNNs). • The observer is applied for a class of non-negative environmental systems. • The learning laws for the weight adjustment in these DNN are obtained with the Lyapunov-like approach. • The implementation of a non-differentiable projection operator ensures the positiveness of the observer states. • Attractive Ellipsoid Method has been applied to analyze the quality of the designed observer. [ABSTRACT FROM AUTHOR]

Copyright of Information & Control is the property of Gai Kan Bian Wei Hui and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

In this paper, a stochastic age-structured HIV/AIDS model with nonlinear incidence rates is proposed. It is of great importance to develop efficient numerical approximation methods to solve this HIV/AIDS model since most stochastic partial differential equations (SPDEs) cannot be solved analytically. From the perspective of biological significance, the exact solution of the HIV/AIDS model must be nonnegative and bounded. Then a modified explicit Euler–Maruyama (EM) scheme is constructed based on a projection operator. The EM scheme could preserves the nonnegativity of the numerical solutions and also make the numerical solutions not outside the domain of the exact solutions. The convergence results between the numerical solutions and the exact solutions are analyzed, and some numerical examples are given to verify our theoretical results. [ABSTRACT FROM AUTHOR]

A technique for coupling an intrusive and non-intrusive uncertainty quantification method is proposed. The intrusive approach uses a combination of polynomial chaos and stochastic Galerkin projection. The non-intrusive method uses numerical integration by combining quadrature rules and the probability density functions of the prescribed uncertainties. A stable coupling procedure between the two methods at an interface is constructed. The efficiency of the hybrid method is exemplified using hyperbolic systems of equations, and verified by numerical experiments. [ABSTRACT FROM AUTHOR]