Nearfield acoustic holography in a moving medium based on particle velocity input using nonsingular propagator

Nearfield acoustic holography in a moving medium is a technique which is typically suitable for sound sources identification in a flow. In the process of sound field reconstruction, sound pressure is usually used as the input, but it may contain considerable background noise due to the interactions between microphones and flow moving at a high velocity. To avoid this problem, particle velocity is an alternative input, which can be obtained by using Laser Doppler Velocimetry in a non-intrusive way. However, there is a singular problem in the conventional propagator relating the particle velocity to the pressure, and it could lead to significant errors or even false results. In view of this, in this paper nonsingular propagators are deduced to realize accurate reconstruction in both cases that the hologram is parallel to and perpendicular to the flow direction. The advantages of the proposed method are analyzed, and simulations are conducted to verify the validation. The results show that the method can overcome the singular problem effectively, and the reconstruction errors are at a low level for different flow velocities, frequencies, and signal-to-noise ratios.

Ingularly perturbed equations in critical cases

Singularly perturbed partial differential equations with small parameters with higher derivatives deserve special attention, which often arise in a variety of applied problems and are used in describing mathematical models of diffusion processes, absorption taking into account small diffusion, filtration of liquids in porous media, chemical kinetics, chromatography, heat and mass transfer, hydrodynamics and many other fields. It is necessary to consider the creation of an asymptotic classification of solutions of singularly perturbed equations using a well-known approach to solving the boundary value problem. In this case, the singular problem is understood as the problem of constructing the asymptotics of the solution of the Cauchy problem for a system of ordinary differential equations with a small parameter with a large derivative. The asymptotics of the solution in all cases is based on the last time interval or the construction of a boundary value problem for a system with a weak clot in an asymptotically large time interval. Purpose - to construct and substantiate the asymptotics of solving a singular initial problem for a system of two nonlinear ordinary differential equations with a small parameter; To date, a number of methods have been developed for constructing asymptotic expansions of solutions to various problems. This is the method of boundary functions developed in the works of A.B. Vasilyeva, M.I. Vishik, L.A. Lusternik, V.F. Butuzov; the regularization method of S. A. Lomov, methods of averaging, VKB, splicing of asymptotic decompositions of A.M. Ilyin and others. All the above methods allow us to obtain asymptotic expansions of solutions for wide classes of equations. At the same time, such singularly perturbed problems often arise, to which ready-made methods are not applicable or do not allow to obtain an effective result. Therefore, the development of methods for solving equations remains a very urgent problem. As a result of the study, an algorithm for constructing an asymptotic classification of the initial solution of the problem with a singular perturbation is given, and approaches to estimating the residual term are also shown.

Guidance and control with fixed-time convergence for an interception missile

This article deals with the problem of partial integrated guidance and control (IGC) design with fixed-time convergence. First of all, two new fixed-time stability systems are proposed, and a novel nonsingular terminal sliding mode with fixed-time convergence is constructed by switching the exponential term of system state variables, which can realize the transition from finite-time convergence to fixed-time convergence. Concurrently, in order to solve the singular problem of terminal sliding mode, a continuous piecewise function is used in the sliding mode surface design. Then, a novel nonsingular terminal sliding mode control with fixed-time convergence is proposed for partial IGC design; that is, the upper-bound of convergence time is independent of the initial states of both missile and target and can be set in advance. In addition, a radial basis function neural network (RBFNN) is used to adaptively estimate and compensate for the uncertainties caused by the target’s maneuvering, so that the design of fixed-time sliding mode controller does not need to know any information about the target maneuver in advance, which enables the proposed controller to be better with robustness. Finally, the effectiveness and merits of the proposed control strategy are shown by the numerical simulation results based on the nonlinear longitudinal model of missile.

Discontinuous perturbations of nonhomogeneous strongly-singular Kirchhoff problems

In this paper, we are concerned with a Kirchhoff problem in the presence of a strongly-singular term perturbed by a discontinuous nonlinearity of the Heaviside type in the setting of Orlicz–Sobolev space. The presence of both strongly-singular and non-continuous terms brings up difficulties in associating a differentiable functional to the problem with finite energy in the whole space $$W_0^{1,\Phi }(\Omega )$$ W 0 1 , Φ ( Ω ) . To overcome this obstacle, we establish an optimal condition for the existence of $$W_0^{1,\Phi }(\Omega )$$ W 0 1 , Φ ( Ω ) -solutions to a strongly-singular problem, which allows us to constrain the energy functional to a subset of $$W_0^{1,\Phi }(\Omega )$$ W 0 1 , Φ ( Ω ) in order to apply techniques of convex analysis and generalized gradient in the sense of Clarke.

Adaptive neural network control of second-order underactuated systems with prescribed performance constraints

This paper studies the trajectory tracking control problem of second-order underactuated system subject to system uncertainties and prescribed performance constraints. By combining radial basis function neural networks (RBFNNs) with input–output linearization methods, an adaptive neural network-based control approach is proposed and the adaptive laws are given through Lyapunov method and Taylor expansion linearization approach. The main contributions of this paper are that: (1) by introducing weight performance function and transformation function, the states never violate the prescribed performance constraints; (2) the control scheme takes the unknown control gain direction into consideration and the singular problem of control design can be avoided; (3) through rigorously stability analysis, all signal of closed-loop system are proved to be uniformly ultimately bounded. The effectiveness of the proposed control scheme was verified by comparative simulation.

Drug places and spaces of problematisation: the melancholy case of a Hungarian needle exchange programme

Purpose This paper aims to explore multiple problematisation processes through a former needle exchange programme run by Kék Pont (a non-governmental organisation) in the 8th district of Budapest. By presenting a collage of ethnographic stories, this paper attempts to preserve tacit knowledge associated with the programme and thereby keep its office alive as a “drug place”, the operation of which was made impossible in 2014. Design/methodology/approach Drawing on the insights of Foucauldian governmentality studies and actor-network theory, this paper focusses on drug use as a problem in its spatial-material settings. Based on ethnographic fieldwork, the contribution traces multiple problematisation processes and related infrastructures. Findings From the needle exchange programme’s perspective, drug use is not a singular problem but the effect of multiple problematisation processes. Although those processes are often in conflict with each other, the question is not which one is right, but how social workers manage to hold them together. It is a fragile achievement that requires years of training and ongoing negotiation with local actors. By eliminating Kék Pont’s 8th district office, the Hungarian Government did not only hinder harm reduction in the area but it had also rendered tacit knowledge associated with the needle exchange programme as a “drug place” inaccessible. Originality/value The paper is a melancholy intervention – an attempt to preserve tacit knowledge that had accumulated at the needle exchange programme. The retelling of ethnographic stories about this “drug place” is one way of ensuring that other drug policies remain imaginable.

A Novel Analytical Inverse Kinematics Method for SSRMS-Type Space Manipulators Based on the POE Formula and the Paden-Kahan Subproblem

Space manipulators which have a similar symmetrical structure with seven revolute joints, such as the space station remote manipulator system (SSRMS), can be called SSRMS-type space manipulators. The analytical inverse kinematics of an SSRMS-type manipulator can be solved by locking a single joint; the locked joint (joint 1, 2, 6, or 7) can be determined by configuration analysis. Although widely used in establishing the kinematics of SSRMS-type manipulators, the Denavit-Hartenberg (DH) method has a singular problem when two adjacent joint axes are nearly parallel. To avoid this problem, this paper proposes a novel analytical inverse kinematics method for SSRMS-type manipulators based on the product of exponentials (POE) formula and the Paden-Kahan subproblem. Because of the symmetrical structure, an SSRMS-type manipulator degrades to two kinds of 6-degree-of-freedom (DOF) manipulators when locking a single joint (joint 1, 2, 6, or 7). The analytical inverse kinematics of these two kinds of 6-DOF manipulators is solved by combining the Paden-Kahan subproblems and geometric and algebraic methods, respectively. The proposed approach is not only singularity free compared with the traditional DH-based methods but also more accurate than the POE-based numerical solution. The simulation results verify the efficiency of the proposed approach.