Second-order Problems Research Articles

Constrained Moving Path Following Control for UAV With Robust Control Barrier Function

This paper studies the moving path following (MPF) problem for fixed-wing unmanned aerial vehicle (UAV) under output constraints and wind disturbances. The vehicle is required to converge to a reference path moving with respect to the inertial frame, while the path following error is not expected to violate the predefined boundaries. Differently from existing moving path following guidance laws, the proposed method removes complex geometric transformation by formulating the moving path following problem into a second-order time-varying control problem. A nominal moving path following guidance law is designed with disturbances and their derivatives estimated by high-order disturbance observers. To guarantee that the path following error will not exceed the prescribed bounds, a robust control barrier function is developed and incorporated into controller design with quadratic program based framework. The proposed method does not require the initial position of the UAV to be within predefined boundaries. And the safety margin concept makes error-constraint be respected even if in a noisy environment. The proposed guidance law is validated through numerical simulations of shipboard landing and hardware-in-the-loop (HIL) experiments.

A finite element-scaled boundary finite element coupled method for corner singularities in 2D second-order radiation problems

In potential flow analyses, singularities at the corners of bodies lead to erroneous pressure integrations and unsolved high-order velocity potentials. While much research has been devoted to addressing the former difficulty, fewer solutions have been proposed for the latter. In non-linear problems, higher derivatives are required on the boundaries, but usually, they are inaccurate and even singular at the corners. This paper introduces a coupling method that combines the scaled boundary finite element method (SBFEM) and the finite element method (FEM) to overcome this challenge. The SBFEM is semi-analytic and can accurately describe the singularities; the FEM is enhanced with Adini elements to achieve higher continuity. By integrating them, the proposed method allows for evaluating second derivatives on the body surface. The singular boundary conditions at the corners are automatically satisfied by the SBFEM, enabling the well-posed solution of boundary value problems (BVPs). The implementation of the proposed method is demonstrated through the solution of the second-order radiation problem of a rectangular box, with fine convergence observed for the first- and second-order velocity potentials and their gradients. The method also provides accurate and efficient direct pressure integrations for second-order wave forces, with results in good agreement with established indirect methods.

Optimization of Mobile Robotic Relay Operation for Minimal Average Wait Time

This paper considers trajectory planning for a mobile robot which persistently relays data between pairs of far-away communication nodes. Data accumulates stochastically at each source, and the robot must move to appropriate positions to enable data offload to the corresponding destination. The robot needs to minimize the average time that data waits at a source before being serviced. We are interested in finding optimal robotic routing policies consisting of 1) locations where the robot stops to relay (relay positions) and 2) conditional transition probabilities that determine the sequence in which the pairs are serviced. We first pose this problem as a non-convex problem that optimizes over both relay positions and transition probabilities. To find approximate solutions, we propose a novel algorithm which alternately optimizes relay positions and transition probabilities. For the former, we find efficient convex partitions of the non-convex relay regions, then formulate a mixed-integer second-order cone problem. For the latter, we find optimal transition probabilities via sequential least squares programming. We extensively analyze the proposed approach and mathematically characterize important system properties related to the robot’s long-term energy consumption and service rate. Finally, through extensive simulation with real channel parameters, we verify the efficacy of our approach.

Peacocks, Penknives and Power

ABSTRACT This article conceptualizes evolutionary theory as a bridge between existing theorizing in strategic communication on the one hand, the mind sciences on the other. It discusses six core concepts of evolutionary psychology that have a bearing on strategic communication theory: a) the human as a highly flexible social species; b) the regulation of individually-minded vs. collectively-minded behavior; c) advanced, symbolic communication as a mode of regulation and its second-order problems; d) a consilient conceptualization of communication; e) evolutionary psychology’s role as a heuristic; and f) the limits of cognitive capacity and the role of heuristic shortcuts. The article concludes with a note on the theory of science in strategic communication research and cautions against the common misunderstanding of evolutionary psychology’s agenda.

Social exclusion with antisocial punishment in spatial public goods game

In the spatial public goods game (SPGG), social exclusion is an effective strategy to quickly promote group cooperation. However, the second-order free riding occurs among cooperators who do not bear additional exclusion costs in the process of exclusion. To ensure that the exclusion strategy works while solving the second-order free-riding problem, we introduce an antisocial punishment strategy. The model employs four counterbalancing strategies: pure cooperators invest into the public pool; the defectors are the first-order free-riders of the cooperators; the excluders restrict the defectors from riding the cooperators with a certain probability, and the excluded defectors cannot share the benefits of the common pool; and the antisocial punishers punish the cooperators. Through the Monte Carlo simulations, we found that the cooperative excluders protected the cooperators from invasion by defectors and defective punishers, and more importantly, the second-order free-riding problem of the system was eliminated by the defective punishers.

Blow-up of Solutions and Local Solvability of an Abstract Cauchy Problem of Second Order with a Noncoercive Source

Blow-up of Solutions and Local Solvability of an Abstract Cauchy Problem of Second Order with a Noncoercive Source

Blow-up of Solutions and Local Solvability of an Abstract Cauchy Problem of Second Order with a Noncoercive Source

An abstract Cauchy problem for a second-order differential equation with nonlinear operator coefficients is considered. The local solvability of the problem in suitable spaces of abstract continuous and differentiable functions is proved. Sufficient conditions for finite-time blow-up of its solutions are obtained.

An Irregular Tiled Array Technique for Microwave Wireless Power Transmission

An irregular tiled array technique with the maximization of beam collection efficiency (BCE) for microwave wireless power transmission (WPT) is addressed in this paper, where the radiating elements are irregularly partitioned into multiple subarrays for reducing the number of radio frequency (RF) chain. The system architectures of WPT based on irregular tiled arrays are analyzed for the exhibition of its low-cost advantages. To achieve a good trade-off between the manufacturing cost and beampattern, a mixed-integer optimization problem (MIOP) accounting for the maximization of BCE satisfying the subarray tiling configuration, scanning direction and peak sidelobe level (SLL) constraints is established. By equivalently reformulating the beampattern, the MIOP in terms of subarray tiling configuration and subarray excitations is decoupled, and a two-stage solution method can be implemented. Firstly, resort to ‘generalized BCE’, the binary quadratic optimization problem (BQOP) for maximizing the BCE at considered scanning angles while guaranteeing the full aperture coverage is reduced to a binary second-order cone optimization problem. After the subarray tiling configuration is determined, the non-convex Rayleigh entropy maximization problem at a given scanning angle with respect to subarray complex excitations while satisfying peak SLL constraint is globally solved by using iterative convex approximation algorithm. Owing to the high efficiency of convex optimization, the BCE is able to monotonically increase to a stable value. Several numerical results with different array size and subarray shapes are provided to assess the effectiveness of the proposed method by comparing to the competitive counterparts in the open literatures.

Optimal conditions for the maximum principle for second-order periodic problems

We provide alternate necessary and/or sufficient conditions on the sign-changing coefficient p(t) for the maximum principle for the second-order periodic problem \(u''=p(t) u + q(t) \) to hold, i.e., for nonnegative \(q\) to yield a nonpositive periodic solution \(u\). See also https://ejde.math.txstate.edu/special/02/h2/abstr.html

Event-Triggered Sliding Mode Neural Network Controller Design for Heterogeneous Multi-Agent Systems

A class of heterogeneous second-order multi-agent consensus problems is studied, in which an event-triggered method is used to improve the feasibility of the control protocol. The sliding mode control method is used to achieve the robustness of the system. A special type of general radial basis function neural network is applied to estimate the uncertainties. The event-triggered mechanism is introduced to reduce the update frequency of the controller and the communication frequency among the agents. Zeno behavior is avoided by ensuring a lower bound between two adjacent trigger instants. Finally, the simulation results are provided to demonstrate that the time evolution of consensus errors eventually approaches zero. The consensus of multi-agent systems is achieved.

Solving SIVPs of Lane–Emden–Fowler Type Using a Pair of Optimized Nyström Methods with a Variable Step Size

This research article introduces an efficient method for integrating Lane–Emden–Fowler equations of second-order singular initial value problems (SIVPs) using a pair of hybrid block methods with a variable step-size mode. The method pairs an optimized Nyström technique with a set of formulas applied at the initial step to circumvent the singularity at the beginning of the interval. The variable step-size formulation is implemented using an embedded-type approach, resulting in an efficient technique that outperforms its counterpart methods that used fixed step-size implementation. The numerical simulations confirm the better performance of the variable step-size implementation.

Reproducing kernel-based piecewise methods for efficiently solving oscillatory systems of second-order initial value problems

Reproducing kernel-based piecewise methods for efficiently solving oscillatory systems of second-order initial value problems

A two-layer Crank–Nicolson linear finite element methods for second-order hyperbolic optimal control problems

In this paper, we consider a two-layer Crank–Nicolson scheme combined with linear finite element approximation for second-order hyperbolic optimal control problems with control constraints. For state and co-state variables, their time derivatives are first reduced to a first-order system then discretized by the two-layer Crank–Nicolson scheme and their space derivatives are discretized by linear finite elements. The control variable is dealt with variational discretization technique. Optimal priori error estimates for state, co-state and control variables are derived. Some numerical examples are presented to illustrate the theoretical convergence rate.

On the Simulations of Second-Order Oscillatory Problems with Applications to Physical Systems

Second-order oscillatory problems have been found to be applicable in studying various phenomena in science and engineering; this is because these problems have the capabilities of replicating different aspects of the real world. In this research, a new hybrid method shall be formulated for the simulations of second-order oscillatory problems with applications to physical systems. The proposed method shall be formulated using the procedure of interpolation and collocation by adopting power series as basis function. In formulating the method, off-step points were introduced within the interval of integration in order to bypass the Dahlquist barrier, improve the accuracy of the method and also upgrade the order of consistence of the method. The paper further validated the some properties of the hybrid method derived and from the results obtained; the new method was found to be consistent, convergent and stable. The simulation results generated as a result of the application of the new method on some second-order oscillatory differential equations also showed that the new hybrid method is computationally reliable.

Force Computation for Dielectrics Using Shape Calculus

Abstract We are concerned with the numerical computation of electrostatic forces/torques in only piece-wise homogeneous materials using the boundary element method (BEM). Conventional force formulas based on the Maxwell stress tensor yield functionals that fail to be continuous on natural trace spaces. Thus their use in conjunction with BEM incurs slow convergence and low accuracy. We employ the remedy discovered in [P. Panchal and R. Hiptmair, Electrostatic force computation with boundary element methods, SMAI J. Comput. Math. 8 (2022), 49–74]. Motivated by the virtual work principle which is interpreted using techniques of shape calculus, and using the adjoint method from shape optimization, we derive stable interface-based force functionals suitable for use with BEM. This is done in the framework of single-trace direct boundary integral equations for second-order transmission problems. Numerical tests confirm the fast asymptotic convergence and superior accuracy of the new formulas for the computation of total forces and torques.

Robust Control Allocation for Space Inertial Sensor under Test Mass Release Phase with Overcritical Conditions

This paper proposes a robust control allocation for the capture control of the space inertial sensor's test mass under overcritical conditions. Uncertainty factors of the test mass control system under the overcritical condition are analyzed first, and a 6-DOF test mass dynamics model with system uncertainty is established. Subsequently, a time-varying weight function is designed to coordinate the allocation of 6-DOF generalized forces. Moreover, a robust control allocation method is proposed to distribute the commanded forces and torques into individual electrodes in an optimal manner, which takes into account the system uncertainties. This method transforms the robust control allocation problem into a second-order cone optimization problem, and its dual problem is introduced to simplify the computational complexity and improve the solving efficiency. Numerical simulation results are presented to illustrate and highlight the fine performance benefits obtained using the proposed robust control allocation method, which improves capture efficiency, increases the security margin and reduces allocation errors.

Three-dimensional impact-angle-constrained cooperative guidance strategy against maneuvering target

In order to improve the multiple-missile cooperative attack capability and penetration capability, this paper investigates two three-dimensional impact-angle-constrained cooperative guidance strategies against maneuvering target for controllable thrust missiles. First, a three-dimensional nonlinear guidance model is established that does not assume small missile lead angles in the guidance process. Second, in the line-of-sight (LOS) direction of the cluster cooperative guidance strategy, the proposed guidance algorithm transforms the simultaneous attack problem into a second-order multiagent consensus problem, which effectively solves the practical problem of low guidance precision provoked by the time-to-go estimation. Then, by combining second-order sliding mode control (SMC) and nonsingular terminal SMC theory, the guidance algorithms in the normal and lateral directions to the LOS are designed, respectively, so that the multi-missile can accurately attack a maneuvering target while satisfying the impact angle constraints. Finally, by utilizing the second-order multiagent consensus tracking control in the leader-following cooperative guidance strategy, a novel leader-following time consistency algorithm is investigated to ensure that the leader and followers can attack the maneuvering target simultaneously. Moreover, the stability of the investigated guidance algorithms is proved mathematically. The effectiveness and superiority of the proposed cooperative guidance strategies are verified by numerical simulations.

Analytical uncertainty propagation for multi-period stochastic optimal power flow

The increase in renewable energy sources (RESs), like wind or solar power, results in growinguncertainty also in transmission grids. This affects grid stability through fluctuating energy supplyand an increased probability of overloaded lines. One key strategy to cope with this uncertainty isthe use of distributed energy storage systems (ESSs). In order to securely operate power systemscontaining renewables and use storage, optimization models are needed that both handle uncertaintyand apply ESSs. This paper introduces a compact dynamic stochastic chance-constrained DC optimalpower flow (CC-OPF) model, that minimizes generation costs and includes distributed ESSs. AssumingGaussian uncertainty, we use affine policies to obtain a tractable, analytically exact reformulation asa second-order cone problem (SOCP). We test the new model on five different IEEE networks withvarying sizes of 5, 39, 57, 118 and 300 nodes and include complexity analysis. The results showthat the model is computationally efficient and robust with respect to constraint violation risk. Thedistributed energy storage system leads to more stable operation with flattened generation profiles.Storage absorbed RES uncertainty, and reduced generation cost.

Joint planning and optimal operation of AC / DC hybrid distribution network considering distributed generation and EV charging station

With the continuous increase in the penetration rate of renewable energy and electric vehicles under the dual carbon goal, the location and capacity of distributed power generation and electric vehicle charging stations have become the key of power grid planning. This paper proposes a joint planning and optimal optimization method for the AC-DC hybrid distribution network with distributed generation and electric vehicle charging station. Firstly, based on the BP artificial neural network prediction algorithm, a prediction model is constructed for the historical data such as wind speed, light intensity, temperature, humidity and air pressure in the region, and the typical daily output characteristics of renewable energy could be obtained. Then according to the driving behavior characteristics of regional electric vehicle users, the electric vehicle charging station model can be proposed. Finally, a joint planning and optimal operation planning model is constructed in the AC/DC hybrid distribution network that takes micro-turbine, energy storage system, electric vehicle charging station and renewable energy system into account. The model is a nonlinear non-convex mixed-integer programming problem, which could be used by linearization and second-order cone relaxation techniques to transform into a mixed-integer second-order cone-convex optimization problem that can be efficiently solved by commercial solvers. The case study takes a modified IEEE33 system as an example, combined with the weather conditions in a certain area, to verify the validity and rationality of the proposed model.

Rational Spectral Collocation Combined with Singularity Separation Method for Second-Order Singular Perturbation Problems

Rational Spectral Collocation Combined with Singularity Separation Method for Second-Order Singular Perturbation Problems