Optimal Shape Factor and Fictitious Radius in the MQ-RBF:Solving Ill-Posed Laplacian Problems

To solve the Laplacian problems,we adopt a meshless method with the multiquadric radial basis function(MQRBF)as a basis whose center is distributed inside a circle with a fictitious radius.A maximal projection technique is developed to identify the optimal shape factor and fictitious radius by minimizing a merit function.A sample function is interpolated by theMQ-RBF to provide a trial coefficient vector to compute the merit function.We can quickly determine the optimal values of the parameters within a preferred rage using the golden section search algorithm.The novel method provides the optimal values of parameters and,hence,an optimal MQ-RBF;the performance of the method is validated in numerical examples.Moreover,nonharmonic problems are transformed to the Poisson equation endowed with a homogeneous boundary condition;this can overcome the problem of these problems being ill-posed.The optimal MQ-RBF is extremely accurate.We further propose a novel optimal polynomial method to solve the nonharmonic problems,which achieves high precision up to an order of 10^(−11).

AN OPTIMAL CONTROL PROBLEM FOR A LOTKA-VOLTERRA COMPETITION MODEL WITH CHEMO-REPULSION

In this paper we study a bilinear optimal control problem for a diffusive Lotka-Volterra competition model with chemo-repulsion in a bounded domain of ℝ^(ℕ),N=2,3.This model describes the competition of two species in which one of them avoid encounters with rivals through a chemo-repulsion mechanism.We prove the existence and uniqueness of weak-strong solutions,and then we analyze the existence of a global optimal solution for a related bilinear optimal control problem,where the control is acting on the chemical signal.Posteriorly,we derive first-order optimality conditions for local optimal solutions using the Lagrange multipliers theory.Finally,we propose a discrete approximation scheme of the optimality system based on the gradient method,which is validated with some computational experiments.

Suitable region of dynamic optimal interpolation for efficiently altimetry sea surface height mapping

The dynamic optimal interpolation(DOI)method is a technique based on quasi-geostrophic dynamics for merging multi-satellite altimeter along-track observations to generate gridded absolute dynamic topography(ADT).Compared with the linear optimal interpolation(LOI)method,the DOI method can improve the accuracy of gridded ADT locally but with low computational efficiency.Consequently,considering both computational efficiency and accuracy,the DOI method is more suitable to be used only for regional applications.In this study,we propose to evaluate the suitable region for applying the DOI method based on the correlation between the absolute value of the Jacobian operator of the geostrophic stream function and the improvement achieved by the DOI method.After verifying the LOI and DOI methods,the suitable region was investigated in three typical areas:the Gulf Stream(25°N-50°N,55°W-80°W),the Japanese Kuroshio(25°N-45°N,135°E-155°E),and the South China Sea(5°N-25°N,100°E-125°E).We propose to use the DOI method only in regions outside the equatorial region and where the absolute value of the Jacobian operator of the geostrophic stream function is higher than1×10^(-11).

Enhancing Renewable Energy Integration:A Gaussian-Bare-Bones Levy Cheetah Optimization Approach to Optimal Power Flow in Electrical Networks

In the contemporary era,the global expansion of electrical grids is propelled by various renewable energy sources(RESs).Efficient integration of stochastic RESs and optimal power flow(OPF)management are critical for network optimization.This study introduces an innovative solution,the Gaussian Bare-Bones Levy Cheetah Optimizer(GBBLCO),addressing OPF challenges in power generation systems with stochastic RESs.The primary objective is to minimize the total operating costs of RESs,considering four functions:overall operating costs,voltage deviation management,emissions reduction,voltage stability index(VSI)and power loss mitigation.Additionally,a carbon tax is included in the objective function to reduce carbon emissions.Thorough scrutiny,using modified IEEE 30-bus and IEEE 118-bus systems,validates GBBLCO’s superior performance in achieving optimal solutions.Simulation results demonstrate GBBLCO’s efficacy in six optimization scenarios:total cost with valve point effects,total cost with emission and carbon tax,total cost with prohibited operating zones,active power loss optimization,voltage deviation optimization and enhancing voltage stability index(VSI).GBBLCO outperforms conventional techniques in each scenario,showcasing rapid convergence and superior solution quality.Notably,GBBLCO navigates complexities introduced by valve point effects,adapts to environmental constraints,optimizes costs while considering prohibited operating zones,minimizes active power losses,and optimizes voltage deviation by enhancing the voltage stability index(VSI)effectively.This research significantly contributes to advancing OPF,emphasizing GBBLCO’s improved global search capabilities and ability to address challenges related to local minima.GBBLCO emerges as a versatile and robust optimization tool for diverse challenges in power systems,offering a promising solution for the evolving needs of renewable energy-integrated power grids.

An Optimization Approach of IoD Deployment for Optimal Coverage Based on Radio Frequency Model

Recently,Internet of Drones(IoD)has garnered significant attention due to its widespread applications.However,deploying IoD for area coverage poses numerous limitations and challenges.These include interference between neighboring drones,the need for directional antennas,and altitude restrictions for drones.These challenges necessitate the development of efficient solutions.This research paper presents a cooperative decision-making approach for an efficient IoDdeployment to address these challenges effectively.The primary objective of this study is to achieve an efficient IoDdeployment strategy thatmaximizes the coverage regionwhile minimizing interference between neighboring drones.In deployment problem,the interference increases as the number of deployed drones increases,resulting in bad quality of communication.On the other hand,deploying a few drones cannot satisfy the coverage demand.To accomplish this,an enhanced version of a concise population-based meta-heuristic algorithm,namely Improved Particle SwarmOptimization(IPSO),is applied.The objective function of IPSO is defined based on the coverage probability,which is primarily influenced by the characteristics of the antennas and drone altitude.A radio frequency(RF)model is derived to evaluate the coverage quality,considering both Line of Sight(LOS)and Non-Line of Sight(NLOS)down-link coverage probabilities for ground communication.It is assumed that each drone is equipped with a directional antenna to optimize coverage in a given region.Extensive simulations are conducted to assess the effectiveness of the proposed approach.Results demonstrate that the proposed method achieves maximum coverage with minimum transmission power.Furthermore,a comparison is made against Collaborative Visual Area Coverage Approach(CVACA),and a game-based approach in terms of coverage quality and convergence speed.The simulation results reveal that our approach outperforms both CVACA and the gamebased schemes in terms of coverage and convergence speed.Comparisons validate the superiority of our approach over existing methods.To assess the robustness of the proposed RFmodel,we have considered two distinct ranges of noise:range1 spanning from−120 to−90 dBm,and range2 spanning from−90 to−70 dBmfor different numbers of UAVs.In summary,this research presents a cooperative decision-making approach for efficient IoD deployment to address the challenges associatedwith area coverage and achieves an optimal coveragewithminimal interference.

Distributed Minimum-Energy Containment Control of Continuous-Time Multi-Agent Systems by Inverse Optimal Control

Dear Editor,This letter focuses on the distributed optimal containment control of continuous-time multi-agent systems(CTMASs)with respect to the minimum-energy performance index over fixed topology.To achieve this,we firstly investigate the optimal containment control problem using the inverse optimal control method,where all states of followers asymptotically converge to the convex hull spanned by the leaders while some quadratic performance indexes get minimized.A sufficient condition for existence of the distributed optimal containment control protocol is derived.By introducing the parametric algebraic Riccati equation(PARE),it is strictly proved that the global performance index can be used to approximate the standard minimumenergy performance index as the parameters tends to infinity.In consequence,the standard minimum-energy cooperative containment control can be solved by local steady state feedback protocols.

Distributed Optimal Formation Control for Unmanned Surface Vessels by a Regularized Game-Based Approach

Dear Editor,This letter explores optimal formation control for a network of unmanned surface vessels(USVs).By designing an individual objective function for each USV,the optimal formation problem is transformed into a noncooperative game.Under this game theoretic framework,the optimal formation is achieved by seeking the Nash equilibrium of the regularized game.A modular structure consisting of a distributed Nash equilibrium seeker and a regulator is proposed.

Policy Gradient Adaptive Dynamic Programming for Model-Free Multi-Objective Optimal Control

Dear Editor,In this letter,the multi-objective optimal control problem of nonlinear discrete-time systems is investigated.A data-driven policy gradient algorithm is proposed in which the action-state value function is used to evaluate the policy.In the policy improvement process,the policy gradient based method is employed.

A Special Issue“Planning and Optimal Operation of New-Type Power System”of Global Energy Interconnection

The power system,as an energy hub,plays a crucial role in the transformation of energy production and consumption.On July 19,2023,the International Energy Agency(IEA)released a Global Electricity Market Report for 2023-2024.This report indicates that the development of the world’s energy production is rapidly moving towards the critical point where the proportion of electricity generated from renewable sources surpasses that from non-renewable sources.

Optimal and robust control of population transfer in asymmetric quantum-dot molecules

We present an optimal and robust quantum control method for efficient population transfer in asymmetric double quantum-dot molecules.We derive a long-duration control scheme that allows for highly efficient population transfer by accurately controlling the amplitude of a narrow-bandwidth pulse.To overcome fluctuations in control field parameters,we employ a frequency-domain quantum optimal control theory method to optimize the spectral phase of a single pulse with broad bandwidth while preserving the spectral amplitude.It is shown that this spectral-phase-only optimization approach can successfully identify robust and optimal control fields,leading to efficient population transfer to the target state while concurrently suppressing population transfer to undesired states.The method demonstrates resilience to fluctuations in control field parameters,making it a promising approach for reliable and efficient population transfer in practical applications.

Adaptive Optimal Output Regulation of Interconnected Singularly Perturbed Systems With Application to Power Systems

This article studies the adaptive optimal output regulation problem for a class of interconnected singularly perturbed systems(SPSs) with unknown dynamics based on reinforcement learning(RL).Taking into account the slow and fast characteristics among system states,the interconnected SPS is decomposed into the slow time-scale dynamics and the fast timescale dynamics through singular perturbation theory.For the fast time-scale dynamics with interconnections,we devise a decentralized optimal control strategy by selecting appropriate weight matrices in the cost function.For the slow time-scale dynamics with unknown system parameters,an off-policy RL algorithm with convergence guarantee is given to learn the optimal control strategy in terms of measurement data.By combining the slow and fast controllers,we establish the composite decentralized adaptive optimal output regulator,and rigorously analyze the stability and optimality of the closed-loop system.The proposed decomposition design not only bypasses the numerical stiffness but also alleviates the high-dimensionality.The efficacy of the proposed methodology is validated by a load-frequency control application of a two-area power system.

Optimal search path planning of UUV in battlefeld ambush scene

Aiming at the practical application of Unmanned Underwater Vehicle(UUV)in underwater combat,this paper proposes a battlefield ambush scene with UUV considering ocean current.Firstly,by establishing these mathematical models of ocean current environment,target movement,and sonar detection,the probability calculation methods of single UUV searching target and multiple UUV cooperatively searching target are given respectively.Then,based on the Hybrid Quantum-behaved Particle Swarm Optimization(HQPSO)algorithm,the path with the highest target search probability is found.Finally,through simulation calculations,the influence of different UUV parameters and target parameters on the target search probability is analyzed,and the minimum number of UUVs that need to be deployed to complete the ambush task is demonstrated,and the optimal search path scheme is obtained.The method proposed in this paper provides a theoretical basis for the practical application of UUV in the future combat.

THE OPTIMAL LARGE TIME BEHAVIOR OF 3D QUASILINEAR HYPERBOLIC EQUATIONS WITH NONLINEAR

We are concerned with the large-time behavior of 3D quasilinear hyperbolic equations with nonlinear damping.The main novelty of this paper is two-fold.First,we prove the optimal decay rates of the second and third order spatial derivatives of the solution,which are the same as those of the heat equation,and in particular,are faster than ones of previous related works.Second,for well-chosen initial data,we also show that the lower optimal L^(2) convergence rate of the k(∈[0,3])-order spatial derivatives of the solution is(1+t)^(-(2+2k)/4).Therefore,our decay rates are optimal in this sense.The proofs are based on the Fourier splitting method,low-frequency and high-frequency decomposition,and delicate energy estimates.

Sequential Inverse Optimal Control of Discrete-Time Systems

This paper presents a novel sequential inverse optimal control(SIOC)method for discrete-time systems,which calculates the unknown weight vectors of the cost function in real time using the input and output of an optimally controlled discrete-time system.The proposed method overcomes the limitations of previous approaches by eliminating the need for the invertible Jacobian assumption.It calculates the possible-solution spaces and their intersections sequentially until the dimension of the intersection space decreases to one.The remaining one-dimensional vector of the possible-solution space’s intersection represents the SIOC solution.The paper presents clear conditions for convergence and addresses the issue of noisy data by clarifying the conditions for the singular values of the matrices that relate to the possible-solution space.The effectiveness of the proposed method is demonstrated through simulation results.

Multi-Time Scale Optimal Scheduling of a Photovoltaic Energy Storage Building System Based on Model Predictive Control

Building emission reduction is an important way to achieve China’s carbon peaking and carbon neutrality goals.Aiming at the problem of low carbon economic operation of a photovoltaic energy storage building system,a multi-time scale optimal scheduling strategy based on model predictive control(MPC)is proposed under the consideration of load optimization.First,load optimization is achieved by controlling the charging time of electric vehicles as well as adjusting the air conditioning operation temperature,and the photovoltaic energy storage building system model is constructed to propose a day-ahead scheduling strategy with the lowest daily operation cost.Second,considering inter-day to intra-day source-load prediction error,an intraday rolling optimal scheduling strategy based on MPC is proposed that dynamically corrects the day-ahead dispatch results to stabilize system power fluctuations and promote photovoltaic consumption.Finally,taking an office building on a summer work day as an example,the effectiveness of the proposed scheduling strategy is verified.The results of the example show that the strategy reduces the total operating cost of the photovoltaic energy storage building system by 17.11%,improves the carbon emission reduction by 7.99%,and the photovoltaic consumption rate reaches 98.57%,improving the system’s low-carbon and economic performance.

Optimal Configuration of Fault Location Measurement Points in DC Distribution Networks Based on Improved Particle Swarm Optimization Algorithm

The escalating deployment of distributed power sources and random loads in DC distribution networks hasamplified the potential consequences of faults if left uncontrolled. To expedite the process of achieving an optimalconfiguration of measurement points, this paper presents an optimal configuration scheme for fault locationmeasurement points in DC distribution networks based on an improved particle swarm optimization algorithm.Initially, a measurement point distribution optimization model is formulated, leveraging compressive sensing.The model aims to achieve the minimum number of measurement points while attaining the best compressivesensing reconstruction effect. It incorporates constraints from the compressive sensing algorithm and networkwide viewability. Subsequently, the traditional particle swarm algorithm is enhanced by utilizing the Haltonsequence for population initialization, generating uniformly distributed individuals. This enhancement reducesindividual search blindness and overlap probability, thereby promoting population diversity. Furthermore, anadaptive t-distribution perturbation strategy is introduced during the particle update process to enhance the globalsearch capability and search speed. The established model for the optimal configuration of measurement points issolved, and the results demonstrate the efficacy and practicality of the proposed method. The optimal configurationreduces the number of measurement points, enhances localization accuracy, and improves the convergence speedof the algorithm. These findings validate the effectiveness and utility of the proposed approach.

Two-Stage Optimal Scheduling of Community Integrated Energy System

From the perspective of a community energy operator,a two-stage optimal scheduling model of a community integrated energy system is proposed by integrating information on controllable loads.The day-ahead scheduling analyzes whether various controllable loads participate in the optimization and investigates the impact of their responses on the operating economy of the community integrated energy system(IES)before and after;the intra-day scheduling proposes a two-stage rolling optimization model based on the day-ahead scheduling scheme,taking into account the fluctuation of wind turbine output and load within a short period of time and according to the different response rates of heat and cooling power,and solves the adjusted output of each controllable device.The simulation results show that the optimal scheduling of controllable loads effectively reduces the comprehensive operating costs of community IES;the two-stage optimal scheduling model can meet the energy demand of customers while effectively and timely suppressing the random fluctuations on both sides of the source and load during the intra-day stage,realizing the economic and smooth operation of IES.

A new optimal adaptive backstepping control approach for nonlinear systems under deception attacks via reinforcement learning

In this paper,a new optimal adaptive backstepping control approach for nonlinear systems under deception attacks via reinforcement learning is presented in this paper.The existence of nonlinear terms in the studied system makes it very difficult to design the optimal controller using traditional methods.To achieve optimal control,RL algorithm based on critic–actor architecture is considered for the nonlinear system.Due to the significant security risks of network transmission,the system is vulnerable to deception attacks,which can make all the system state unavailable.By using the attacked states to design coordinate transformation,the harm brought by unknown deception attacks has been overcome.The presented control strategy can ensure that all signals in the closed-loop system are semi-globally ultimately bounded.Finally,the simulation experiment is shown to prove the effectiveness of the strategy.

Matrix Riccati Equations in Optimal Control

In this paper, the matrix Riccati equation is considered. There is no general way for solving the matrix Riccati equation despite the many fields to which it applies. While scalar Riccati equation has been studied thoroughly, matrix Riccati equation of which scalar Riccati equations is a particular case, is much less investigated. This article proposes a change of variable that allows to find explicit solution of the Matrix Riccati equation. We then apply this solution to Optimal Control.

Optimal timing for plastic surgical procedures for common congenital anomalies:A review

Apart from listening to the cry of a healthy newborn,it is the declaration by the attending paediatrician in the labour room that the child is normal which brings utmost joy to parents.The global incidence of children born with congenital anomalies has been reported to be 3%-6%with more than 90%of these occurring in low-and middle-income group countries.The exact percentages/total numbers of children requiring surgical treatment cannot be estimated for several reasons.These children are operated under several surgical disciplines,viz,paediatric-,plastic reconstructive,neuro-,cardiothoracic-,orthopaedic surgery etc.These conditions may be life-threatening,e.g.,trachea-oesophageal fistula,critical pulmonary stenosis,etc.and require immediate surgical intervention.Some,e.g.,hydrocephalus,may need intervention as soon as the patient is fit for surgery.Some,e.g.,patent ductus arteriosus need‘wait and watch’policy up to a certain age in the hope of spontaneous recovery.Another extremely important category is that of patients where the operative intervention is done based on their age.Almost all the congenital anomalies coming under care of a plastic surgeon are operated as elective surgery(many as multiple stages of correction)at appropriate ages.There are advantages and disadvantages of intervention at different ages.In this article,we present a review of optimal timings,along with reasoning,for surgery of many of the common congenital anomalies which are treated by plastic surgeons.Obstetricians,paediatricians and general practitioners/family physicians,who most often are the first ones to come across such children,must know to guide the parents appropriately and convincingly impress upon the them as to why their child should not be operated immediately and also the consequences of too soon or too late.