Resilience Against Replay Attacks:A Distributed Model Predictive Control Scheme for Networked Multi-Agent Systems

In this paper,a resilient distributed control scheme against replay attacks for multi-agent networked systems subject to input and state constraints is proposed.The methodological starting point relies on a smart use of predictive arguments with a twofold aim:1)Promptly detect malicious agent behaviors affecting normal system operations;2)Apply specific control actions,based on predictive ideas,for mitigating as much as possible undesirable domino effects resulting from adversary operations.Specifically,the multi-agent system is topologically described by a leader-follower digraph characterized by a unique leader and set-theoretic receding horizon control ideas are exploited to develop a distributed algorithm capable to instantaneously recognize the attacked agent.Finally,numerical simulations are carried out to show benefits and effectiveness of the proposed approach.

Distributed modeling of direct solar radiation on rugged terrain of the Yellow River Basin

Due to the influences of local topographical factors and terrain inter-shielding, calculation of direct solar radiation （DSR） quantity of rugged terrain is very complex. Based on digital elevation model （DEM） data and meteorological observations, a distributed model for calculating DSR over rugged terrain is developed. This model gives an all-sided consideration on factors influencing th a resolution of 1 km × 1 km for thDSR. Using the developed model, normals of annual DSR quantity wie Yellow River Basin was generated, with DEM data as the general characterization of terrain. Characteristics of DSR quantity influenced by geographic and topographic factors over rugged terrain were analyzed thoroughly. Results suggest that： influenced by local topographic factors, i.e. azimuth, slope and so on, and annual DSR quantity over mountainous area has a clear spatial difference; annual DSR quantity of sunny slope （or southern slope） of mountains is obviously larger than that of shady slope （or northern slope）. The calculated DSR quantity of the Yellow River Basin is provided in the same way as other kinds of spatial information and can be employed as basic geographic data for relevant studies as well.

Distributed Modeling of Extraterrestrial Solar Radiation Over the Rugged Terrains of Pakistan

In Pakistan,the solar analogue has been addressed but its surface geographical parameterization has given least attention.Inappropriate density of stations and their spatial coverage particularly in difficult peripheral national territories,little or no solar radiation data,non-satisfactory sunshine hours data,and low quality of ground observed cloud cover data create a situation in which the spatial modeling of Extraterrestrial Solar Radiation(ESR) and its ground parameterization got sufficient scope.The Digital Elevation Model (DEM) input into Geographic Information System (GIS) is a compatible tool to demonstrate the spatial distribution of ESR over the rugged terrains of the study domain.For the first time,distributed modeling of ESR is done over the rugged terrains of Pakistan,based on DEM and ArcGIS..Results clearly depict that the complex landforms profoundly disrupt the zonal distribution of ESR in Pakistan.The screening impact of topography is higher on spatial distribution of ESR in winter and considerably low in summer.The combined effect of topography and latitude is obvious.Hence,the model was further testified by plotting Rb (ratio of ESR quantity over rugged terrain against plane surface) against azimuth at different latitudes with different angled slopes.The results clearly support the strong screening effect of rugged terrain through out the country especially in Himalayas,Karakoram and Hindukush (HKH),western border mountains and Balochistan Plateau.This model can be instrumental as baseline geospatial information for scientific investigations in Pakistan,where substantial fraction of national population is living in mountainous regions.

Distributed model predictive control for multiagent systems with improved consistency

This paper addresses an improved distributed model predictive control （DMPC） scheme for multiagent systems with an attempt to improving its consistency. The deviation between what an agent is actually doing and what its neighbors believe that agent is doing is penalized in the cost function of each agent. At each sampling instant the compatibility constraint of each agent is set tighter than the previous sampling instant. Like the traditional approach, the performance cost is utilized as the Lyapunov function to prove closed-looped stability. The closed-loop stability is guaranteed if the weight matrix for deviation in the cost function are sufficiently large. The proposed distributed control scheme is formulated as quadratic programming with quadratic constraints. A numerical example is given to illustrate the effectiveness of the proposed scheme.

Solution for Distributed Model of Groundwater System with PCG2 for Naolihe Basin in Sanjiang Plain

PCG2 （Preconditioned Conjugate-Gradient Method 2）, the most popular mothod used in groundwater field, was used to solve the distributed model of large-scale groundwater system. Its principle and effect was analyzed mathematically, and verified by some specific examples. Numerical results acquired by PCG2 are accurate, it demonstrates that PCG2 is effective on methodology itself and man-ralated operation. So PCG2 is worthy of popularizing in the area of groundwater system for numerical analysis.

Distributed model predictive control based on adaptive sampling mechanism

In this work,an adaptive sampling control strategy for distributed predictive control is proposed.According to the proposed method,the sampling rate of each subsystem of the accused object is determined based on the periodic detection of its dynamic behavior and calculations made using a correlation function.Then,the optimal sampling interval within the period is obtained and sent to the corresponding sub-prediction controller,and the sampling interval of the controller is changed accordingly before the next sampling period begins.In the next control period,the adaptive sampling mechanism recalculates the sampling rate of each subsystem’s measurable output variable according to both the abovementioned method and the change in the dynamic behavior of the entire system,and this process is repeated.Such an adaptive sampling interval selection based on an autocorrelation function that measures dynamic behavior can dynamically optimize the selection of sampling rate according to the real-time change in the dynamic behavior of the controlled object.It can also accurately capture dynamic changes,meaning that each sub-prediction controller can more accurately calculate the optimal control quantity at the next moment,significantly improving the performance of distributed model predictive control(DMPC).A comparison demonstrates that the proposed adaptive sampling DMPC algorithm has better tracking performance than the traditional DMPC algorithm.

Hydrological Modelling of Sidi Jabeur Watershed (Morocco) Using Spatially Distributed Model ATHYS

The objective of this study is to model the hydrology in the Sidi Jabeur basin, located in Bouregreg watershed at the north-central of Morocco, using the spatially distributed model (ATHYS) in order to understand and determine the different watershed hydrological processes. The study requires the collection of a series of data as inputs models namely rainfall data, water quantity, soil occupation, digital terrain model and requires also a calibration in order to evaluate the model in validation phase. The simulation results are obtained from the validation phase aim to replicate the operation of Sidi Jabeur watershed, and present a suitable adjustment perspective of the observed hydrograph. These results show that the objective is achieved and a model distributed like ATHYS plays an effective role in improving the efficiency and presents a high advantage in anticipation of runoff volume.

Autonomous Vehicle Platoons In Urban Road Networks:A Joint Distributed Reinforcement Learning and Model Predictive Control Approach

In this paper, platoons of autonomous vehicles operating in urban road networks are considered. From a methodological point of view, the problem of interest consists of formally characterizing vehicle state trajectory tubes by means of routing decisions complying with traffic congestion criteria. To this end, a novel distributed control architecture is conceived by taking advantage of two methodologies: deep reinforcement learning and model predictive control. On one hand, the routing decisions are obtained by using a distributed reinforcement learning algorithm that exploits available traffic data at each road junction. On the other hand, a bank of model predictive controllers is in charge of computing the more adequate control action for each involved vehicle. Such tasks are here combined into a single framework:the deep reinforcement learning output(action) is translated into a set-point to be tracked by the model predictive controller;conversely, the current vehicle position, resulting from the application of the control move, is exploited by the deep reinforcement learning unit for improving its reliability. The main novelty of the proposed solution lies in its hybrid nature: on one hand it fully exploits deep reinforcement learning capabilities for decisionmaking purposes;on the other hand, time-varying hard constraints are always satisfied during the dynamical platoon evolution imposed by the computed routing decisions. To efficiently evaluate the performance of the proposed control architecture, a co-design procedure, involving the SUMO and MATLAB platforms, is implemented so that complex operating environments can be used, and the information coming from road maps(links,junctions, obstacles, semaphores, etc.) and vehicle state trajectories can be shared and exchanged. Finally by considering as operating scenario a real entire city block and a platoon of eleven vehicles described by double-integrator models, several simulations have been performed with the aim to put in light the main f eatures of the proposed approach. Moreover, it is important to underline that in different operating scenarios the proposed reinforcement learning scheme is capable of significantly reducing traffic congestion phenomena when compared with well-reputed competitors.

CBF-Based Distributed Model Predictive Control for Safe Formation of Autonomous Mobile Robots

A distributed model predictive control(DMPC)method based on robust control barrier function(RCBF)is developed to achieve the safe formation target of multi-autonomous mobile robot systems in an uncertain disturbed environment.The first step is to analyze the safety requirements of the system during safe formation and categorize them into collision avoidance and distance connectivity maintenance.RCBF constraints are designed based on collision avoidance and connectivity maintenance requirements,and security constraints are achieved through a combination.Then,the specified safety constraints are integrated with the objective of forming a multi-autonomous mobile robot formation.To ensure safe control,the optimization problem is integrated with the DMPC method.Finally,the RCBF-DMPC algorithm is proposed to ensure iterative feasibility and stability while meeting the constraints and expected objectives.Simulation experiments illustrate that the designed algorithm can achieve cooperative formation and ensure system security.

Application of distributed model predictive control based on neighborhood optimization in gauge-looper integrated system of tandem hot rolling

To solve the coupling relationship between the strip automatic gauge control and the looper control in traditional control strategy of tandem hot rolling,a distributed model predictive control(DMPC)strategy for the tandem hot rolling was explored,and a series of simulation experiments were carried out.Firstly,based on the state space analysis method,the multivariable dynamic transition process of hot strip rolling was studied,and the state space model of a gauge-looper integrated system in tandem hot rolling was established.Secondly,DMPC strategy based on neighborhood optimization was proposed,which fully considered the coupling relationship in this integrated system.Finally,a series of experiments simulating disturbances and emergency situations were completed with actual rolling data.The experimental results showed that the proposed DMPC control strategy had better performance compared with the traditional proportional-integral control and centralized model predictive control,which is applicable for the gauge-looper integrated system.

Distributed Economic MPC for Synergetic Regulation of the Voltage of an Island DC Micro-Grid

In this paper,distributed model predictive control(DMPC) for island DC micro-grids(MG) with wind/photovoltaic(PV)/battery power is proposed,which coordinates all distributed generations(DG) to stabilize the bus voltage together with the insurance of having computational efficiency under a real-time requirement.Based on the feedback of the bus voltage,the deviation of the current is dispatched to each DG according to cost over the prediction horizon.Moreover,to avoid the excessive fluctuation of the battery power,both the discharge-charge switching times and costs are considered in the model predictive control(MPC) optimization problems.A Lyapunov constraint with a time-varying steady-state is designed in each local MPC to guarantee the stabilization of the entire system.The voltage stabilization of the MG is achieved by this strategy with the cooperation of DGs.The numeric results of applying the proposed method to a MG of the Shanghai Power Supply Company shows the effectiveness of the distributed economic MPC.

Virtually coupled train set control subject to space-time separation:A distributed economic MPC approach with emergency braking configuration

The emerging virtual coupling technology aims to operate multiple train units in a Virtually Coupled Train Set(VCTS)at a minimal but safe distance.To guarantee collision avoidance,the safety distance should be calculated using the state-of-the-art space-time separation principle that separates the Emergency Braking(EB)trajectories of two successive units during the whole EB process.In this case,the minimal safety distance is usually numerically calculated without an analytic formulation.Thus,the constrained VCTS control problem is hard to address with space-time separation,which is still a gap in the existing literature.To solve this problem,we propose a Distributed Economic Model Predictive Control(DEMPC)approach with computation efficiency and theoretical guarantee.Specifically,to alleviate the computation burden,we transform implicit safety constraints into explicitly linear ones,such that the optimal control problem in DEMPC is a quadratic programming problem that can be solved efficiently.For theoretical analysis,sufficient conditions are derived to guarantee the recursive feasibility and stability of DEMPC,employing compatibility constraints,tube techniques and terminal ingredient tuning.Moreover,we extend our approach with globally optimal and distributed online EB configuration methods to shorten the minimal distance among VCTS.Finally,experimental results demonstrate the performance and advantages of the proposed approaches.

The effects of cold region meteorology and specific environment on the number of hospital admissions for chronic kidney disease:An investigate with a distributed lag nonlinear model

Objective:To explore the effects of daily mean temperature(°C),average daily air pressure(hPa),humidity(%),wind speed(m/s),particulate matter(PM)2.5(μg/m3)and PM10(μg/m3)on the admission rate of chronic kidney disease(CKD)patients admitted to the Second Affiliated Hospital of Harbin Medical University in Harbin and to identify the indexes and lag days that impose the most critical influence.Methods:The R language Distributed Lag Nonlinear Model(DLNM),Excel,and SPSS were used to analyze the disease and meteorological data of Harbin from 01 January 2010 to 31 December 2019 according to the inclusion and exclusion criteria.Results:Meteorological factors and air pollution influence the number of hospitalizations of CKD to vary degrees in cold regions,and differ in persistence or delay.Non-optimal temperature increases the risk of admission of CKD,high temperature increases the risk of obstructive kidney disease,and low temperature increases the risk of other major types of chronic kidney disease.The greater the temperature difference is,the higher its contribution is to the risk.The non-optimal wind speed and non-optimal atmospheric pressure are associated with increased hospital admissions.PM2.5 concentrations above 40μg/m3 have a negative impact on the results.Conclusion:Cold region meteorology and specific environment do have an impact on the number of hospital admissions for chronic kidney disease,and we can apply DLMN to describe the analysis.

Finer topographic data improves distribution modeling of Picea crassifolia in the northern Qilian Mountains

The Qilian Mountains, a national key ecological function zone in Western China, play a pivotal role in ecosystem services. However, the distribution of its dominant tree species, Picea crassifolia (Qinghai spruce), has decreased dramatically in the past decades due to climate change and human activity, which may have influenced its ecological functions. To restore its ecological functions, reasonable reforestation is the key measure. Many previous efforts have predicted the potential distribution of Picea crassifolia, which provides guidance on regional reforestation policy. However, all of them were performed at low spatial resolution, thus ignoring the natural characteristics of the patchy distribution of Picea crassifolia. Here, we modeled the distribution of Picea crassifolia with species distribution models at high spatial resolutions. For many models, the area under the receiver operating characteristic curve (AUC) is larger than 0.9, suggesting their excellent precision. The AUC of models at 30 m is higher than that of models at 90 m, and the current potential distribution of Picea crassifolia is more closely aligned with its actual distribution at 30 m, demonstrating that finer data resolution improves model performance. Besides, for models at 90 m resolution, annual precipitation (Bio12) played the paramount influence on the distribution of Picea crassifolia, while the aspect became the most important one at 30 m, indicating the crucial role of finer topographic data in modeling species with patchy distribution. The current distribution of Picea crassifolia was concentrated in the northern and central parts of the study area, and this pattern will be maintained under future scenarios, although some habitat loss in the central parts and gain in the eastern regions is expected owing to increasing temperatures and precipitation. Our findings can guide protective and restoration strategies for the Qilian Mountains, which would benefit regional ecological balance.

A unified Minorization-Maximization approach for estimation of general mixture models

The mixed distribution model is often used to extract information from heteroge-neous data and perform modeling analysis.When the density function of mixed distribution is complicated or the variable dimension is high,it usually brings challenges to the parameter es-timation of the mixed distribution model.The application of MM algorithm can avoid complex expectation calculations,and can also solve the problem of high-dimensional optimization by decomposing the objective function.In this paper,MM algorithm is applied to the parameter estimation problem of mixed distribution model.The method of assembly and decomposition is used to construct the substitute function with separable parameters,which avoids the problems of complex expectation calculations and the inversion of high-dimensional matrices.

Modeling load distribution for rural photovoltaic grid areas using image recognition

Expanding photovoltaic(PV)resources in rural-grid areas is an essential means to augment the share of solar energy in the energy landscape,aligning with the“carbon peaking and carbon neutrality”objectives.However,rural power grids often lack digitalization;thus,the load distribution within these areas is not fully known.This hinders the calculation of the available PV capacity and deduction of node voltages.This study proposes a load-distribution modeling approach based on remote-sensing image recognition in pursuit of a scientific framework for developing distributed PV resources in rural grid areas.First,houses in remote-sensing images are accurately recognized using deep-learning techniques based on the YOLOv5 model.The distribution of the houses is then used to estimate the load distribution in the grid area.Next,equally spaced and clustered distribution models are used to adaptively determine the location of the nodes and load power in the distribution lines.Finally,by calculating the connectivity matrix of the nodes,a minimum spanning tree is extracted,the topology of the network is constructed,and the node parameters of the load-distribution model are calculated.The proposed scheme is implemented in a software package and its efficacy is demonstrated by analyzing typical remote-sensing images of rural grid areas.The results underscore the ability of the proposed approach to effectively discern the distribution-line structure and compute the node parameters,thereby offering vital support for determining PV access capability.

Virtual target guidance-based distributed model predictive control for formation control of multiple UAVs

The paper proposes a Virtual Target Guidance(VTG)-based distributed Model Predictive Control(MPC) scheme for formation control of multiple Unmanned Aerial Vehicles(UAVs).First, a framework of distributed MPC scheme is designed in which each UAV only shares the information with its neighbors, and the obtained local Finite-Horizon Optimal Control Problem(FHOCP) can be solved by swarm intelligent optimization algorithm.Then, a VTG approach is developed and integrated into the distributed MPC scheme to achieve trajectory tracking and obstacle avoidance.Further, an event-triggered mechanism is proposed to reduce the computational burden for UAV formation control, which takes into consideration the predictive state errors as well as the convergence of cost function.Numerical simulations show that the proposed VTG-based distributed MPC scheme is more computationally efficient to achieve formation control of multiple UAVs in comparison with the traditional distributed MPC method.

Robust distributed model predictive consensus of discrete-time multi-agent systems:a self-triggered approach

This study investigates the consensus problem of a nonlinear discrete-time multi-agent system(MAS)under bounded additive disturbances.We propose a self-triggered robust distributed model predictive control consensus algorithm.A new cost function is constructed and MAS is coupled through this function.Based on the proposed cost function,a self-triggered mechanism is adopted to reduce the communication load.Furthermore,to overcome additive disturbances,a local minimum-maximum optimization problem under the worst-case scenario is solved iteratively by the model predictive controller of each agent.Sufficient conditions are provided to guarantee the iterative feasibility of the algorithm and the consensus of the closed-loop MAS.For each agent,we provide a concrete form of compatibility constraint and a consensus error terminal region.Numerical examples are provided to illustrate the effectiveness and correctness of the proposed algorithm.

Analysis and Optimum Design of Differential Inductors Using Distributed Capacitance Model

A distributed capacitance model for monolithic inductors is developed to predict the equivalently parasitical capacitances of the inductor.The ratio of the self-resonant frequency (f SR) of the differential-driven symmetric inductor to the f SR of the single-ended driven inductor is firstly predicted and explained.Compared with a single-ended configuration,experimental data demonstrate that the differential inductor offers a 127% greater maximum quality factor and a broader range of operating frequencies.Two differential inductors with low parasitical capacitance are developed and validated.

Nonlinear Distributed Model Predictive Control for Multiple Missiles Against Maneuvering Target with a Trajectory Predictor

This study aims to solve the problem of multi-missile simultaneous attacks on maneuvering target.The challenges include multimissile cooperative control and target's trajectory prediction.A controller based on nonlinear distributed model predictive control(NDMPC)is designed for multiple missiles against a maneuvering target,and a trajectory prediction inethod based on particle swarm optimization(PSO)algorithm is proposed.This study has mainly completed the following three aspects of work.Firstly,the cost function of the cont roller is constructed to optimize the accuracy and synchronization of the multi-missile system with consideration of collision avoidance.Secondly,the velocity control of the leading missile is designed by using the range-to-go in-formation in real time to ensure the attack fficiency and the control of the terminal velocity difference.Finally,a kinematic model of the target is cstimated by using short-term real-time data with the PSO algorithm.The established model is employed to predict the target trajectory in the interval between radar scans.Numerical simulation results of two different s enarios demonstrate the effectiveness of the proposed cooperative guidance approach.