Robust H_∞ and H_2 Static Output Feedback Control of Discrete-time Piecewise Affine Singular Systems with Norm-bounded Uncertainties

This paper is concerned with the problem of designing robust H∞and H2static output feedback controllers for a class of discrete-time piecewise-affine singular systems with norm-bounded time-varying parameters uncertainties. Based on a piecewise singular Lyapunov function combined with S-procedure,Projection lemma and some matrix inequality convexifying techniques,sufficient conditions in terms of linear matrix inequalities are given for the existence of an output-feedback controller for the discrete-time piecewiseaffine singular systems with a prescribed H∞disturbance attenuation level,and the H2norm is smaller than a given positive number. It is shown that the controller gains can be obtained by solving a family of LMIs parameterized by one or two scalar variables. The numerical examples are given to illustrate the effectiveness of the proposed design methods.

Determination of uncertainties of geomechanical parameters of metamorphic rocks using petrographic analyses

Geomechanical parameters of intact metamorphic rocks determined from laboratory testing remain highly uncertain because of the great intrinsic variability associated with the degrees of metamorphism.The aim of this paper is to develop a proper methodology to analyze the uncertainties of geomechanical characteristics by focusing on three domains,i.e.data treatment process,schistosity angle,and mineralogy.First,the variabilities of the geomechanical laboratory data of Westwood Mine(Quebec,Canada)were examined statistically by applying different data treatment techniques,through which the most suitable outlier methods were selected for each parameter using multiple decision-making criteria and engineering judgment.Results indicated that some methods exhibited better performance in identifying the possible outliers,although several others were unsuccessful because of their limitation in large sample size.The well-known boxplot method might not be the best outlier method for most geomechanical parameters because its calculated confidence range was not acceptable according to engineering judgment.However,several approaches,including adjusted boxplot,2MADe,and 2SD,worked very well in the detection of true outliers.Also,the statistical tests indicate that the best-fitting probability distribution function for geomechanical intact parameters might not be the normal distribution,unlike what is assumed in most geomechanical studies.Moreover,the negative effects of schistosity angle on the uniaxial compressive strength(UCS)variabilities were reduced by excluding the samples within a specific angle range where the UCS data present the highest variation.Finally,a petrographic analysis was conducted to assess the associated uncertainties such that a logical link was found between the dispersion and the variabilities of hard and soft minerals.

Seasonal Characteristics of Forecasting Uncertainties in Surface PM_(2.5)Concentration Associated with Forecast Lead Time over the Beijing-Tianjin-Hebei Region

Forecasting uncertainties among meteorological fields have long been recognized as the main limitation on the accuracy and predictability of air quality forecasts.However,the particular impact of meteorological forecasting uncertainties on air quality forecasts specific to different seasons is still not well known.In this study,a series of forecasts with different forecast lead times for January,April,July,and October of 2018 are conducted over the Beijing-Tianjin-Hebei(BTH)region and the impacts of meteorological forecasting uncertainties on surface PM_(2.5)concentration forecasts with each lead time are investigated.With increased lead time,the forecasted PM_(2.5)concentrations significantly change and demonstrate obvious seasonal variations.In general,the forecasting uncertainties in monthly mean surface PM_(2.5)concentrations in the BTH region due to lead time are the largest(80%)in spring,followed by autumn(~50%),summer(~40%),and winter(20%).In winter,the forecasting uncertainties in total surface PM_(2.5)mass due to lead time are mainly due to the uncertainties in PBL heights and hence the PBL mixing of anthropogenic primary particles.In spring,the forecasting uncertainties are mainly from the impacts of lead time on lower-tropospheric northwesterly winds,thereby further enhancing the condensation production of anthropogenic secondary particles by the long-range transport of natural dust.In summer,the forecasting uncertainties result mainly from the decrease in dry and wet deposition rates,which are associated with the reduction of near-surface wind speed and precipitation rate.In autumn,the forecasting uncertainties arise mainly from the change in the transport of remote natural dust and anthropogenic particles,which is associated with changes in the large-scale circulation.

Assessment of earthquake location uncertainties for the design of local seismic networks

The ability to estimate earthquake source locations,along with the appraisal of relevant uncertainties,is paramount in monitoring both natural and human-induced micro-seismicity.For this purpose,a monitoring network must be designed to minimize the location errors introduced by geometrically unbalanced networks.In this study,we first review different sources of errors relevant to the localization of seismic events,how they propagate through localization algorithms,and their impact on outcomes.We then propose a quantitative method,based on a Monte Carlo approach,to estimate the uncertainty in earthquake locations that is suited to the design,optimization,and assessment of the performance of a local seismic monitoring network.To illustrate the performance of the proposed approach,we analyzed the distribution of the localization uncertainties and their related dispersion for a highly dense grid of theoretical hypocenters in both the horizontal and vertical directions using an actual monitoring network layout.The results expand,quantitatively,the qualitative indications derived from purely geometrical parameters(azimuthal gap(AG))and classical detectability maps.The proposed method enables the systematic design,optimization,and evaluation of local seismic monitoring networks,enhancing monitoring accuracy in areas proximal to hydrocarbon production,geothermal fields,underground natural gas storage,and other subsurface activities.This approach aids in the accurate estimation of earthquake source locations and their associated uncertainties,which are crucial for assessing and mitigating seismic risks,thereby enabling the implementation of proactive measures to minimize potential hazards.From an operational perspective,reliably estimating location accuracy is crucial for evaluating the position of seismogenic sources and assessing possible links between well activities and the onset of seismicity.

Uncertainties of landslide susceptibility prediction:influences of different study area scales and mapping unit scales

This study aims to investigate the effects of different mapping unit scales and study area scales on the uncertainty rules of landslide susceptibility prediction(LSP).To illustrate various study area scales,Ganzhou City in China,its eastern region(Ganzhou East),and Ruijin County in Ganzhou East were chosen.Different mapping unit scales are represented by grid units with spatial resolution of 30 and 60 m,as well as slope units that were extracted by multi-scale segmentation method.The 3855 landslide locations and 21 typical environmental factors in Ganzhou City are first determined to create spatial datasets with input-outputs.Then,landslide susceptibility maps(LSMs)of Ganzhou City,Ganzhou East and Ruijin County are pro-duced using a support vector machine(SVM)and random forest(RF),respectively.The LSMs of the above three regions are then extracted by mask from the LSM of Ganzhou City,along with the LSMs of Ruijin County from Ganzhou East.Additionally,LSMs of Ruijin at various mapping unit scales are generated in accordance.Accuracy and landslide suscepti-bility indexes(LSIs)distribution are used to express LSP uncertainties.The LSP uncertainties under grid units significantly decrease as study area scales decrease from Ganzhou City,Ganzhou East to Ruijin County,whereas those under slope units are less affected by study area scales.Of course,attentions should also be paid to the broader representativeness of large study areas.The LSP accuracy of slope units increases by about 6%–10%compared with those under grid units with 30 m and 60 m resolution in the same study area's scale.The significance of environmental factors exhibits an averaging trend as study area scale increases from small to large.The importance of environmental factors varies greatly with the 60 m grid unit,but it tends to be consistent to some extent in the 30 m grid unit and the slope unit.

Robust decentralized H_∞ control of multi-channel systems with norm-bounded parametric uncertainties

A robust decentralized H∞ control problem for uncertain multi-channel systems is considered. The uncertainties are assumed to be time-invariant, norm-bounded, and exist in both the system and control input matrices. The dynamic output feedback is mainly dealt with. A necessary and sufficient condition for the uncertain multi-channel system to be stabilized robustly with a specified disturbance attenuation level is derived based on the bounded real lemma, which is reduced to a feasibility problem of a nonlinear matrix inequality （NMI）. A two-stage homotopy method is used to solve the NMI iteratively. First, a decentralized controller for the nominal system with no uncertainty is computed by imposing structural constraints on the coefficient matrices of the controller gradually. Then the decentralized controller is modified, again gradually, to cope with the uncertainties. On each stage, a variable is fixed alternately at the iterations to reduce the NMI to a linear matrix inequality （LMI）. A given example shows the efficiency of this method.

EXPONENTIAL ESTIMATES FOR STOCHASTIC DELAY EQUATIONS WITH NORM-BOUNDED UNCERTAINTIES

This paper presents the sufficient conditions for the exponential stability of linear or semi-linear stochastic delay equations with time-varying norm bounded parameter uncertainties.Exponen-tial estimates for the solutions are also obtained by using a modified Lyapunov-Krasovski functional.These conditions can be tested numerically using interior point algorithms.

Adaptive Leader-Follower Consensus Control of Multiple Flexible Manipulators With Actuator Failures and Parameter Uncertainties

In this paper,the leader-follower consensus problem for a multiple flexible manipulator network with actuator failures,parameter uncertainties,and unknown time-varying boundary disturbances is addressed.The purpose of this study is to develop distributed controllers utilizing local interactive protocols that not only suppress the vibration of each flexible manipulator but also achieve consensus on joint angle position between actual followers and the virtual leader.Following the accomplishment of the reconstruction of the fault terms and parameter uncertainties,the adaptive neural network method and parameter estimation technique are employed to compensate for unknown items and bounded disturbances.Furthermore,the Lyapunov stability theory is used to demonstrate that followers’angle consensus errors and vibration deflections in closed-loop systems are uniformly ultimately bounded.Finally,the numerical simulation results confirm the efficacy of the proposed controllers.

Adaptive recurrent neural network for uncertainties estimation in feedback control system

In this paper,a recurrent neural network(RNN)is used to estimate uncertainties and implement feedback control for nonlinear dynamic systems.The neural network approximates the uncertainties related to unmodeled dynamics,parametric variations,and external disturbances.The RNN has a single hidden layer and uses the tracking error and the output as feedback to estimate the disturbance.The RNN weights are online adapted,and the adaptation laws are developed from the stability analysis of the controlled system with the RNN estimation.The used activation function,at the hidden layer,has an expression that simplifies the adaptation laws from the stability analysis.It is found that the adaptive RNN enhances the tracking performance of the feedback controller at the transient and steady state responses.The proposed RNN based feedback control is applied to a DC–DC converter for current regulation.Simulation and experimental results are provided to show its effectiveness.Compared to the feedforward neural network and the conventional feedback control,the RNN based feedback control provides good tracking performance.

Influence of uncertainties: A focus on block volume and shape assessment for rockfall analysis

Block size and shape depend on the state of fracturing of the rock mass and,consequently,on the geometrical features of the discontinuity sets(mainly orientation,spacing,and persistence).The development of non-contact surveying techniques applied to rock mass characterization offers significant advantages in terms of data numerosity,precision,and accuracy,allowing for performing a rigorous statistical analysis of the database.This fact is particularly evident when dealing with rockfall phenomena:uncertainties in spacing and orientation data could significantly amplify the uncertainties connected with in situ block size distribution(IBSD),which represents a relation between each possible value of the volume and its probability of not being exceeded.In addition to volume,block shape can be considered as a derived parameter that suffers from uncertainties.Many attempts to model the possible trajectories of blocks considering their actual shape have been proposed,aiming to reproduce the effect on motion.The authors proposed analytical equations for calculating the expected value and variance of volume distributions,based on the geometrically correct equation for block volume in the case of three discontinuity sets.They quantify and discuss the effect of both volume and shape variability through a synthetic case study.Firstly,a fictitious rock mass with three discontinuity sets is assumed as the source of rockfall.The IBSDs obtained considering different spacing datasets are quantitatively compared,and the overall uncertainty effect is assessed,proving the correctness of the proposed equations.Then,block shape distributions are obtained and compared,confirming the variability of shapes within the same IBSD.Finally,a comparison between trajectory simulations on the synthetic slope is reported,aiming to highlight the effects of the propagation of uncertainties to block volume and shape estimation.The benefits of an approach that can quantify the uncertainties are discussed from the perspective of improving the reliability of simulations.

A Novel Two-Stage Scheduling Approach for a Hybrid Floating Photovoltaic-Battery-Hydropower Plant Considering Uncertainties

The application of floating photovoltaics (PVs) in hydropower plants has gained increasing interest in forming hybrid energy systems (HESs). It enhances the operational benefits of the existing hydropower plants. However, uncertainties of PV and load powers can present great challenges to scheduling HESs. To address these uncertainties, this paper proposes a novel two-stage optimization approach that combines distributionally robust chance-constrained (DRCC) and robust-stochastic optimization (RSO) approaches to minimize the operational cost of an HES. In the first stage, the scheduling of each device is obtained via the DRCC approach considering the PV power and load forecast errors. The second stage provides a robust near real time energy dispatch according to different scenarios of PV power and load demand. The solution of the RSO problem is obtained via a novel double-layer particle swarm optimization algorithm. The performance of the proposed approach is compared to the traditional stochastic and robust-stochastic approaches. Simulation results de- monstrate the superiority of the proposed two-stage approach and its solution method in terms of operational cost and execution time.

Fourth-Order Predictive Modelling: II. 4th-BERRU-PM Methodology for Combining Measurements with Computations to Obtain Best-Estimate Results with Reduced Uncertainties

This work presents a comprehensive fourth-order predictive modeling (PM) methodology that uses the MaxEnt principle to incorporate fourth-order moments (means, covariances, skewness, kurtosis) of model parameters, computed and measured model responses, as well as fourth (and higher) order sensitivities of computed model responses to model parameters. This new methodology is designated by the acronym 4th-BERRU-PM, which stands for “fourth-order best-estimate results with reduced uncertainties.” The results predicted by the 4th-BERRU-PM incorporates, as particular cases, the results previously predicted by the second-order predictive modeling methodology 2nd-BERRU-PM, and vastly generalizes the results produced by extant data assimilation and data adjustment procedures.

Non-Negative Adaptive Mechanism-Based Sliding Mode Control for Parallel Manipulators with Uncertainties

In this paper,a non-negative adaptive mechanism based on an adaptive nonsingular fast terminal sliding mode control strategy is proposed to have finite time and high-speed trajectory tracking for parallel manipulators with the existence of unknown bounded complex uncertainties and external disturbances.The proposed approach is a hybrid scheme of the online non-negative adaptive mechanism,tracking differentiator,and nonsingular fast terminal sliding mode control(NFTSMC).Based on the online non-negative adaptive mechanism,the proposed control can remove the assumption that the uncertainties and disturbances must be bounded for the NFTSMC controllers.The proposed controller has several advantages such as simple structure,easy implementation,rapid response,chattering-free,high precision,robustness,singularity avoidance,and finite-time convergence.Since all control parameters are online updated via tracking differentiator and non-negative adaptive law,the tracking control performance at high-speed motions can be better in real-time requirement and disturbance rejection ability.Finally,simulation results validate the effectiveness of the proposed method.

Dynamic analysis and experimental study of vibro-acoustic system with uncertainties at middle frequencies

To take into account the influence of uncetainties on the dynamic response of the vibro-acousitc structure, a hybrid modeling technique combining the finite element method（FE）and the statistic energy analysis（SEA） is proposed to analyze vibro-acoustics responses with uncertainties at middle frequencies. The mid-frequency dynamic response of the framework-plate structure with uncertainties is studied based on the hybrid FE-SEA method and the Monte Carlo（MC）simulation is performed so as to provide a benchmark comparison with the hybrid method. The energy response of the framework-plate structure matches well with the MC simulation results, which validates the effectiveness of the hybrid FE-SEA method considering both the complexity of the vibro-acoustic structure and the uncertainties in mid-frequency vibro-acousitc analysis. Based on the hybrid method, a vibroacoustic model of a construction machinery cab with random properties is established, and the excitations of the model are measured by experiments. The responses of the sound pressure level of the cab and the vibration power spectrum density of the front windscreen are calculated and compared with those of the experiment. At middle frequencies, the results have a good consistency with the tests and the prediction error is less than 3. 5dB.

Solvability Condition for Robust Stabilization Problem of Control Systems with Parameter Uncertainties

Aim The solvability condition for robust stabilization problem associated with a plant family P(s,δ) having parameter uncertainty δ was considered. Methods Using Youla parameterization of the stabilizers this problem was transformed into a strong stabilization problem associated with a related plant family G (s, δ). Results A necessary solvability condition was established in terms of the parity interlacing property of each element in G(s,δ). Another apparently necessary solvability condition is that every element in P(s,δ) must be stabilizable. Conclusion The two conditions will be compared with each other and it will be shown that every element in G(s,δ) possesses parity interlacing property if P(s,δ) is stabilizable.

Future Changes and Uncertainties in Temperature and Precipitation over China Based on CMIP5 Models

Climate changes in future 21 st century China and their uncertainties are evaluated based on 22 climate models from the Coupled Model Intercomparison Project Phase 5（CMIP5）. By 2081–2100, the annual mean surface air temperature（SAT） is predicted to increase by 1.3℃± 0.7℃, 2.6℃± 0.8℃ and 5.2℃± 1.2℃ under the Representative Concentration Pathway（RCP） scenarios RCP2.6, RCP4.5 and RCP8.5, relative to 1986–2005, respectively. The future change in SAT averaged over China increases the most in autumn/winter and the least in spring, while the uncertainty shows little seasonal variation.Spatially, the annual and seasonal mean SAT both show a homogeneous warming pattern across China, with a warming rate increasing from southeastern China to the Tibetan Plateau and northern China, invariant with time and emissions scenario.The associated uncertainty in SAT decreases from northern to southern China. Meanwhile, by 2081–2100, the annual mean precipitation increases by 5% ± 5%, 8% ± 6% and 12% ± 8% under RCP2.6, RCP4.5 and RCP8.5, respectively. The national average precipitation anomaly percentage, largest in spring and smallest in winter, and its uncertainty, largest in winter and smallest in autumn, show visible seasonal variations. Although at a low confidence level, a homogeneous wetting pattern is projected across China on the annual mean scale, with a larger increasing percentage in northern China and a weak drying in southern China in the early 21 st century. The associated uncertainty is also generally larger in northern China and smaller in southwestern China. In addition, both SAT and precipitation usually show larger seasonal variability on the sub-regional scale compared with the national average.

Sensitivity of key factors and uncertainties in health risk assessment of benzene pollutant

Predicting long-term potential human health risks from contaminants in the multimedia environment requires the use of models. However, there is uncertainty associated with these predictions of many parameters which can be represented by ranges or probability distributions rather than single value. Based on a case study with information from an actual site contaminated with benzene, this study describes the application of MMSOILS model to predict health risk and distributions of those predictions generated using Monte Carlo techniques. A sensitivity analysis was performed to evaluate which of the random variables are most important in producing the predicted distributions of health risks. The sensitivity analysis shows that the predicted distributions can be accurately reproduced using a small subset of the random variables. The practical implication of this analysis is the ability to distinguish between important versus unimportant random variables in terms of their sensitivity to selected endpoints. This directly translates into a reduction in data collection and modeling effort. It was demonstrated that how correlation coefficient could be used to evaluate contributions to overall uncertainty from each parameter. The integrated uncertainty analysis shows that although drinking groundwater risk is similar with inhalation air risk, uncertainties of total risk come dominantly from drinking groundwater route. Most percent of the variance of total risk comes from four random variables.

Optimized design of drilling and blasting operations in open pit mines under technical and economic uncertainties by system dynamic modelling

Drilling and blasting are the two most significant operations in open pit mines that play a crucial role in downstream stages. While previous research has focused on optimizing these operations as two separate parts or merely in a specific parameter, this paper proposes a system dynamic model(SDM) for drilling and blasting operations as an interactive system. In addition, some technical and economic uncertainties such as rock density, uniaxial compressive strength, bit life and operating costs are considered in this system to evaluate the different optimization results. For this purpose, Vensim simulation software is utilized as a powerful dynamic tool for both modelling and optimizing under deterministic and uncertain conditions. It is concluded that an integrated optimization as opposed to the deterministic approach can be efficiently achieved. This however is dependent on the parameters that are considered as uncertainties.

Discussion on determination of gas content of coal and uncertainties of measurement

Gas content of coal is mostly determined using a direct method, particularly in coal mining where mine safety is of paramount importance. Direct method consists of measuring directly the volume of gas desorbed from coal in several steps, from solid then crushed coal. In mixed gas conditions the composition of the desorbed gas is also measured to account for contribution of various coal seam gas in the mix. The determination of gas content using the direct method is associated with errors of measurement of volume of gas but also the errors associated with measurement of composition of the desorbed gas. These errors lead to uncertainties in reporting the gas content and composition of in-situ seam gas. This paper discusses the current direct method practised in Australia and potential errors and uncertainty associated with this method. Generic methods of estimate of uncertainties are also developed and are to be included in reporting gas content of coal. A method of direct measurement of remaining gas in coal following the completion of standard gas content testing is also presented. The new method would allow the determination of volume of almost all gas in coal and therefore the value of total gas content. This method is being considered to be integrated into a new standard for gas content testing.

The Roles of Spatial Locations and Patterns of Initial Errors in the Uncertainties of Tropical Cyclone Forecasts

In this study, a series of sensitivity experiments were performed for two tropical cyclones （TCs）, TC Longwang （2005） and TC Sinlaku （2008）, to explore the roles of locations and patterns of initial errors in uncertainties of TC forecasts. Specifically, three types of initial errors were generated and three types of sensitive areas were determined using conditional nonlinear optimal perturbation （CNOP）, first singular vector （FSV）, and composite singular vector （CSV） methods. Additionally, random initial errors in randomly selected areas were considered. Based on these four types of initial errors and areas, we designed and performed 16 experiments to investigate the impacts of locations and patterns of initial errors on the nonlinear developments of the errors, and to determine which type of initial errors and areas has the greatest impact on TC forecasts. Overall, results from the experiments indicate the following： （1） The impact of random errors introduced into the sensitive areas was greater than that of errors themselves fixed in the randomly selected areas. From the perspective of statisticul analysis, and by comparison, the impact of random errors introduced into the CNOP target area was greatest. （2） The initial errors with CNOP, CSV, or FSV patterns were likely to grow faster than random errors. （3） The initial errors with CNOP patterns in the CNOP target areas had the greatest impacts on the final verification forecasts.