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For accelerating the technology development and facilitating the reliable operation of lithium-ion batteries, accurate prediction for battery remaining useful life (RUL) are both critical. In this paper, a 1D CNN-BiLSTM method is proposed to extract the RUL prediction of lithium-ion battery of Electric Vehicles (EVs). By using one dimensional convolutional neural network (1D CNN) and bidirectional long short-term memory (BiLSTM) neural network simultaneously, selecting the ELU activation function to apply to the convolutional layer, a hybrid neural network is proposed to improve the accuracy and stability of lithium-ion battery RUL prediction. The 1D CNN is used to fully mine the deep features of lithium-ion SOH data, while the BiLSTM is adopted to study the deep features in two directions, and the RUL prediction of lithium-ion battery is output through dense layer. To verify the effectiveness of the proposed method, the battery data of the National Aeronautics and Space Administration (NASA) are utilized to make some comparisons among the RNN model, LSTM model, BiLSTM model and hybrid neural network model. The results show that the hybrid one has higher generalization ability and prediction accuracy than the others.

In the charging process of electric vehicles (EVs), high voltage and high current charging methods are widely used to reduce charging time, resulting in severe battery heating and an increased risk of fire. To improve fire detection efficiency, this paper proposes a real-time fire and flame detection method for electric vehicle charging station based on Machine Vision. The algorithm introduces the Kmeans + + algorithm in the GhostNet-YOLOv4 model to rescreen anchor boxes for flame smoke targets to optimize the classification quality for the complex and variable features of flame smoke targets; and introduces the coordinate attention (CA) module after the lightweight backbone network GhostNet to improve the classification quality. In this paper, we use EV charging station monitoring video as a model detection input source to achieve real-time detection of multiple pairs of sites. The experimental results demonstrate that the improved algorithm has a model parameter number of 11.436M, a mAP value of 87.70 percent, and a video detection FPS value of 75, which has a good continuous target tracking capability and satisfies the demand for real-time monitoring and is crucial for the safe operation of electric vehicle charging stations and the emergency extinguishing of fires.

Afforestation has significantly affected interactions between soil nutrients and microbial enzymes. To understand the detailed variations in extracellular enzyme activity and their link with soil nutrient availability after returning farmland (FL) to forest, soil samples were collected from FL and three afforested lands, Robinia pseudoacacia L. forest (RP), Caragana korshinskii Kom. forest (CK), and abandoned land (AL) in the Loess Hilly Region of northern China. The soil enzymes: β-glucosidase (BG), N-acetylglucosaminidase (NAG), alkaline phosphatase (AP), and leucine aminopeptidase (LAP); their stoichiometric ratios; and soil properties such as soil organic carbon, total nitrogen (TN), total phosphorus (TP), dissolved organic carbon, dissolved organic nitrogen, available phosphorus, soil moisture content (SMC), soil bulk density, and pH were measured. The BG activity showed similar trends as AP activity during afforestation, reaching the highest level in CK and showing a value 205% higher than that in FL. The NAG and LAP activities were not altered by afforestation; only the (NAG + LAP) : AP ratio decreased significantly by 44 to 60%. The BG : AP and (NAG + LAP) : AP ratios were strongly correlated with pH. Compared with other soil physicochemical properties, the soil moisture content greatly affected soil enzyme activity. The most relevant nutrients for the enzymes and stoichiometry were TN and TN : TP. Thus, our results suggest that soil enzyme activity and its stoichiometry are sensitive to changes in soil physical and chemical properties and total soil nutrients content, particularly pH, SMC, TN, and TN : TP.

Soil microbial communities are closely associated with aboveground plant communities and soil properties. This study explored the dynamics of soil bacterial communities during the plant growing season and their interaction with soil carbon and nitrogen, physicochemical properties, plant biomass and diversity following afforestation. The study investigated afforested lands containing Robinia pseudoacacia L (RP) and Caragana korshinskii Kom (CK), as well as abandoned land (AL) and farmland (FL) in the Loess Hilly Region of northern China. After establishment on former FL for 40 years, the Richness and Shannon's index, above-ground herbaceous biomass (AGB) and below-ground biomass (BGB) in RP and CK increased by 0.5, 0.1, 1.2 and 1.7 times, respectively, compared with AL. Additionally, the soil organic carbon (SOC), total nitrogen (TN), dissolved organic carbon/nitrogen (DOC/N) and microbial biomass carbon/nitrogen (MBC/N) increased by 1.7, 1.9, 0.8 and 2.5 times, respectively, while the soil bacterial abundance and alpha diversity (Shannon index) increased by 4.7% and 2.0% compared with FL. During the growing season, the soil carbon and nitrogen content was higher in August or October than in April or June. Particularly, the AGB, DOC and MBC showed a temporal pattern of normal distribution that was 36.7%, 48.2% and 74.9% higher in August than the rest of the study period. The BGB also increased by 123.5% in October compared with June in all study areas. The soil bacterial abundance in afforested lands was also higher in October, and beta bacterial diversity (Principal coordinates analysis plots: PCoA) was greater in June and August than in April and October. The dominant bacterial taxa, Proteobacteria and Bacteroidetes, were significantly higher in afforested lands than in FL, and Proteobacteria increased from April to October, while Actinobacteria and Acidobacteria peaked in June or August. These seasonal changes in the soil bacterial community were significantly correlated with carbon and nitrogen levels of soil and plant biomass, especially with DOC and BGB. Additionally, soil variables explained 41.2% of the total variation in bacterial-dominant phyla, while plant biomass only explained 20.2% of it, which indicates that soil properties are more important controlling factors of the bacterial community than plant biomass. In conclusion, soil variables change seasonally, which drives the composition and diversity of the soil bacterial community to exhibit a temporal pattern over the growing season after return of AL to forest.

The effects of vegetation restoration on plant characteristics and soil physicochemical properties have been widely documented; however, knowledge of the variation in soil ecoenzymatic activity and stoichiometry remains limited, particularly with respect to their relationship with plant and soil variables in restored ecosystems. Here, the vegetation and soil from one farmland and two restored land-use types (Robinia pseudoacacia plantations: RP and abandoned lands: AL) of four age classes (10, 18, 28, and 43-years) were investigated and sampled on the Loess Plateau, China. The activity of C, N, and P-acquiring enzymes (β-1,4-glucosidase, BG; β-1,4-N-acetylglucosaminidase, NAG; leucine aminopeptidase, LAP; and alkaline phosphatase, AP) and other major influencing factors (soil physical properties, soil nutrient contents, and microbial biomass) were determined. It was found that both restoration time and vegetation types significantly affect plant characteristics, soil physical properties, soil nutrient content, and microbial biomass. Soil BG, NAG + LAP, and AP enzyme activities were higher in RP and AL than in farmland, and increased with restoration time in AL. For RP, the activity of these enzymes increased from year 10 to year 28, then decreased from year 28 to year 43. Soil ecoenzymatic C:P and N:P activity ratios were ordered: farmland > AL > RP, and decreased with restoration time in AL and RP; thus, P limitation was stronger in RP than in AL and increased with restoration time in both AL and RP. Soil ecoenzymatic C:N:P acquisition ratios of farmland, AL, and RP deviated from the 1:1:1 ratio and depended on the availability of environmental nutrients and demand for microbial nutrients. The vegetation characteristics and soil physical properties were closely related to the nutrient acquisitions of microbes and, ultimately, contributed towards shaping soil ecoenzymatic activity and stoichiometry (particularly vegetation coverage, belowground biomass, soil water content, soil bulk density, and pH). Furthermore, variation in soil ecoenzymatic activity and stoichiometry was better accounted by dissolved nutrients in the soil (particularly C and N) and microbial biomass (particularly N and P) than by plant characteristics and soil properties. Overall, this study demonstrates that the C:N:P stoichiometry of soil microbes and ecoenzymatic activity is nutrient dependent, rather homeostatic, with the potential to influence nutrient cycling on the Loess Plateau.

We report a high-resolution and wide-range thermometer using a fiber Bragg grating Fabry–Perot cavity (FBG-FP) combined with beat frequency interrogation. Two distributed feedback (DFB) lasers are locked to the FBG-FP sensing head and a hydrogen cyanide H13C14N (HCN) gas cell, respectively, both using the Pound-Drever-Hall (PDH) technique. The light beams from two lasers are brought together to interfere on a photodetector producing a beat frequency signal which provides a measure of the temperature change. Our sensor exhibits a dynamic range of ∼109 °C, a high resolution of 2×10−4 °C with an averaging time of 1 s. By introducing the reference frequency, the sensor has demonstrated good long-term stability. This sensor provides a useful tool for those fields where resolving slight temperature changes is crucial, such as deep ocean temperature measurement.

Land degradation in drylands threatens vulnerable ecosystems and socioeconomic development. Currently, NDVI derived from remotely sensed data is the main tool used for degradation detection. Three indicators have usually been used to detect land degradation: (1) NDVI trends for visible degradation, (2) residual for human-induced potential degradation, and (3) sensitivity of vegetation to rainfall for functional degradation. However, few studies have integrated and compared these three indicators. In this study, we used Global Inventory Monitoring and Modelling System Version (GIMMS 3.1) NDVI dataset and Multiple Source Weighted-Ensemble Precipitation (MSWEP) rainfall dataset (1982-2015) and applied linear regression, Time Series Segmented and Residual Trend (TSS-RESTREND), and Sequential Regression (SeRGs) methods to detect degradation in southern Africa. The results showed that degradation was detected by these three respective indicators in 18.7%, 11.3%, and 7.1% of the study area. Degradation from any one type was found to occupy 27.21% of the total area, whereas the co-occurrence of two or more types only occupied 3.84%. These results indicate the dominant discrepancies among these indicators and the independent relationships among the degradation processes. Despite significantly greening, potential degradation and functional degradation were still observed. On the regional scale, spatial patterns of degradation were affected by different levels of aridity. On the national scale, the proportions of degradation were still influenced by increased population, inadequate policies, and other factors. This study highlights the need to detect degradation with multiple indicators and improves our understanding of degradation types and intensity.

Understanding the constraints on light-use efficiency (LUE) created by high evaporative water demand (vapor-pressure deficit; VPD) and restricted water supply (soil moisture content; SMC) is crucial for understanding and simulating vegetation productivity, particularly in arid and semi-arid regions. However, the relative impacts of VPD and SMC on photosynthesis are unclear, as we lack a mechanistic understanding of them and their interactions. In this study, we quantified the relative roles of VPD and SMC in limiting LUE and analyzed the interactions among VPD, SMC, and LUE in China’s Heihe River Basin using data from CO2 and water flux stations and weather stations along a climatic gradient. We found a threshold for VPD’s restriction of LUE; above the threshold, LUE decreased at only 3.6% to 23.1% of the rate below the threshold. As SMC decreased, however, the VPD threshold increased, and the reduction of LUE caused by VPD decreased significantly, which is more than half lower than that in moister regions. Therefore, both VPD and SMC played essential roles in LUE limitation and the resulting reduction of photosynthesis caused by water stress. A threshold also existed for heat flux and the correlation between SMC and LUE; the strength of the correlation first decreased and then increased with increasing VPD. Our results clarified the relative impacts of VPD and SMC on photosynthesis, and can improve simulation and prediction of plant productivity.

In this paper, a hybrid neural network is proposed by combining one dimensional convolutional neural network (1D CNN) and bidirectional long short-term memory (BiLSTM) neural network to improve the accuracy and stability of remaining useful life (RUL) prediction. 1D CNN-BiLSTM hybrid neural network has the ability to extract deep features in data and to save the memory of historical input information. To verify the authority of the proposed method, the lithium-ion battery data of the Center for Advanced Life Cycle Engineering (CALCE) are utilized to make some comparisons among the 1D CNN model, LSTM model and other neural network models. The results show that the hybrid one has higher prediction accuracy than the others.

To elucidate the effects of land-use types and afforestation age on litter decomposition, soil nutrient dynamics, and their relationship with substrate quality and soil environmental conditions, soil and litter samples were collected from farmland as well as four afforested land-use types (Robinia pseudoacacia: Rps; Caragana korshinskii: Cko; Pinus tabulaeformis: Pta; and Armeniaca sibirica: Asi), with each land-use type having three succession chronosequences (10, 25, and 40 a) in the Gaoxigou catchment area. These twelve afforested lands were converted from similar farmlands, and litterbag experiments were conducted in each land to determine litter decomposition rate (LDR). In addition, the carbon, nitrogen, and phosphorus contents and stoichiometry in soil and litter, soil properties, and litter biomass were determined. The results showed that soil environmental conditions such as soil water content, bulk density, pH, and temperature improved with afforestation age. Soil nutrient contents were higher in afforested lands and increased with afforestation age. The soil organic carbon (OC), total nitrogen (TN), and total phosphorus (TP) were positively correlated with the litter biomass, soil microbial carbon, and soil water content, but were negatively correlated with the soil bulk density, pH, and temperature. The litter OC, TN, and TP contents were mainly affected by the land-use types without being influenced by afforestation age. LDR is the main litter factor affecting soil nutrients, and is significantly influenced by substrate quality and environmental conditions, especially litter TN and N:P ratio, soil water content, and pH. The annual rates of increase for soil OC and TN during the initial (farmland–10a) and middle (10–25 a) periods were significantly higher than those during the later period (25–40 a) in Rps and Cko, but the Pta forest showed a completely opposite trend, which can be explained by a synchronous change in the LDR driven by the soil water content. In addition, the soil OC, TN, and TP contents were positively correlated with the litter TN, TP, and biomass, but had no correlation with the litter OC. The N:P ratio can be used as an indicator to reveal a tight coupling among soil and litter nutrients. Overall, these results provide evidence that litter decomposition in afforestation systems is linked to soil nutrient dynamics, and is mainly limited by substrate quality and environmental conditions.

The goal of this study was to determine the dynamics of physicochemical properties and biological activities of soil, and their relationship following afforestation. Soil samples were collected at 0–10 cm from five Pinus tabulaeformis plantation forests restored for 15, 25, 30, 45, and 70 years, as well as a millet (Setaria italica) farmland in the Damaiji catchment area. These five afforested lands were converted from similar farmlands. The activities of catalase (CAT), saccharase (SAC), urease (URE) and alkaline phosphatase (ALP), microbial biomass, soil water content, pH, soil bulk density, soil organic carbon (SOC), total nitrogen (TN), ammonium nitrogen, nitrate nitrogen, total phosphorus (TP), and available phosphorus (AP) were measured. The results revealed that the contents of SOC, TN, AP, microbial biomass C, N, and P, CAT, SAC, URE, and ALP in the P. tabulaeformis forest soil were significantly higher than those in the farmland by 64.97%–262.02%, 75.44%–254.28%, 46.63%–114.21%, 125.95%–554.83%, 101.35%–464.21%, 15.80%–167.35%, 22.57%–49.95%, 96.78%–145.73%, 6.98%–56.08% and 89.15%–177.89%, respectively. The soil properties, microbial biomass, enzymatic activities, and C:P and N:P ratios in soil and microbial biomass improved with increasing plantation chronosequence. Variations in C:N:P stoichiometry and higher C:P and N:P ratios in the soil and microbial biomass revealed the P limitation. Simultaneously, N:P ratios included more serviceable information that reflected the relationship between soil and microbes. Soil enzymatic activities had a high correlation with soil nutrient cycling and could be indicators of soil fertility status, particularly for ALP. The significant correlation between SOC, TN, enzymatic activities, and microbial biomass revealed that the substrate availability of carbon and nitrogen could influence the activity of soil enzymes and microorganisms. This study demonstrated that soil enzymatic activities and microorganisms respond to the process of afforestation and hence have the potential to affect nutrient balance and quality of soil.

The Amazon River is the largest river in the world in terms of freshwater discharge and sediment load. Understanding the fluvial sediment transport processes operating in the Amazon basin is critical because the Amazon basin has great research value for the sustainable development of local and global ecosystems. This study investigated changes in the mainstream sediment flux in the Amazon River system during 1996–2018. At the Obidos gauge station (on the Amazon mainstream), sediment loading significantly increased during 1996–2007 (earlier half of the study period), but the trend then reversed and sediment loading decreased during 2007–2018 (later period). River runoff was relatively stable during 1996–2018. The monthly sediment load and sediment concentration at Obidos were not synchronized with monthly runoff because of the asynchronism of the peak water discharges of the Solimoes, Madeira, and Negro Rivers. We infer that the significant increase in sediment flux from the Solimoes River was an important factor affecting the observed sediment increase at Obidos during 1996–2007. Besides, the increasing wash-load sediment flux at Manacapuru (on the Amazon tributary) should be derived from the Middle and Lower Solimoes River, because the sediment transport from the Upper Solimoes River was decreasing. We also found that the reversal of the sediment load trend at Obidos could be partly influenced by the decreasing trend of sediment transport from the Madeira River, and dam construction was one of the important causes. The reduced sediment loading in the Amazon mainstream will have major implications for the downstream ecosystem. Because planned dam constructions are expected to quadruple the number of dams in the Amazon basin, we suggest that the risk of wetland and muddy coast degradation caused by intensive hydropower development is an important pending issue.

Soil microorganisms play an important role in the functional connection of nutrient cycling between plants and soil ecosystems, but the exact responses of microbial communities to change in plant characteristics and soil properties remain uncertain. We analyzed the soil microbial communities of afforested tree stands of varying ages to assess the effects of vegetation and soil quality on soil microbial communities. We studied Robinia pseudoacacia plantations in the Loess Plateau for three age classes (RP13, RP29, and RP44), and compared results from these classes to one farmland (FL) control. The responses of soil microbial communities to changes in understory flora and soil physicochemical properties, including the Shannon index, richness, coverage, and biomass were analyzed. Compared with FL, afforestation significantly increased the Shannon index, species richness, coverage, and biomass of understory plants, which were highest in RP29. The concentrations of soil organic carbon (SOC), total nitrogen (TN), nitrate nitrogen (NO3−-N), and ammoniacal nitrogen (NH4+-N) were highest in RP44. The soil microbial community diversity index was significantly affected by afforestation. The relative abundances of bacterial populations were also affected, with Proteobacteria being dominant in RP29 and Actinobacteria being dominant in FL. Similarly, in fungi, the relative abundance of Basidiomycota was highest in FL, while the relative abundances of Zygomycota were highest in RP29. Pearson correlation analysis revealed that the Shannon and Chao indices of soil fungi were significantly positively correlated with SOC and NH4+-N. RDA showed that SOC, NH4+-N, and soil water content (SWC) were significantly associated with soil bacterial community composition. Soil fungal community composition were significantly affected by the Shannon and Richness indexes of understory flora. The results showed that characteristics of understory flora, soil properties, and soil microbial community composition were all affected by afforestation. The composition of the fungal community was correlated with changes in the diversity of understory flora. The changes in nutrients such as organic carbon and inorganic nitrogen was the key to the changes of soil microorganisms as plant colonization.

To deal with the disturbances of wave and current in the heading control of Autonomous Underwater Vehicles (AUVs), an optimal disturbances rejection control (ODRC) approach for AUVs in shallow water environment is designed to realize this application. Based on the quadratic optimal control theory, the AUVs heading control problem can be expressed as a coupled two-point boundary value (TPBV) problem. Using a recently developed successive approximation approach, the coupled TPBV problem is transformed into solving a decoupled linear state equation sequence and a linear adjoint equation sequence. By iteratively solving the two equation sequences, the approximate ODRC law is obtained. ALuenbergerobserver is constructed to estimate wave disturbances. Simulation is provided to demonstrate the effectiveness of the presented approach.

This paper considers the optimal control problem for time-delay bilinear systems affected by sinusoidal disturbances with known frequency and measurable amplitude and phase. Firstly, using the differential homeomorphism, a time-delay bilinear system affected by sinusoidal disturbances is changed to a time-delay pseudo linear system through the coordinate transformation. Then the system with time-delay in control variable is transformed to a linear controllable system without delay using model transformation. At last based on the theory of linear quadratic optimal control, an optimal control law which is used to eliminate the influence of the disturbances is derived from a Riccati equation and Matrix equations. The simulation results show the effectiveness of the method.

The comparison required the assignment of the mass fraction of folic acid present as the main component in the comparison sample. Performance in the comparison is representative of a laboratory's measurement capability for the purity assignment of organic compounds of medium structural complexity [molecular weight range 300–500] and high polarity (pKOW < −2). Methods used by the eighteen participating NMIs or DIs were based on a mass balance (summation of impurities) or qNMR approach, or the combination of data obtained using both methods. The qNMR results tended to give slightly lower values for the content of folic acid, albeit with larger associated uncertainties, compared with the results obtained by mass balance procedures. Possible reasons for this divergence are discussed in the report, without reaching a definitive conclusion as to their origin. The comparison demonstrates that for a structurally complex polar organic compound containing a high water content and presenting a number of additional analytical challenges, the assignment of the mass fraction content property value of the main component can reasonably be achieved with an associated relative standard uncertainty in the assigned value of 0.5% Main text To reach the main text of this paper, click on Final Report. Note that this text is that which appears in Appendix B of the BIPM key comparison database kcdb.bipm.org/. The final report has been peer-reviewed and approved for publication by the CCQM, according to the provisions of the CIPM Mutual Recognition Arrangement (CIPM MRA).

This paper presents a method of designing optimal dynamic compensator for a class of typical chemical reaction process-CSTR systems. Firstly, the model of nonlinear CSTR system is provided, Secondly, by using feedback linearization method, the nonlinear system is converted into a linear system, then according to the LQR theory, the methods of designing dynamic compensator is designed, and we analyze the asymptotic stability of the optimal regulator which has been compensated. At last, the simulation results show the effectiveness of the method.

This paper addresses the motion control problem of underactuated autonomous underwater vehicles (AUV) in vehicle plane affected by disturbances. Firstly, a six degrees-of-freedom AUV model with its body-fixed coordinate system is decoupled, simplified, and linear zed, and the depth control model and the wave model are obtained; Then a optimal output feedback disturbances rejection control law is proposed with a higher mean-square convergence rate, which is derived from a Riccati equation and Sylvester matrix equation according to the quadratic performance indexes. The proposed controller consists of a feedforward disturbance rejection item and an optimal output feedback item. Finally, the controller is applied to the dive plane control of AUV with wave force disturbances, and simulation results are presented to verify the effectiveness of the methods.

The optimal control problem for nonlinear systems with control time-delay affected by external disturbance is considered. A model transformation is first presented, which transforms the nonlinear system with time-delay into a system without delay formally. To solve the optimal control problem for nonlinear systems with time-delay is transformed into optimal control problem for non-delay nonlinear systems. Based on the optimal control theory, the two-point boundary value (TPBV) problem is constructed. By using the successive approximation approach, the nonlinear optimal control problem is transformed into a sequence of nonhomogeneous linear TPBV problems. we get approximate optimal control law by solving a Riccati matrix equation and two Stein matrix equations using successive approximation method. A simulation example shows that the approximate approach is effective and robust with respect to exogenous persistent disturbances.

This paper considers the optimal control problem for bilinear system with time-delay in control input based on state feedback. Firstly, we change a bilinear system with time-delay in control action model to a time-delay pseudo linear system model by local linearization. Through the Artstein transformation, a linear controllable system without delay is obtained. Then based on the theory of linear quadratic optimal control, a optimal controller is designed by solving the Riccati equation. At last, the simulation results show the effectiveness of the method.

The optimal tracking control problem for bilinear system affected by external disturbances based on state feedback is considered. Based on the concept of relative order of the output with respect to the input, firstly, a model of bilinear system affected by disturbances is changed to a model of pseudo linear system through the coordinate transformation. Then based on the theory of linear quadratic optimal control, eventually, the optimal control law is obtained by solving the two-point boundary value problem. At last, simulation examples show that the algorithm is effective.

This paper considers the optimal disturbance attenuation and rejection problem for MIMO systems affected by external sinusoidal disturbances based on stability degree constraint. The objective is to find an LQR optimal controller, by which the cost function minimum and the state with the optimal having a higher mean-square convergence rate can be obtained. A LQR control law is derive from a Riccati equation and Matrix equations. We give the existence and uniqueness conditions of the optimal control law. Finally, a practical example is given to illustrate the effectiveness of the theory

This paper presents the successive approximation procedure of the optimal solution for an infinite-time bilinear-quadratic optimal control problem. For a given bilinear system affected by period disturbances, a sequence of linear problems is constructed, and their solutions are shown to converge to the desired solution. By solving iterative the sequences, the optimal control law is obtained. By comparing the quadratic performance indexes, we can obtain an infinite-time approximate optimal disturbance control law. A simulation case is used to demonstrate the efficiency of the new approach.

It is shown in this paper that the successive approximation procedure simplifies computations of the optimal solution of a bilinear-quadratic optimal tacking control(OTC) problem. The bilinear system we study is affected by external disturbances. On the bases of the studies of Zijad and Hofer where the optimal solution has been obtained in the terms of a sequence of the differential equations, in the presented method only solutions of a sequence of the differential equations are required. A chemical reactor example is used to demonstrate the efficiency of the method.

Considering the persistent disturbances and the restraint of control variables in multivariable time-varying systems, an approximate singular optimal control method is presented, which makes use of a non-singular control problem instead of singular one. Firstly, this method presents the sufficient and necessary condition for the existent of non-singular optimal control law. Then the approximate optimal control law is obtained by optimizing according to the restraint of control variables, which improves the singular control method. The simulation result demonstrates its effectiveness.