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Sliding mode-based adaptive tube model predictive control for robotic manipulators with model uncertainty and state constraints

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Control Theory and Technology 2023年第3期21卷 334-351页

作者： Erlong Kang Yang Liu Hong Qiao State Key Laboratory of Multimodal Artificial Intelligence Systems Institute of AutomationChinese Academy of SciencesBeijing 100190China Beijing Key Laboratory of Research and Application for Robotic Intelligence of Hand-Eye-Brain Interaction Beijing 100190China The School of Mechanical Engineering University of Science and Technology BeijingBeijing 100083China University of Chinese Academy of Sciences Beijing 100049China CAS Center for Excellence in Brain Science and Intelligence Technology Shanghai 200031China

In this paper,the optimal tracking control for robotic manipulators with state constraints and uncertain dynamics is investigated,and a sliding mode-based adaptive tube model predictive control method is proposed.First,utilizing the high-order fully actuated system approach,the nominal model of the robotic manipulator is constructed as the predictive model.Based on the nominal model,a nominal model predictive controller with the sliding mode is designed,which relaxes the terminal constraints,and realizes the accurate and stable tracking of the desired trajectory by the nominal system.Then,an auxiliary controller based on the node-adaptive neural networks is constructed to dynamically compensate nonlinear uncertain dynamics of the robotic manipulator.Furthermore,the estimation deviation between the nominal and actual states is limited to the tube invariant sets.At the same time,the recursive feasibility of nominal model predictive control is verified,and the ultimately uniformly boundedness of all variables is proved according to the Lyapunov theorem.Finally,experiments show that the robotic manipulator can achieve fast and efficient trajectory tracking under the action of the proposed method.

关键词： Tube-based model predictive control-Robotic manipulator Sliding mode Node-adaptive neural networks model uncertainty

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Optimal Reinsurance and Dividend Under model uncertainty

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Journal of Systems Science & Complexity 2023年第3期36卷 1116-1143页

作者： LIU Jingzhen WANG Yike ZHANG Ning China Institute for Actuarial Science Central University of Finance and EconomicsBeijing 100081China School of Finance&Chinese Fintech Research Center Central University of Finance and EconomicsBeijing 100081China

In this paper,the authors analyze the optimal reinsurance and dividend problem with model uncertainty for an insurer.Here the model uncertainty represents possible deviations between the real market and the assumed model.In addition to the incorporation of model uncertainty into the traditional diffusion surplus process,the authors include a penalty function in the objective function.The proposed goal is to find the optimal reinsurance and dividend strategy that maximizes the expected discounted dividend before ruin in the worst case of all possible scenarios,namely,the worst market.Using a dynamic programming approach,the problem is reduced to solving a Hamilton-Jacob-Bellman-Isaac(HJBI)equation with singular control.This problem is more difficult than the traditional robust control or singular control problem.Here,the authors prove that the value function is the unique solution to this HJBI equation with singular control.Moreover,the authors present a verification theorem when a smooth solution can be found,and derive closed-form solution when the function in the objective function is specified.

关键词： Hamilton-Jacobi-Bellman-Isaac equation model uncertainty optimal dividend proportional reinsurance

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A Nonlinear Representation of model uncertainty in a Convective-Scale Ensemble Prediction System

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Advances in Atmospheric Sciences 2022年第9期39卷 1432-1450页

作者： Zhizhen XU Jing CHEN Mu MU Guokun DAI Yanan MA Department of Atmospheric and Oceanic Sciences&Institute of Atmospheric Sciences Fudan UniversityShanghai 200438China Numerical Weather Prediction Center China Meteorological AdministrationBeijing 100081China Chinese Academy of Meteorological Sciences China Meteorological AdministrationBeijing 100081China

How to accurately address model uncertainties with consideration of the rapid nonlinear error growth characteristics in a convection-allowing system is a crucial issue for performing convection-scale ensemble forecasts.In this study,a new nonlinear model perturbation technique for convective-scale ensemble forecasts is developed to consider a nonlinear representation of model errors in the Global and Regional Assimilation and Prediction Enhanced System(GRAPES)Convection-Allowing Ensemble Prediction System(CAEPS).The nonlinear forcing singular vector(NFSV)approach,that is,conditional nonlinear optimal perturbation-forcing(CNOP-F),is applied in this study,to construct a nonlinear model perturbation method for GRAPES-CAEPS.Three experiments are performed:One of them is the CTL experiment,without adding any model perturbation;the other two are NFSV-perturbed experiments,which are perturbed by NFSV with two different groups of constraint radii to test the sensitivity of the perturbation magnitude constraint.Verification results show that the NFSV-perturbed experiments achieve an overall improvement and produce more skillful forecasts compared to the CTL experiment,which indicates that the nonlinear NFSV-perturbed method can be used as an effective model perturbation method for convection-scale ensemble forecasts.Additionally,the NFSV-L experiment with large perturbation constraints generally performs better than the NFSV-S experiment with small perturbation constraints in the verification for upper-air and surface weather variables.But for precipitation verification,the NFSV-S experiment performs better in forecasts for light precipitation,and the NFSV-L experiment performs better in forecasts for heavier precipitation,indicating that for different precipitation events,the perturbation magnitude constraint must be carefully selected.All the findings above lay a foundation for the design of nonlinear model perturbation methods for future CAEPSs.

关键词： Convection-Allowing Ensemble Prediction System model uncertainty nonlinear forcing singular vector

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model uncertainty Representation for a Convection-Allowing Ensemble Prediction System Based on CNOP-P

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Advances in Atmospheric Sciences 2020年第8期37卷 817-831页

作者： Lu WANG Xueshun SHEN Juanjuan LIU Bin WANG Asset Operation Centre China Meteorological AdministrationBeijing 100081China State Key Laboratory of Severe Weather Chinese Academy of Meteorological SciencesBeijing 100081China Numerical Weather Prediction Center/National Meteorological Center China Meteorological AdministrationBeijing 100081China Institute of Atmosphere Physics Chinese Academy of SciencesBeijing 100029China Center for Earth System Science Tsinghua UniversityBeijing 100084China

Formulating model uncertainties for a convection-allowing ensemble prediction system(CAEPS)is a much more challenging problem compared to well-utilized approaches in synoptic weather forecasting.A new approach is proposed and tested through assuming that the model uncertainty should reasonably describe the fast nonlinear error growth of the convection-allowing model,due to the fast developing character and strong nonlinearity of convective events.The Conditional Nonlinear Optimal Perturbation related to Parameters(CNOP-P)is applied in this study.Also,an ensemble approach is adopted to solve the CNOP-P problem.By using five locally developed strong convective events that occurred in pre-rainy season of South China,the most sensitive parameters were detected based on CNOP-P,which resulted in the maximum variations in precipitation.A formulation of model uncertainty is designed by adding stochastic perturbations into these sensitive parameters.Through comparison ensemble experiments by using all the 13 heavy rainfall cases that occurred in the flood season of South China in 2017,the advantages of the CNOP-P-based method are examined and verified by comparing with the well-utilized stochastically perturbed physics tendencies(SPPT)scheme.The results indicate that the CNOP-P-based method has potential in improving the under-dispersive problem of the current CAEPS.

关键词： CNOP-P convective scale model uncertainty ensemble forecastforecast

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Reliability estimation of mechanical seals based on bivariate dependence analysis and considering model uncertainty

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Chinese Journal of Aeronautics 2021年第5期34卷 554-572页

作者： Rentong CHEN Chao ZHANG Shaoping WANG Yujie QIAN School of Automation Science and Electrical Engineering Beihcmg UniversityBeijing 100083China Research Institute for Frontier Science Beihang UniversityBeijing 100083China Beijing Advanced Innovation Center for Big Data-Based Precision Medicine Beihcmg UniversityBeijing100083China Ningbo Institute of Technology Beihang UniversityNingbo 315800China

The reliability estimation of mechanical seals is of crucial importance due to their wide applications in pumps in various mechanical systems.Failure of mechanical seals might cause leakage,and might lead to system failure and other relevant consequences.In this study,the reliability estimation for mechanical seals based on bivariate dependence analysis and considering model uncertainty is proposed.The friction torque and leakage rate are two degradation performance indicators of mechanical seals that can be described by the Wiener process,Gamma process,and inverse Gaussian process.The dependence between the two indicators can be described by different copula functions.Then the model uncertainty is considered in the reliability estimation using the Bayesian model Average(BMA)method,while the unknown parameters in the model are estimated by Bayesian Markov Chain Monte Carlo(MCMC)method.A numerical simulation study and fatigue crack study are conducted to demonstrate the effectiveness of the BMA method to capture model uncertainty.A degradation test of mechanical seals is conducted to verify the proposed model.The optimal stochastic process models for two performance indicators and copula function are determined based on the degradation data.The results show the necessity of using the BMA method in degradation modeling.

关键词： Bayesian model Average Copula Dependence analysis Mechanical seal model uncertainty Reliability estimation

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The Risk Transfer of Non-tradable Risks under model uncertainty

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Acta Mathematica Sinica,English Series 2012年第8期28卷 1597-1614页

作者： Yu Lian FAN Department of Mathematics North China University of Technology

In the context of model uncertainty, we study the optimal design and the pricing of financial instruments aiming to hedge some of non-tradable risks. For the existence of model uncertainty, the preference can be represented by the robust expected utility （also called maxmin expected utility） which can be put in the framework of sublinear expectation. The problem of maximizing the issuer＇s robust expected utility under the constraint imposed by the buyer can be transformed to the problem of minimizing the issuer＇s convex measure under the corresponding constraint. And here the convex measure measures not only the risks but also the model uncertainties.

关键词： model uncertainty sublinear expectation indifference pricing risk measure

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Cost-Benefit Assessment of Inspection and Repair Planning for Ship Structures Considering Corrosion model uncertainty

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China Ocean Engineering 2005年第3期19卷 409-420页

作者：李典庆唐文勇张圣坤 State Key Laboratory of Water Resources and Hydropower Engineering Sciences Wuhan University Wuhan 430072 ChinaSchool of Naval Ocean and Civil Engineering Shanghai Jiao Tong University Shanghai200030 China School of Naval Ocean and Civil Engineering Shanghai Jiao Tong University Shanghai200030 China

Owing to high costs and unnecessary inspections necessitated by the traditional inspection planning for ship structures, the risk-based inspection and repair planning should be investigated for the most cost-effective inspection. This paper aims to propose a cost-benefit assessment model of risk-based inspection and repair planning for ship structures subjected to corrosion deterioration. Then, the benefit-cost ratio is taken to be an index for the selection of the optimal inspection and repair strategy. The planning problem is formulated as an optimization problem where the benefit-cost ratio for the expected lifetime is maximized with a constraint on the minimum acceptalbe reliability index. To account for the effect of corrosion model uncertainty on the cost-benefit assessment, two corrosion models, namgly, Paik＇ s model and Guedes Soares＇ model, are adopted for analysis. A numerical example is presented to illustrate the proposed method. Sensitivity studies are also providet. The results indicate that the proposed method of risk-based cost-benefit analysis can effectively integrate the economy with reliability of the inspection and repair planning. A balance can be achieved between the risk cost and total expected inspection and repair costs with the proposed method, which is very. effective in selecting the optimal inspection and repair strategy. It is pointed out that the corrosion model uncertainty and parametric uncertaintg have a significant impact on the cost-benefit assessment of inspection and repair planning.

关键词： ship structures inspection and repair planning cost-benefit model uncertainty

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Financial asset price bubbles under model uncertainty

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Probability, uncertainty and Quantitative Risk 2017年第1期2卷 334-362页

作者： Francesca Biagini Jacopo Mancin Workgroup Financial and Insurance Mathematics Department of MathematicsLudwig-Maximilians UniversitatTheresienstraße 3980333 MunichGermany Department of Mathematics University of OsloBox 1053Blindern0316 OsloNorway

We study the concept of financial bubbles in a market model endowed with a set P of probability measures,typically mutually singular to each other.In this setting,we investigate a dynamic version of robust superreplication,which we use to introduce the notions of bubble and robust fundamental value in a way consistent with the existing literature in the classical case P={P}.Finally,we provide concrete examples illustrating our results.

关键词： Financial bubbles model uncertainty

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Characterizing model uncertainty of upper-bound limit analysis on slopes using 3D rotational failure mechanism

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Rock Mechanics Bulletin 2023年第1期2卷 38-43页

作者： X.Z.Li H.Jiang Q.J.Pan L.H.Zhao School of Civil Engineering Central South UniversityNo.22Shaoshan South RoadChangshaHunan Province410075People's Republic of China Department of Resources and Environment Hunan Nonferrous Metals Vocational and Technical CollegeZhuzhouHunan412006People's Republic of China

The slope stability assessment is a classical problem in geotechnical engineering.This topic have attracted many researcher’s attention and various theoretical models for predicting critical slope heights or safety factors in the light of the limit equilibrium(LE)method and the kinematical approach of limit analysis(LA)method.Meanwhile,a large number of experimental studies have been conducted to check the slope stability.Using centrifuge testing results,this paper aims to employ Bayesian method to characterize the model uncertainties of the classical three-dimensional rotational failure mechanism proposed by Michalowski and Drescher(2009)to predict critical slope heights in frictional soils,by incorporating the test uncertainties and parameter uncertainties.The obtained results show that the LA three-dimensional rotational failure mechanism overestimates the critical slope height compared with the LE method,and the experimental observational uncertainty has negligible influences on the posterior statistics of model uncertainty.

关键词： model uncertainty Slope stability Upper-bound limit analysis Bayesian analysis Centrifuge testing

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Double-factor Fading Memory Kalman Filter for Compensating model uncertainty

Double-factor Fading Memory Kalman Filter for Compensating M...

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第40届中国控制会议

作者： Fangwenchang Fu Jie Zhou College of Mathematics Sichuan University

In order to solve the divergence problem of Kalman filter caused by the model uncertainty in the dynamic system,this paper proposes an adaptive filter called double-factor fading memory Kalman filter.In fact,the recursive formulas of state estimations in Kalman filter can be derived by minimizing a quadratic cost function.To compensate for the different degrees of model uncertainty in the motion equation and the measurement equation,this paper introduces two fading factors into the weight matrices of the lost function.The values of fading factors can be calculated by iteratively solving the equations that assume the theoretic covariance matrices of innovations and residuals equals to the sample covariance matrices of innovations and residuals respectively,and then state estimations expressed by fading factors can be obtained.

关键词： Kalman filter model uncertainty adaptive filter fading factor sample covariance matrix

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