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Fault-observer-based iterative learning model predictive controller for trajectory tracking of hypersonic vehicles 被引量:2
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作者 CUI Peng GAO Changsheng AN Ruoming 《Journal of Systems Engineering and Electronics》 2025年第3期803-813,共11页
This work proposes the application of an iterative learning model predictive control(ILMPC)approach based on an adaptive fault observer(FOBILMPC)for fault-tolerant control and trajectory tracking in air-breathing hype... This work proposes the application of an iterative learning model predictive control(ILMPC)approach based on an adaptive fault observer(FOBILMPC)for fault-tolerant control and trajectory tracking in air-breathing hypersonic vehicles.In order to increase the control amount,this online control legislation makes use of model predictive control(MPC)that is based on the concept of iterative learning control(ILC).By using offline data to decrease the linearized model’s faults,the strategy may effectively increase the robustness of the control system and guarantee that disturbances can be suppressed.An adaptive fault observer is created based on the suggested ILMPC approach in order to enhance overall fault tolerance by estimating and compensating for actuator disturbance and fault degree.During the derivation process,a linearized model of longitudinal dynamics is established.The suggested ILMPC approach is likely to be used in the design of hypersonic vehicle control systems since numerical simulations have demonstrated that it can decrease tracking error and speed up convergence when compared to the offline controller. 展开更多
关键词 hypersonic vehicle actuator fault tracking control iterative learning control(ILC) model predictive control(mpc) fault observer
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Cascade explicit tube model predictive controller:application for a multi-robot system
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作者 Ehsan Soleimani Amirhossein Nikoofard Erfan Nejabat 《Control Theory and Technology》 2025年第2期237-252,共16页
In recent years,there has been a growing demand for more efficient and robust control strategies in cooperative multi-robot systems.This paper introduces the cascade explicit tube model predictive controller(CET-MPC),... In recent years,there has been a growing demand for more efficient and robust control strategies in cooperative multi-robot systems.This paper introduces the cascade explicit tube model predictive controller(CET-MPC),a control architecture designed specifically for distributed aerial robot systems.By integrating an explicit model predictive controller(MPC)with a tube MPC,our approach significantly reduces online computational demands while enhancing robustness against disturbances such as wind and measurement noise,as well as uncertainties in inertia parameters.Further,we incorporate a cascade controller to minimize steady-state errors and improve system performance dynamically.The results of this assessment provide valuable insights into the effectiveness and reliability of the CET-MPC approach under realistic operating conditions.The simulation results of flight scenarios for multi-agent quadrotors demonstrate the controller’s stability and accurate tracking of the desired path.By addressing the complexities of quadrotors’six degrees of freedom,this controller serves as a versatile solution applicable to a wide range of multi-robot systems with varying degrees of freedom,demonstrating its adaptability and scalability beyond the quadrotor domain. 展开更多
关键词 Explicit model predictive control(mpc) Tube mpc Cascade controller QUADROTOR Multi-agent system Distributed formation control
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Model Predictive Optimization and Control of Quadruped Whole-Body Locomotion
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作者 Chao Cun Qunting Yang +2 位作者 Zhijun Li MengChu Zhou Jianxin Pang 《IEEE/CAA Journal of Automatica Sinica》 2025年第10期2103-2114,共12页
In this paper,a framework of model predictive optimization and control for quadruped whole-body locomotion is presented,which enables dynamic balance and minimizes the control effort.First,we propose a hierarchical co... In this paper,a framework of model predictive optimization and control for quadruped whole-body locomotion is presented,which enables dynamic balance and minimizes the control effort.First,we propose a hierarchical control scheme consisting of two modules.The first layer is to find an optimal ground reaction force(GRF)by employing inner model predictive control(MPC)along a full motor gait cycle,ensuring the minimal energy consumption of the system.Based on the output GRF of inner layer,the second layer is designed to prioritize tasks for motor execution sequentially using an outer model predictive control.In inner MPC,an objective function about GRF is designed by using a model with relatively long time horizons.Then a neural network solver is used to obtain the optimal GRF by minimizing the objective function.By using a two-layered MPC architecture,we design a hybrid motion/force controller to handle the impedance of leg joints and robotic uncertainties including external perturbation.Finally,we perform extensive experiments with a quadruped robot,including the crawl and trotting gaits,to verify the proposed control framework. 展开更多
关键词 Hybrid motion/force control model predictive control(mpc) neural-dynamics QUADRUPED whole-body control
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Model Predictive Control Method Based on Data-Driven Approach for Permanent Magnet Synchronous Motor Control System
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作者 LI Songyang CHEN Wenbo WAN Heng 《Journal of Shanghai Jiaotong university(Science)》 2025年第2期270-279,共10页
Permanent magnet synchronous motor(PMSM)is widely used in alternating current servo systems as it provides high eficiency,high power density,and a wide speed regulation range.The servo system is placing higher demands... Permanent magnet synchronous motor(PMSM)is widely used in alternating current servo systems as it provides high eficiency,high power density,and a wide speed regulation range.The servo system is placing higher demands on its control performance.The model predictive control(MPC)algorithm is emerging as a potential high-performance motor control algorithm due to its capability of handling multiple-input and multipleoutput variables and imposed constraints.For the MPC used in the PMSM control process,there is a nonlinear disturbance caused by the change of electromagnetic parameters or load disturbance that may lead to a mismatch between the nominal model and the controlled object,which causes the prediction error and thus affects the dynamic stability of the control system.This paper proposes a data-driven MPC strategy in which the historical data in an appropriate range are utilized to eliminate the impact of parameter mismatch and further improve the control performance.The stability of the proposed algorithm is proved as the simulation demonstrates the feasibility.Compared with the classical MPC strategy,the superiority of the algorithm has also been verified. 展开更多
关键词 permanent magnet synchronous motor(PMSM) model predictive control(mpc) data-driven model predictive control(DDmpc)
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Virtual target guidance-based distributed model predictive control for formation control of multiple UAVs 被引量:29
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作者 Zhihao CAI Longhong WANG +2 位作者 Jiang ZHAO Kun WU Yingxun WANG 《Chinese Journal of Aeronautics》 SCIE EI CAS CSCD 2020年第3期1037-1056,共20页
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... 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. 展开更多
关键词 Distributed model predictive control(mpc) Event-triggered mechanism Formation control Obstacle avoidance Unmanned Aerial Vehicles(UAVs) Virtual Target Guidance(VTG)
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Finite-Control-Set Model Predictive Control of Permanent Magnet Synchronous Motor Drive Systems——An Overview 被引量:14
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作者 Teng Li Xiaodong Sun +3 位作者 Gang Lei Zebin Yang Youguang Guo Jianguo Zhu 《IEEE/CAA Journal of Automatica Sinica》 SCIE EI CSCD 2022年第12期2087-2105,共19页
Permanent magnet synchronous motors(PMSMs)have been widely employed in the industry. Finite-control-set model predictive control(FCS-MPC), as an advanced control scheme, has been developed and applied to improve the p... Permanent magnet synchronous motors(PMSMs)have been widely employed in the industry. Finite-control-set model predictive control(FCS-MPC), as an advanced control scheme, has been developed and applied to improve the performance and efficiency of the holistic PMSM drive systems. Based on the three elements of model predictive control, this paper provides an overview of the superiority of the FCS-MPC control scheme and its shortcomings in current applications. The problems of parameter mismatch, computational burden, and unfixed switching frequency are summarized. Moreover, other performance improvement schemes, such as the multi-vector application strategy, delay compensation scheme, and weight factor adjustment, are reviewed. Finally, future trends in this field is discussed, and several promising research topics are highlighted. 展开更多
关键词 Computational burden finite control set(FCS) model predictive control(mpc) permanent magnet synchronous motor(PMSM) robust operation switching frequency
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Robust model predictive control for discrete uncertain nonlinear systems with time-delay via fuzzy model 被引量:7
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作者 SU Cheng-li WANG Shu-qing 《Journal of Zhejiang University-Science A(Applied Physics & Engineering)》 SCIE EI CAS CSCD 2006年第10期1723-1732,共10页
An extended robust model predictive control approach for input constrained discrete uncertain nonlinear systems with time-delay based on a class of uncertain T-S fuzzy models that satisfy sector bound condition is pre... An extended robust model predictive control approach for input constrained discrete uncertain nonlinear systems with time-delay based on a class of uncertain T-S fuzzy models that satisfy sector bound condition is presented. In this approach, the minimization problem of the “worst-case” objective function is converted into the linear objective minimization problem in- volving linear matrix inequalities (LMIs) constraints. The state feedback control law is obtained by solving convex optimization of a set of LMIs. Sufficient condition for stability and a new upper bound on robust performance index are given for these kinds of uncertain fuzzy systems with state time-delay. Simulation results of CSTR process show that the proposed robust predictive control approach is effective and feasible. 展开更多
关键词 Uncertain Takagi-Sugeno fuzzy model TIME-DELAY model predictive control mpc Linear matrix inequalities(LMIs) Robustness
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Energy Control of Plug-In Hybrid Electric Vehicles Using Model Predictive Control With Route Preview 被引量:5
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作者 Yang Zhao Yanguang Cai Qiwen Song 《IEEE/CAA Journal of Automatica Sinica》 SCIE EI CSCD 2021年第12期1948-1955,共8页
The paper proposes an adoption of slope,elevation,speed and route distance preview to achieve optimal energymanagement of plug-in hybrid electric vehicles(PHEVs).Theapproach is to identify route features from historic... The paper proposes an adoption of slope,elevation,speed and route distance preview to achieve optimal energymanagement of plug-in hybrid electric vehicles(PHEVs).Theapproach is to identify route features from historical and real-time traffic data,in which information fusion model and trafficprediction model are used to improve the information accuracy.Then,dynamic programming combined with equivalent con-sumption minimization strategy is used to compute an optimalsolution for real-time energy management.The solution is thereference for PHEV energy management control along the route.To improve the system's ability of handling changing situation,the study further explores predictive control model in the real-time control of the energy.A simulation is performed to modelPHEV under above energy control strategy with route preview.The results show that the average fuel consumption of PHEValong the previewed route with model predictive control(MPC)strategy can be reduced compared with optimal strategy andbase control strategy. 展开更多
关键词 Energy management model predictive control(mpc) optimal control plug-in hybrid electric vehicle(PHEV)
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Model predictive control for adaptive cruise control with multi-objectives: comfort,fuel-economy,safety and car-following 被引量:37
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作者 Li-hua LUO Hong LIU Ping LI Hui WANG 《Journal of Zhejiang University-Science A(Applied Physics & Engineering)》 SCIE EI CAS CSCD 2010年第3期191-201,共11页
For automated vehicles,comfortable driving will improve passengers’ satisfaction.Reducing fuel consumption brings economic profits for car owners,decreases the impact on the environment and increases energy sustainab... For automated vehicles,comfortable driving will improve passengers’ satisfaction.Reducing fuel consumption brings economic profits for car owners,decreases the impact on the environment and increases energy sustainability.In addition to comfort and fuel-economy,automated vehicles also have the basic requirements of safety and car-following.For this purpose,an adaptive cruise control (ACC) algorithm with multi-objectives is proposed based on a model predictive control (MPC) framework.In the proposed ACC algorithm,safety is guaranteed by constraining the inter-distance within a safe range; the requirements of comfort and car-following are considered to be the performance criteria and some optimal reference trajectories are introduced to increase fuel-economy.The performances of the proposed ACC algorithm are simulated and analyzed in five representative traffic scenarios and multiple experiments.The results show that not only are safety and car-following objectives satisfied,but also driving comfort and fuel-economy are improved significantly. 展开更多
关键词 Adaptive cruise control (ACC) Multi-objectives Comfort Fuel-economy model predictive control mpc
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Machine Learning Accelerated Real-Time Model Predictive Control for Power Systems 被引量:3
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作者 Ramij Raja Hossain Ratnesh Kumar 《IEEE/CAA Journal of Automatica Sinica》 SCIE EI CSCD 2023年第4期916-930,共15页
This paper presents a machine-learning-based speedup strategy for real-time implementation of model-predictive-control(MPC)in emergency voltage stabilization of power systems.Despite success in various applications,re... This paper presents a machine-learning-based speedup strategy for real-time implementation of model-predictive-control(MPC)in emergency voltage stabilization of power systems.Despite success in various applications,real-time implementation of MPC in power systems has not been successful due to the online control computation time required for large-sized complex systems,and in power systems,the computation time exceeds the available decision time used in practice by a large extent.This long-standing problem is addressed here by developing a novel MPC-based framework that i)computes an optimal strategy for nominal loads in an offline setting and adapts it for real-time scenarios by successive online control corrections at each control instant utilizing the latest measurements,and ii)employs a machine-learning based approach for the prediction of voltage trajectory and its sensitivity to control inputs,thereby accelerating the overall control computation by multiple times.Additionally,a realistic control coordination scheme among static var compensators(SVC),load-shedding(LS),and load tap-changers(LTC)is presented that incorporates the practical delayed actions of the LTCs.The performance of the proposed scheme is validated for IEEE 9-bus and 39-bus systems,with±20%variations in nominal loading conditions together with contingencies.We show that our proposed methodology speeds up the online computation by 20-fold,bringing it down to a practically feasible value(fraction of a second),making the MPC real-time and feasible for power system control for the first time. 展开更多
关键词 Machine learning model predictive control(mpc) neural network perturbation control voltage stabilization
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Robust model predictive control for continuous uncertain systems with state delay 被引量:4
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作者 Chunyan HAN Xiaohua LIU Huanshui ZHANG 《控制理论与应用(英文版)》 EI 2008年第2期189-194,共6页
This paper is concerned with robust model predictive control for linear continuous uncertain systems with state delay and control constraints, A piecewise constant control sequence is calculated by minimizing the uppe... This paper is concerned with robust model predictive control for linear continuous uncertain systems with state delay and control constraints, A piecewise constant control sequence is calculated by minimizing the upper-bound of the infinite horizon quadratic cost function, At each sampling time, the sufficient conditions for the existence of the model predictive control are derived, and expressed as a set of linear matrix inequalities. The robust stability of the closed-loop svstems is guaranteed bv the proposed design method. A numerical example is given to illustrate the main results. 展开更多
关键词 model predictive control mpc Robust control Linear matrix inequality (LMI) Time-delay systems
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Model Predictive Control of Nonlinear Systems: Stability Region and Feasible Initial Control 被引量:5
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作者 Xiao-Bing Hu Wen-Hua Chen 《International Journal of Automation and computing》 EI 2007年第2期195-202,共8页
This paper proposes a new method for model predictive control (MPC) of nonlinear systems to calculate stability region and feasible initial control profile/sequence, which are important to the implementations of MPC... This paper proposes a new method for model predictive control (MPC) of nonlinear systems to calculate stability region and feasible initial control profile/sequence, which are important to the implementations of MPC. Different from many existing methods, this paper distinguishes stability region from conservative terminal region. With global linearization, linear differential inclusion (LDI) and linear matrix inequality (LMI) techniques, a nonlinear system is transformed into a convex set of linear systems, and then the vertices of the set are used off-line to design the controller, to estimate stability region, and also to determine a feasible initial control profile/sequence. The advantages of the proposed method are demonstrated by simulation study. 展开更多
关键词 model predictive control mpc stability region terminal region linear differential inclusion (LDI) linear matrix inequality (LMI).
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Operation Efficiency Optimisation Modelling and Application of Model Predictive Control 被引量:3
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作者 Xiaohua Xia Jiangfeng Zhang 《IEEE/CAA Journal of Automatica Sinica》 SCIE EI 2015年第2期166-172,共7页
The efficiency of any energy system can be charaterised by the relevant efficiency components in terms of performance, operation, equipment and technology(POET). The overall energy efficiency of the system can be opti... The efficiency of any energy system can be charaterised by the relevant efficiency components in terms of performance, operation, equipment and technology(POET). The overall energy efficiency of the system can be optimised by studying the POET energy efficiency components. For an existing energy system, the improvement of operation efficiency will usually be a quick win for energy efficiency. Therefore, operation efficiency improvement will be the main purpose of this paper. General procedures to establish operation efficiency optimisation models are presented. Model predictive control, a popular technique in modern control theory, is applied to solve the obtained energy models. From the case studies in water pumping systems, model predictive control will have a prosperous application in more energy efficiency problems. 展开更多
关键词 model predictive control(mpc) operation efficiency energy efficiency
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Hybrid Dynamic Variables-Dependent Event-Triggered Fuzzy Model Predictive Control 被引量:4
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作者 Xiongbo Wan Chaoling Zhang +2 位作者 Fan Wei Chuan-Ke Zhang Min Wu 《IEEE/CAA Journal of Automatica Sinica》 SCIE EI CSCD 2024年第3期723-733,共11页
This article focuses on dynamic event-triggered mechanism(DETM)-based model predictive control(MPC) for T-S fuzzy systems.A hybrid dynamic variables-dependent DETM is carefully devised,which includes a multiplicative ... This article focuses on dynamic event-triggered mechanism(DETM)-based model predictive control(MPC) for T-S fuzzy systems.A hybrid dynamic variables-dependent DETM is carefully devised,which includes a multiplicative dynamic variable and an additive dynamic variable.The addressed DETM-based fuzzy MPC issue is described as a “min-max” optimization problem(OP).To facilitate the co-design of the MPC controller and the weighting matrix of the DETM,an auxiliary OP is proposed based on a new Lyapunov function and a new robust positive invariant(RPI) set that contain the membership functions and the hybrid dynamic variables.A dynamic event-triggered fuzzy MPC algorithm is developed accordingly,whose recursive feasibility is analysed by employing the RPI set.With the designed controller,the involved fuzzy system is ensured to be asymptotically stable.Two examples show that the new DETM and DETM-based MPC algorithm have the advantages of reducing resource consumption while yielding the anticipated performance. 展开更多
关键词 Dynamic event-triggered mechanism(DETM) hybrid dynamic variables model predictive control(mpc) robust positive invariant(RPI)set T-S fuzzy systems
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A Computationally Efficient Aggregation Optimization Strategy of Model Predictive Control 被引量:4
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作者 杜晓宁 Xi +2 位作者 Yugeng Li Shaoyuan 《High Technology Letters》 EI CAS 2002年第2期68-71,共4页
Model Predictive Control (MPC) is a popular technique and has been successfully used in various industrial applications. However, the big drawback of MPC involved in the formidable on line computational effort limits ... Model Predictive Control (MPC) is a popular technique and has been successfully used in various industrial applications. However, the big drawback of MPC involved in the formidable on line computational effort limits its applicability to relatively slow and/or small processes with a moderate number of inputs. This paper develops an aggregation optimization strategy for MPC that can improve the computational efficiency of MPC. For the regulation problem, an input decaying aggregation optimization algorithm is presented by aggregating all the original optimized variables on control horizon with the decaying sequence in respect of the current control action. 展开更多
关键词 model predictive control (mpc) on line computational effor
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A state estimation based constrained model predictive control system 被引量:2
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作者 刘斌 Zou Tao 《High Technology Letters》 EI CAS 2010年第4期373-377,共5页
In this paper,the model predictive control based on the state estimation for a constrained system isinvestigated.By modifying the constraints for the predictive state,the control sequence becomes feasiblefor the real ... In this paper,the model predictive control based on the state estimation for a constrained system isinvestigated.By modifying the constraints for the predictive state,the control sequence becomes feasiblefor the real system,i.e.,the system state is guaranteed to be in the constraint domain.It s also provedthat the close-loop system is asymptotically stable and the system state converges to the origin.The conclusionis verified through simulation. 展开更多
关键词 ESTIMATION model predictive control mpc feasible STABILITY
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Model-based Predictive Control for Spatially-distributed Systems Using Dimensional Reduction Models 被引量:2
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作者 Meng-Ling Wang Ning Li Shao-Yuan Li 《International Journal of Automation and computing》 EI 2011年第1期1-7,共7页
In this paper, a low-dimensional multiple-input and multiple-output (MIMO) model predictive control (MPC) configuration is presented for partial differential equation (PDE) unknown spatially-distributed systems ... In this paper, a low-dimensional multiple-input and multiple-output (MIMO) model predictive control (MPC) configuration is presented for partial differential equation (PDE) unknown spatially-distributed systems (SDSs). First, the dimension reduction with principal component analysis (PCA) is used to transform the high-dimensional spatio-temporal data into a low-dimensional time domain. The MPC strategy is proposed based on the online correction low-dimensional models, where the state of the system at a previous time is used to correct the output of low-dimensional models. Sufficient conditions for closed-loop stability are presented and proven. Simulations demonstrate the accuracy and efficiency of the proposed methodologies. 展开更多
关键词 Spatially-distributed system principal component analysis (PCA) time/space separation dimension reduction model predictive control mpc).
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Finite-Time Stabilization for Constrained Discrete-time Systems by Using Model Predictive Control 被引量:1
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作者 Bing Zhu Xiaozhuoer Yuan +1 位作者 Li Dai Zhiwen Qiang 《IEEE/CAA Journal of Automatica Sinica》 SCIE EI CSCD 2024年第7期1656-1666,共11页
In this paper, a model predictive control(MPC)framework is proposed for finite-time stabilization of linear and nonlinear discrete-time systems subject to state and control constraints. The proposed MPC framework guar... In this paper, a model predictive control(MPC)framework is proposed for finite-time stabilization of linear and nonlinear discrete-time systems subject to state and control constraints. The proposed MPC framework guarantees the finite-time convergence property by assigning the control horizon equal to the dimension of the overall system, and only penalizing the terminal cost in the optimization, where the stage costs are not penalized explicitly. A terminal inequality constraint is added to guarantee the feasibility and stability of the closed-loop system.Initial feasibility can be improved via augmentation. The finite-time convergence of the proposed MPC is proved theoretically,and is supported by simulation examples. 展开更多
关键词 CONSTRAINTS deadbeat control finite-time stabilization model predictive control(mpc)
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Predictive control of a class of bilinear systems based on global off-line models 被引量:1
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作者 ZHANG Ri-dong WANG Shu-qing 《Journal of Zhejiang University-Science A(Applied Physics & Engineering)》 SCIE EI CAS CSCD 2006年第12期1984-1988,共5页
A new multi-step adaptive predictive control algorithm for a class of bilinear systems is presented. The structure of the bilinear system is converted into a simple linear model by using nonlinear support vector machi... A new multi-step adaptive predictive control algorithm for a class of bilinear systems is presented. The structure of the bilinear system is converted into a simple linear model by using nonlinear support vector machine (SVM) dynamic approximation with analytical control law derived. The method does not need on-line parameters estimation because the system’s internal model has been transformed into an off-line global model. Compared with other traditional methods, this control law reduces on-line parameter estimating burden. In addition, its overall linear behavior treating method allows an analytical control law available and avoids on-line nonlinear optimization. Simulation results are presented in the article to illustrate the efficiency of the method. 展开更多
关键词 Bilinear systems model predictive control mpc Adaptive control Support vector machine (SVM)
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An Efficient Constrained Model Predictive Control Algorithm Based on Approximate Computation 被引量:1
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作者 Du Xiaoning, Xi Yugeng & Li Shaoyuan Institute of Automation, Shanghai Jiaotong University, Shanghai 200030, P.R.China 《Journal of Systems Engineering and Electronics》 SCIE EI CSCD 2002年第1期42-47,共6页
The on line computational burden related to model predictive control (MPC) of large scale constrained systems hampers its real time applications and limits it to slow dynamic process with moderate number of inputs.... The on line computational burden related to model predictive control (MPC) of large scale constrained systems hampers its real time applications and limits it to slow dynamic process with moderate number of inputs. To avoid this, an efficient and fast algorithm based on aggregation optimization is proposed in this paper. It only optimizes the current control action at time instant k , while other future control sequences in the optimization horizon are approximated off line by the linear feedback control sequence, so the on line optimization can be converted into a low dimensional quadratic programming problem. Input constraints can be well handled in this scheme. The comparable performance is achieved with existing standard model predictive control algorithm. Simulation results well demonstrate its effectiveness. 展开更多
关键词 model predictive control (mpc) Receding horizon control (RHC) Approximate computation.
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