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Parametric variational solution of linear-quadratic optimal control problems with control inequality constraints 被引量:4
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作者 彭海军 高强 +2 位作者 张洪武 吴志刚 钟万勰 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2014年第9期1079-1098,共20页
A parametric variational principle and the corresponding numerical algo- rithm are proposed to solve a linear-quadratic (LQ) optimal control problem with control inequality constraints. Based on the parametric varia... A parametric variational principle and the corresponding numerical algo- rithm are proposed to solve a linear-quadratic (LQ) optimal control problem with control inequality constraints. Based on the parametric variational principle, this control prob- lem is transformed into a set of Hamiltonian canonical equations coupled with the linear complementarity equations, which are solved by a linear complementarity solver in the discrete-time domain. The costate variable information is also evaluated by the proposed method. The parametric variational algorithm proposed in this paper is suitable for both time-invariant and time-varying systems. Two numerical examples are used to test the validity of the proposed method. The proposed algorithm is used to astrodynamics to solve a practical optimal control problem for rendezvousing spacecrafts with a finite low thrust. The numerical simulations show that the parametric variational algorithm is ef- fective for LQ optimal control problems with control inequality constraints. 展开更多
关键词 parametric variational principle optimal control inequality constraint linear complementarity ASTRODYNAMICS linear-quadratic (LQ)
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Global Optimization for Solving Linear Non-Quadratic Optimal Control Problems
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作者 Jinghao Zhu 《Journal of Applied Mathematics and Physics》 2016年第10期1859-1869,共11页
This paper presents a global optimization approach to solving linear non-quadratic optimal control problems. The main work is to construct a differential flow for finding a global minimizer of the Hamiltonian function... This paper presents a global optimization approach to solving linear non-quadratic optimal control problems. The main work is to construct a differential flow for finding a global minimizer of the Hamiltonian function over a Euclid space. With the Pontryagin principle, the optimal control is characterized by a function of the adjoint variable and is obtained by solving a Hamiltonian differential boundary value problem. For computing an optimal control, an algorithm for numerical practice is given with the description of an example. 展开更多
关键词 linear Non-quadratic optimal control Pontryagin Principle Global optimization Hamiltonian Differential Boundary Value Problem
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Linear Quadratic Optimal Control for Systems Governed by First-Order Hyperbolic Partial Differential Equations
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作者 XUE Xiaomin XU Juanjuan ZHANG Huanshui 《Journal of Systems Science & Complexity》 SCIE EI CSCD 2024年第1期230-252,共23页
This paper focuses on linear-quadratic(LQ)optimal control for a class of systems governed by first-order hyperbolic partial differential equations(PDEs).Different from most of the previous works,an approach of discret... This paper focuses on linear-quadratic(LQ)optimal control for a class of systems governed by first-order hyperbolic partial differential equations(PDEs).Different from most of the previous works,an approach of discretization-then-continuousization is proposed in this paper to cope with the infinite-dimensional nature of PDE systems.The contributions of this paper consist of the following aspects:(1)The differential Riccati equations and the solvability condition of the LQ optimal control problems are obtained via the discretization-then-continuousization method.(2)A numerical calculation way of the differential Riccati equations and a practical design way of the optimal controller are proposed.Meanwhile,the relationship between the optimal costate and the optimal state is established by solving a set of forward and backward partial difference equations(FBPDEs).(3)The correctness of the method used in this paper is verified by a complementary continuous method and the comparative analysis with the existing operator results is presented.It is shown that the proposed results not only contain the classic results of the standard LQ control problem of systems governed by ordinary differential equations as a special case,but also support the existing operator results and give a more convenient form of computation. 展开更多
关键词 Discretization-then-continuousization method first-order hyperbolic partial differential equations forward and backward partial difference equations linear quadratic optimal control.
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Least Squares Solution for Discrete Time Nonlinear Stochastic Optimal Control Problem with Model-Reality Differences 被引量:2
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作者 Sie Long Kek Jiao Li Kok Lay Teo 《Applied Mathematics》 2017年第1期1-14,共14页
In this paper, an efficient computational approach is proposed to solve the discrete time nonlinear stochastic optimal control problem. For this purpose, a linear quadratic regulator model, which is a linear dynamical... In this paper, an efficient computational approach is proposed to solve the discrete time nonlinear stochastic optimal control problem. For this purpose, a linear quadratic regulator model, which is a linear dynamical system with the quadratic criterion cost function, is employed. In our approach, the model-based optimal control problem is reformulated into the input-output equations. In this way, the Hankel matrix and the observability matrix are constructed. Further, the sum squares of output error is defined. In these point of views, the least squares optimization problem is introduced, so as the differences between the real output and the model output could be calculated. Applying the first-order derivative to the sum squares of output error, the necessary condition is then derived. After some algebraic manipulations, the optimal control law is produced. By substituting this control policy into the input-output equations, the model output is updated iteratively. For illustration, an example of the direct current and alternating current converter problem is studied. As a result, the model output trajectory of the least squares solution is close to the real output with the smallest sum squares of output error. In conclusion, the efficiency and the accuracy of the approach proposed are highly presented. 展开更多
关键词 Least SQUARES SOLUTION STOCHASTIC optimal control linear quadratic REGULATOR Sum SQUARES of Output Error INPUT-OUTPUT Equations
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Optimal Feedback Control of Nonlinear Variable-Speed Marine Current Turbine Using a Two-Mass Model
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作者 Rajae Gaamouche Abdelbari Redouane +2 位作者 Imad El harraki Bouchra Belhorma Abdennebi El Hasnaoui 《Journal of Marine Science and Application》 CSCD 2020年第1期83-95,共13页
This paper presents a contribution related to the control of nonlinear variable-speed marine current turbine(MCT)without pitch operating below the rated marine current speed.Given that the operation of the MCT can be ... This paper presents a contribution related to the control of nonlinear variable-speed marine current turbine(MCT)without pitch operating below the rated marine current speed.Given that the operation of the MCT can be divided into several operating zones on the basis of the marine current speed,the system control objectives are different for each zone.To deal with this issue,we develop a new control approach based on a linear quadratic regulator with variable generator torque.Our proposed approach enables the optimization of the rotational speed of the turbine,which maximizes the power extracted by the MCT and minimizes the transient loads on the drivetrain.The novelty of our study is the use of a real profile of marine current speed from the northern coasts of Morocco.The simulation results obtained using MATLAB Simulink indicate the effectiveness and robustness of the proposed control approach on the electrical and mechanical parameters with the variations of marine current speed. 展开更多
关键词 Marine current turbine Two-mass model Tip speed ratio linearIZATION optimal control linear quadratic regulator(LQR)
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Theoretical Study of Double Cost Function Linear Quadratic Regulator(LQR)
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作者 姜澜 王信义 永井正夫 《Journal of Beijing Institute of Technology》 EI CAS 2000年第1期80-86,共7页
Double cost function linear quadratic regulator (DLQR) is developed from LQR theory to solve an optimal control problem with a general nonlinear cost function. In addition to the traditional LQ cost function, anothe... Double cost function linear quadratic regulator (DLQR) is developed from LQR theory to solve an optimal control problem with a general nonlinear cost function. In addition to the traditional LQ cost function, another free form cost function was introduced to express the physical need plainly and optimize weights of LQ cost function using the search algorithms. As an instance, DLQR was applied in determining the control input in the front steering angle compensation control (FSAC) model for heavy duty vehicles. The brief simulations show that DLQR is powerful enough to specify the engineering requirements correctly and balance many factors effectively. The concept and applicable field of LQR are expanded by DLQR to optimize the system with a free form cost function. 展开更多
关键词 optimal control linear quadratic regulator (LQR) search algorithm front steering angle compensation control
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Adaptive Linear Quadratic Regulator for Continuous-Time Systems With Uncertain Dynamics 被引量:3
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作者 Sumit Kumar Jha Shubhendu Bhasin 《IEEE/CAA Journal of Automatica Sinica》 SCIE EI CSCD 2020年第3期833-841,共9页
In this paper, adaptive linear quadratic regulator(LQR) is proposed for continuous-time systems with uncertain dynamics. The dynamic state-feedback controller uses inputoutput data along the system trajectory to conti... In this paper, adaptive linear quadratic regulator(LQR) is proposed for continuous-time systems with uncertain dynamics. The dynamic state-feedback controller uses inputoutput data along the system trajectory to continuously adapt and converge to the optimal controller. The result differs from previous results in that the adaptive optimal controller is designed without the knowledge of the system dynamics and an initial stabilizing policy. Further, the controller is updated continuously using input-output data, as opposed to the commonly used switched/intermittent updates which can potentially lead to stability issues. An online state derivative estimator facilitates the design of a model-free controller. Gradient-based update laws are developed for online estimation of the optimal gain. Uniform exponential stability of the closed-loop system is established using the Lyapunov-based analysis, and a simulation example is provided to validate the theoretical contribution. 展开更多
关键词 ADAPTIVE optimal control continuous POLICY UPDATE linear quadratic REGULATOR UNCERTAIN system dynamics
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Optimal Decoupling Control Method and Its Application to a Ball Mill Coal-pulverizing System 被引量:3
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作者 Yue Fu Chengwen Hong Jingyi Li 《IEEE/CAA Journal of Automatica Sinica》 SCIE EI CSCD 2018年第6期1035-1043,共9页
Abstract-The conventional optimal tracking control method cannot realize decoupling control of linear systems with a strong coupling property. To solve this problem, in this paper, an optimal decoupling control method... Abstract-The conventional optimal tracking control method cannot realize decoupling control of linear systems with a strong coupling property. To solve this problem, in this paper, an optimal decoupling control method is proposed, which can simultaneousiy provide optimal performance. The optimal decoupling controller is composed of an inner-loop decoupling controller and an outer-loop optimal tracking controller. First, by introducing one virtual control variable, the original differential equation on state is converted to a generalized system on output. Then, by introducing the other virtual control variable, and viewing the coupling terms as the measurable disturbances, the generalized system is open-loop decoupled. Finally, for the decoupled system, the optimal tracking control method is used. It is proved that the decoupling control is optimal for a certain performance index. Simulations on a ball mill coal-pulverizing system are conducted. The results show the effectiveness and superiority of the proposed method as compared with the conventional optimal quadratic tracking (LQT) control method. 展开更多
关键词 Ball mill coal-pulverizing system linear system optimal decoupling control optimal quadratic tracking (LQT)control.
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Fuzzy Optimal Control Design for Ship Steering
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作者 EJAZ Muhammad CHEN Mou 《Transactions of Nanjing University of Aeronautics and Astronautics》 EI CSCD 2019年第3期459-467,共9页
This paper presents a method to design a control scheme for nonlinear systems using fuzzy optimal control.In the design process,the nonlinear system is first converted into local subsystems using sector non linearity ... This paper presents a method to design a control scheme for nonlinear systems using fuzzy optimal control.In the design process,the nonlinear system is first converted into local subsystems using sector non linearity approach of Takagi Sugeno(T S)fuzzy modeling.For each local subsystem,an optimal control is designed.Then,the parameters of local controllers are defuzzified to construct a global optimal controller.To prove the effectiveness of this control scheme,simulations are performed using the mathematical model of Esso Osaka tanker ship for set point regulation with and without disturbance and reference tracking.In addition,the simulation results are compared with that of a PID controller for further verification and validation.It has been shown that the proposed optimal controller can be used for the nonlinear ship steering with good rise time,zero steady state error and fast settling time. 展开更多
关键词 Takagi Sugeno(T S) fuzzy modeling optimal control optimal linear quadratic TRACKER (LQT) SHIP STEERING
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STOCHASTIC DIFFERENTIAL EQUATIONS AND STOCHASTIC LINEAR QUADRATIC OPTIMAL CONTROL PROBLEM WITH LEVY PROCESSES 被引量:7
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作者 Huaibin TANG Zhen WU 《Journal of Systems Science & Complexity》 SCIE EI CSCD 2009年第1期122-136,共15页
In this paper, tile authors first study two kinds of stochastic differential equations (SDEs) with Levy processes as noise source. Based on the existence and uniqueness of the solutions of these SDEs and multi-dimen... In this paper, tile authors first study two kinds of stochastic differential equations (SDEs) with Levy processes as noise source. Based on the existence and uniqueness of the solutions of these SDEs and multi-dimensional backward stochastic differential equations (BSDEs) driven by Levy pro- cesses, the authors proceed to study a stochastic linear quadratic (LQ) optimal control problem with a Levy process, where the cost weighting matrices of the state and control are allowed to be indefinite. One kind of new stochastic Riccati equation that involves equality and inequality constraints is derived from the idea of square completion and its solvability is proved to be sufficient for the well-posedness and the existence of optimal control which can be of either state feedback or open-loop form of the LQ problems. Moreover, the authors obtain the existence and uniqueness of the solution to the Riccati equation for some special cases. Finally, two examples are presented to illustrate these theoretical results. 展开更多
关键词 Backward stochastic differential equation generalized stochastic Riccati equation Levy process stochastic linear quadratic optimal control.
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Optimization problems for switched systems with impulsive control 被引量:1
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作者 JunhaoHU HuayouWANG +1 位作者 XinzhiLIU BmLIU 《控制理论与应用(英文版)》 EI 2005年第1期93-100,共8页
By using Impulsive Maximum Principal and three stage optimization method,this paper discusses optimization problems for linear impulsive switched systems with hybridcontrols, which includes continuous control and impu... By using Impulsive Maximum Principal and three stage optimization method,this paper discusses optimization problems for linear impulsive switched systems with hybridcontrols, which includes continuous control and impulsive control. The linear quadratic optimizationproblems without constraints such as optimal hybrid control, optimal stability and optimalswitching instants are addressed in detail. These results are applicable to optimal control problemsin economics,mechanics, and management. 展开更多
关键词 impulsive control switched systems optimIZATION linear quadratic maximumprincipal
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Discrete-time inverse linear quadratic optimal control over fnite time-horizon under noisy output measurements 被引量:1
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作者 Han Zhang Yibei Li Xiaoming Hu 《Control Theory and Technology》 EI CSCD 2021年第4期563-572,共10页
In this paper,the problem of inverse quadratic optimal control over fnite time-horizon for discrete-time linear systems is considered.Our goal is to recover the corresponding quadratic objective function using noisy o... In this paper,the problem of inverse quadratic optimal control over fnite time-horizon for discrete-time linear systems is considered.Our goal is to recover the corresponding quadratic objective function using noisy observations.First,the identifability of the model structure for the inverse optimal control problem is analyzed under relative degree assumption and we show the model structure is strictly globally identifable.Next,we study the inverse optimal control problem whose initial state distribution and the observation noise distribution are unknown,yet the exact observations on the initial states are available.We formulate the problem as a risk minimization problem and approximate the problem using empirical average.It is further shown that the solution to the approximated problem is statistically consistent under the assumption of relative degrees.We then study the case where the exact observations on the initial states are not available,yet the observation noises are known to be white Gaussian distributed and the distribution of the initial state is also Gaussian(with unknown mean and covariance).EM-algorithm is used to estimate the parameters in the objective function.The efectiveness of our results are demonstrated by numerical examples. 展开更多
关键词 Inverse optimal control linear quadratic regulator Statistical consistency EM-ALGORITHM
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Mean-field stochastic linear quadratic optimal control problems: closed-loop solvability 被引量:1
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作者 Xun Li Jingrui Sun Jiongmin Yong 《Probability, Uncertainty and Quantitative Risk》 2016年第1期37-60,共24页
An optimal control problem is studied for a linear mean-field stochastic differential equation with a quadratic cost functional.The coefficients and the weighting matrices in the cost functional are all assumed to be ... An optimal control problem is studied for a linear mean-field stochastic differential equation with a quadratic cost functional.The coefficients and the weighting matrices in the cost functional are all assumed to be deterministic.Closedloop strategies are introduced,which require to be independent of initial states;and such a nature makes it very useful and convenient in applications.In this paper,the existence of an optimal closed-loop strategy for the system(also called the closedloop solvability of the problem)is characterized by the existence of a regular solution to the coupled two(generalized)Riccati equations,together with some constraints on the adapted solution to a linear backward stochastic differential equation and a linear terminal value problem of an ordinary differential equation. 展开更多
关键词 Mean-field stochastic differential equation linear quadratic optimal control Riccati equation Regular solution Closed-loop solvability
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Linear quadratic optimal control of conditional McKean-Vlasov equation with random coefficients and applications 被引量:1
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作者 Huyen Pham 《Probability, Uncertainty and Quantitative Risk》 2016年第1期252-277,共26页
We consider the optimal control problem for a linear conditional McKeanVlasov equation with quadratic cost functional.The coefficients of the system and the weighting matrices in the cost functional are allowed to be ... We consider the optimal control problem for a linear conditional McKeanVlasov equation with quadratic cost functional.The coefficients of the system and the weighting matrices in the cost functional are allowed to be adapted processes with respect to the common noise filtration.Semi closed-loop strategies are introduced,and following the dynamic programming approach in(Pham and Wei,Dynamic programming for optimal control of stochastic McKean-Vlasov dynamics,2016),we solve the problem and characterize time-consistent optimal control by means of a system of decoupled backward stochastic Riccati differential equations.We present several financial applications with explicit solutions,and revisit,in particular,optimal tracking problems with price impact,and the conditional mean-variance portfolio selection in an incomplete market model. 展开更多
关键词 Stochastic McKean-Vlasov SDEs Random coefficients linear quadratic optimal control Dynamic programming Riccati equation Backward stochastic differential equation
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Linear quadratic optimal controller for cable-driven parallel robots
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作者 ABDOLSHAH SHOJAEI BARJUEI 《Frontiers of Mechanical Engineering》 SCIE CSCD 2015年第4期344-351,共8页
In recent years, various cable-driven parallel robots have been investigated for their advantages, such as low structural weight, high acceleration, and large work- space, over serial and conventional parallel systems... In recent years, various cable-driven parallel robots have been investigated for their advantages, such as low structural weight, high acceleration, and large work- space, over serial and conventional parallel systems. However, the use of cables lowers the stiffness of these robots, which in turn may decrease motion accuracy. A linear quadratic (LQ) optimal controller can provide all the states of a system for the feedback, such as position and velocity. Thus, the application of such an optimal controller in cable-driven parallel robots can result in more efficient and accurate motion compared to the performance of classical controllers such as the proportional-integral-derivative controller. This paper presents an approach to apply the LQ optimal controller on cabledriven parallel robots. To employ the optimal control theory, the static and dynamic modeling of a 3-DOF planar cable-driven parallel robot (Feriba-3) is developed. The synthesis of the LQ optimal control is described, and the significant experimental results are presented and discussed. 展开更多
关键词 cable-driven parallel robot linear quadratic optimal control ACCURACY
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Multistage Uncertain Random Linear Quadratic Optimal Control
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作者 CHEN Xin ZHU Yuanguo 《Journal of Systems Science & Complexity》 SCIE EI CSCD 2020年第6期1847-1872,共26页
In this paper,linear quadratic(LQ)optimal control problems are investigated for two types of uncertain random systems which consider the coefficient of the perturbed term as a constant vector or a vector-valued functi... In this paper,linear quadratic(LQ)optimal control problems are investigated for two types of uncertain random systems which consider the coefficient of the perturbed term as a constant vector or a vector-valued function of state vector and control vector.First,the uncertain random optimal control model is established under expected value criterion.Second,based on Bellman’s principle,recurrence equations are presented for settling such problem.Then by applying the recurrence equations and chance theory,the analytical expressions of the optimal results for the LQ problems are derived.Furthermore,some examples and an application are given to show the effectiveness of our results. 展开更多
关键词 linear quadratic problem optimal control recurrence equations uncertain random system
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Identifiability and Solvability in Inverse Linear Quadratic Optimal Control Problems
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作者 LI Yibei WAHLBERG Bo HU Xiaoming 《Journal of Systems Science & Complexity》 SCIE EI CSCD 2021年第5期1840-1857,共18页
In this paper, the inverse linear quadratic(LQ) problem over finite time-horizon is studied.Given the output observations of a dynamic process, the goal is to recover the corresponding LQ cost function. Firstly, by co... In this paper, the inverse linear quadratic(LQ) problem over finite time-horizon is studied.Given the output observations of a dynamic process, the goal is to recover the corresponding LQ cost function. Firstly, by considering the inverse problem as an identification problem, its model structure is shown to be strictly globally identifiable under the assumption of system invertibility. Next, in the noiseless case a necessary and sufficient condition is proposed for the solvability of a positive semidefinite weighting matrix and its unique solution is obtained with two proposed algorithms under the condition of persistent excitation. Furthermore, a residual optimization problem is also formulated to solve a best-fit approximate cost function from sub-optimal observations. Finally, numerical simulations are used to demonstrate the effectiveness of the proposed methods. 展开更多
关键词 Inverse optimal control linear quadratic regulators model identifiability
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履带车辆主动悬挂多点布置优化
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作者 凌启辉 陈昕 +3 位作者 戴巨川 何兴云 杨书仪 郭勇 《振动.测试与诊断》 EI CSCD 北大核心 2024年第2期397-403,416,共8页
为实现履带车辆主动悬挂减振性能和能耗达到综合最优,基于正交试验方法开展履带车辆主动悬挂多点布置优化设计。首先,建立了履带车辆悬挂系统动力学模型,并通过道路模拟试验验证了该模型的合理性;其次,开展了履带车辆悬挂系统正交试验,... 为实现履带车辆主动悬挂减振性能和能耗达到综合最优,基于正交试验方法开展履带车辆主动悬挂多点布置优化设计。首先,建立了履带车辆悬挂系统动力学模型,并通过道路模拟试验验证了该模型的合理性;其次,开展了履带车辆悬挂系统正交试验,分析了4种典型路面下各子悬挂对悬挂系统减振性能影响的敏感性;最后,设计了主动悬挂作动器的6个布置方案,通过建立基于线性二次最优(linear quadratic regulator,简称LQR)控制的履带车辆主动悬挂动力学模型,分析了典型路面下各布置方案对悬挂系统减振性能的影响规律及能耗变化规律。结果表明,通过对履带车辆主动悬挂作动器的布置优化,可以实现悬挂减振性能和能耗之间的平衡。 展开更多
关键词 履带车辆 主动悬挂 道路模拟试验 优化 基于线性二次最优控制
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Parameter Optimization of Linear Quadratic Controller Based on Genetic Algorithm 被引量:2
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作者 李纪敏 尚朝轩 邹明虎 《Tsinghua Science and Technology》 SCIE EI CAS 2007年第S1期208-211,共4页
The selection of weighting matrix in design of the linear quadratic optimal controller is an important topic in the control theory. In this paper, an approach based on genetic algorithm is presented for selecting the ... The selection of weighting matrix in design of the linear quadratic optimal controller is an important topic in the control theory. In this paper, an approach based on genetic algorithm is presented for selecting the weighting matrix for the optimal controller. Genetic algorithm is adaptive heuristic search algorithm premised on the evolutionary ideas of natural selection and genetic. In this algorithm, the fitness function is used to evaluate individuals and reproductive success varies with fitness. In the design of the linear quadratic optimal controller, the fitness function has relation to the anticipated step response of the system. Not only can the controller designed by this approach meet the demand of the performance indexes of linear quadratic controller, but also satisfy the anticipated step response of close-loop system. The method possesses a higher calculating efficiency and provides technical support for the optimal controller in engineering application. The simulation of a three-order single-input single-output (SISO) system has demonstrated the feasibility and validity of the approach. 展开更多
关键词 genetic algorithm weighting matrix linear quadratic controller parameter optimization
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基于轴距预瞄的虚拟轨道列车主动悬架控制策略
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作者 王雨恒 杨蔡进 +2 位作者 徐菁 周帅 张卫华 《动力学与控制学报》 2024年第5期69-77,共9页
针对虚拟轨道列车垂向振动问题,基于轴距预瞄原理设计了一种列车主动悬架控制策略.首先,考虑线性滤波白噪声路面不平度激励,建立了列车—路面耦合振动模型;其次,结合列车轴距预瞄信息,利用线性二次型高斯(Linear Quadratic Gaussian, L... 针对虚拟轨道列车垂向振动问题,基于轴距预瞄原理设计了一种列车主动悬架控制策略.首先,考虑线性滤波白噪声路面不平度激励,建立了列车—路面耦合振动模型;其次,结合列车轴距预瞄信息,利用线性二次型高斯(Linear Quadratic Gaussian, LQG)控制理论设计了列车主动悬架LQG控制器,并基于自适应粒子群算法(Adaptive Particle Swarm Optimization, APSO)对控制器的权重系数进行优化;最后,研究了列车在随机路面和脉冲路面激励作用下的垂向振动特性.仿真结果表明,本文所设计的列车主动悬架控制策略能明显降低列车在随机路面和脉冲路面激励作用下各节车体的垂向振动,且针对不同等级路面和车速工况,均有良好的鲁棒性,有效提高了虚拟轨道列车的乘坐舒适性. 展开更多
关键词 虚拟轨道列车 主动悬架控制 轴距预瞄 线性二次型高斯控制 自适应粒子群算法
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