Theoretical Study of Double Cost Function Linear Quadratic Regulator(LQR)

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.

Robust Fuzzy Tracking Control for Nonlinear Networked Control Systems with Integral Quadratic Constraints

This paper investigates the robust tracking control problcm for a class of nonlinear networked control systems （NCSs） using the Takagi-Sugeno （T-S） fuzzy model approach. Based on a time-varying delay system transformed from the NCSs, an augmented Lyapunov function containing more useful information is constructed. A less conservative sufficient condition is established such that the closed-loop systems stability and time-domain integral quadratic constraints （IQCs） are satisfied while both time-varying network- induced delays and packet losses are taken into account. The fuzzy tracking controllers design scheme is derived in terms of linear matrix inequalities （LMIs） and parallel distributed compensation （PDC）. Furthermore, robust stabilization criterion for nonlinear NCSs is given as an extension of the tracking control result. Finally, numerical simulations are provided to illustrate the effectiveness and merits of the proposed method.

Adaptive Linear Quadratic Regulator for Continuous-Time Systems With Uncertain Dynamics

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.

Linear Quadratic Integral Control for the Active Suspension of Vehicle

The quarter model of an active suspension is established in the form of controllable autoregressive moving average （CARMA） model. An accelerometer can be mounted on the wheel hub for measuring road disturbance; this signal is used to identify the CARMA model parameters by recursive forgetting factors least square method. The linear quadratic integral （LQI） control method for the active suspension is presented. The LQI control algorithm is fit for vehicle suspension control, for the control performance index can comprise multi controlled variables. The simulation results show that the vertical acceleration and suspension travel both are decreased with the LQI control in the low frequency band, and the suspension travel is increased with the LQI control in the middle or high frequency band. The suspension travel is very small in the middle or high frequency band, the suspension bottoming stop will not happen, so the vehicle ride quality can be improved apparently by the LQI control.

Parametric variational solution of linear-quadratic optimal control problems with control inequality constraints

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.

One Kind of Fully Coupled Linear Quadratic Stochastic Control Problem with Random Jumps

有随机的一个种有点线性的二次的随机的控制问题跳被学习。最佳的控制的明确的形式被获得。最佳的控制能被证明唯一。一个种概括 Riccati 方程系统被介绍，它的解决之可能性被讨论。为有随机的最佳的控制问题的线性反馈管理者跳被概括 Riccati 方程系统的解决方案给。

欠驱动两自由度机械臂LQG/LTR控制

针对欠驱动机械臂系统的快速稳定控制中存在着的系统过程噪声和传感器观测噪声的干扰问题,设计了具有回路传输恢复的线性二次高斯(linear quadratic Gaussian control with loop transfer recovery, LQG/LTR)控制器。该控制器由卡尔曼滤波器和最优状态反馈增益调节器两部分组成,并进一步使用了回路传输恢复技术提高了控制系统稳定裕度。仿真试验表明:LQG/LTR控制方法相比于线性二次型调节器控制方法具有更加出色的动态品质,能很好地抑制噪声造成的系统不稳定问题,使得机械臂快速稳定在期望位置,具备良好的稳定性和鲁棒性。

Numerical solutions of linear quadratic control for time-varying systems via symplectic conservative perturbation

Optimal control system of state space is a conservative system, whose approximate method should be symplectic conservation. Based on the precise integration method, an algorithm of symplectic conservative perturbation is presented. It gives a uniform way to solve the linear quadratic control （LQ control） problems for linear timevarying systems accurately and efficiently, whose key points are solutions of differential Riccati equation （DRE） with variable coefficients and the state feedback equation. The method is symplectic conservative and has a good numerical stability and high precision. Numerical examples demonstrate the effectiveness of the proposed method.

A Control Strategy Combining Fuzzy Control and Linear Quadratic Control for Acrobots

A control strategy based on a combination of fuzzy control and linear quadratic control to control the acrobot is presented. The control torque to swing up is directly derived based on the energy of the acrobot. A fuzzy controller is designed to regulate the amplitude of the control torque from the energy during the upswing. After the acrobot enters a neighborhood of the straight up equilibrium position, a linear quadratic regulator is designed to balance it. The proposed control strategy simplifies the control of the acrobot and achieves better performance. The simulation results show the validity of the control strategy.

Global Optimization for Solving Linear Non-Quadratic Optimal Control Problems

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.

基于最优控制理论的国产光抽运小铯钟频率控制算法

原子钟频率控制是时间保持工作中的关键技术.当前守时工作中的频率控制主要针对国外微波钟采用开环控制算法,但由于国产光抽运小铯钟(下称国产钟)的工作原理和性能不同于国外同类型原子钟,因此该算法不能很好适应国产钟.为了提升我国标准时间的自主性和安全性,本文基于国产钟的噪声特性,在最优控制理论的框架下研究了线性二次高斯控制算法,该算法属于闭环控制算法,从同步时间、频率控制准确度和频率控制稳定度方面研究国产钟性能,最后分析了不同控制间隔对国产钟性能的影响.结果表明随着二次损失函数中约束矩阵W_(R)的增大,同步时间延长,控制准确度降低,控制短期稳定度提高.W_(R)相同情况下,随着控制间隔的增大,同步时间延长,控制准确度降低,控制短期稳定度提高,对于W_(R)=1时,控制间隔为1 h的同步时间为5小时,控制准确度为1.83 ns,1 h的Allan偏差为1.81×10^(-13);控制间隔为8 h的同步时间为28 h,控制准确度为4.48 ns,1 h的Allan偏差为1.48×10^(-13).控制国产光抽运小铯钟的中长期稳定度都得到提高.

无人驾驶车辆路径跟踪混合控制策略研究

针对单一控制算法无法同时满足无人驾驶车辆对路径跟踪精度和控制器求解速度需求的问题,提出一种基于线性二次型调节器(LQR)和模型预测控制(MPC)的混合控制策略。该策略在低速工况下使用线性二次型调节器、在高速工况下使用模型预测控制算法进行路径跟踪控制,在此基础上设计基于有限状态机(FSM)的控制算法切换机制,并通过遗传算法(GA)对控制参数进行优化,基于CarSim和MATLAB/Simulink仿真平台对混合控制策略进行仿真验证,并进一步完成了实车试验。试验结果表明,所设计的混合控制策略能够在提高跟踪精度的基础上缩短计算时间,与单一控制算法相比,平均横向误差和平均航向误差分别减小了26.3%和39.6%,平均计算时间缩短了10.9%。

履带车辆主动悬挂多点布置优化

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。

基于改进势场法的智能车超车动态路径规划

为了改进人工势场法(artificial potential field,APF)在智能车高速超车状态下规划出的轨迹规范性差、安全性得不到保障、以及路径不平滑的问题。设计用于指引智能车换道的换道引力势场,以保证换道轨迹的规范性;构建异向分布结构的障碍车斥力势场提高换道的安全性;并建立带有转向缺口的道路中心线斥力势场和设计平滑代价函数优化规划出的轨迹点,使规划出的路径更加平滑。基于线性二次型调节器(linear quadratic regulator,LQR)设计路径跟踪控制器跟踪规划出的路径。通过Simulink与Carsim联合仿真,结果表明:所改进的APF算法能规划出更加合理的路径,设计的LQR路径跟踪控制器跟踪误差趋近于零,能够较好地控制车辆完成超车换道。

基于模型预测控制的车辆路径跟踪控制技术研究

以车辆三自由度动力学模型为研究对象,对自动驾驶车辆模型预测控制算法进行研究。结合魔术轮胎模型线性区域和小角度假设理论对车辆动力学模型进行简化处理,设计基于模型预测控制算法的路径跟踪控制器。使用MATLAB/CarSim联合仿真平台,选用多组工况进行仿真试验。设定车辆的速度分别为低速、中速、高速3种状态,并且使用线性二次型最优控制器进行换道工况路径跟踪,与模型预测控制器进行控制效果对比与分析,结果表明,模型预测控制算法路径跟踪控制效果更加优秀。

单级旋转倒立摆系统辨识与随动稳定控制方法研究

针对单级旋转倒立摆系统参数辨识和随动稳定控制问题,首先建立倒立摆在不受外力控制,摆杆自然下垂的顺摆模型,基于顺摆模型采用快速傅里叶变换方法对系统参数进行辨识;然后推导顺摆模型与倒摆模型之间的关系,进一步得到倒立摆的倒摆模型;根据辨识出的倒摆模型,采用线性二次型控制器对其进行稳定控制,并进行了数值仿真与实物实验验证。研究结果表明,通过辨识得到的系统模型更加精确,对比直接测量参数得到的系统模型,控制效果更好,且能对随动输入指令进行更优的跟随。该方法可以有效避免量测误差,提高模型的准确性,为火炮随动稳定控制提供参考。

无人车换道轨迹与跟踪控制研究

无人车换道是自动驾驶领域的关键技术,针对无人车换道轨迹规划与跟踪控制问题,选择纯电动汽车作为研究对象,设计了一种考虑横纵向协同控制的轨迹跟踪控制器。首先,通过解耦将车辆换道简化为横向运动和纵向运动。根据路径跟踪误差动力学模型设计了线性二次型调节器路径跟踪控制器,并引入前馈控制设计了前馈-反馈LQR横向控制器,以此降低系统稳态误差。随后,考虑位置-速度误差设计了双PID纵向控制器,对车辆速度进行跟踪。选用五次多项式曲线规划换道轨迹。最后,通过Matlab和CarSim搭建联合仿真平台,对所设计的换道轨迹跟踪横纵向协同控制器进行测试研究。结果表明:在双车道换道工况下,该控制器能够较高精度地跟踪换道轨迹,车辆的距离偏差和航向角偏差最大分别为0.01 m和0.007 rad,可见具有良好的精确性和稳定性。

基于LQG的混合电磁悬架阻尼-刚度设计及试验研究

提出了一种具有三种模式的混合电磁悬架,三种模式分别侧重于悬架的平顺性、轮胎接地性和综合性能,协调了悬架平顺性与轮胎接地性之间的矛盾。建立了混合电磁悬架的动力学模型,确定了各个模式下LQG控制策略的加权系数。在不同的模式下分析了刚度、阻尼对于悬架动力学性能以及悬架能耗特性的影响,确定了不同模式下刚度和阻尼的取值,并进行了仿真分析。结果表明:混合电磁悬架相比于传统被动悬架能够有效改善悬架动力学性能,且相比于主动悬架能明显减少能量消耗。最后进行了试验研究,试验结果与仿真结果基本一致,验证了仿真结果的正确性,表明混合电磁悬架能够减少悬架主动控制时的能量消耗。

具有未知参数的LQG对偶控制算法研究

对于具有未知参数的LQG(Linear quadratic Gaussian)问题,提出了一种次优对偶控制方法,用Kalman滤波处理过程噪声和测量噪声,用前一时刻的后验概率对Cost-to-go进行线性近似,然后,用动态规划获得了次优控制律.最后,用一个例子说明了本文设计的控制器的实施过程.结果表明,该控制律具有良好的对偶性质,并能在学习和控制之间实现较好平衡.

基于LQG的独立变桨控制技术对风电机组气动载荷影响研究

基于多体动力学理论建立风力发电机组动力学模型,针对风轮载荷分布不均问题,在传统变桨距控制策略的基础上,提出基于线性二次高斯算法(LQG)的独立变桨距控制策略,并在Matlab/Simulink中构建控制模型,实现风力机系统的联合仿真,对提出的控制策略与传统的变桨控制策略进行仿真比较。研究结果表明:文中提出的独立变桨控制技术不仅可以实现功率控制,而且有效地降低了风电机组关键部件的疲劳载荷。在载荷优化方面比传统PI控制器效果更明显,更适合大型风电机组变桨距控制。