Sliding mode control of uncertain systems with distributed time-delay: parameter-dependent Lyapunov functional approach

The robust stability and robust sliding mode control problems are studied for a class of linear distributed time-delay systems with polytopic-type uncertainties by applying the parameter-dependent Lyapunov functional approach combining with a new method of introducing some relaxation matrices and tuning parameters, which can be chosen properly to lead to a less conservative result. First, a sufficient condition is proposed for robust stability of the autonomic system; next, the sufficient conditions of the robust stabilization controller and the existence condition of sliding mode are developed. The results are given in terms of linear matrix inequalities （LMIs）, which can be solved via efficient interior-point algorithms. A numerical example is presented to illustrate the feasibility and advantages of the proposed design scheme.

Hybrid Predictive Control Based on High-Order Differential State Observers and Lyapunov Functions for Switched Nonlinear Systems

In this paper, a hybrid predictive controller is proposed for a class of uncertain switched nonlinear systems based on high-order differential state observers and Lyapunov functions. The main idea is to design an output feedback bounded controller and a predictive controller for each subsystem using high-order differential state observers and Lyapunov functions, to derive a suitable switched law to stabilize the closed-loop subsystem, and to provide an explicitly characterized set of initial conditions. For the whole switched system, based on the high-order differentiator, a suitable switched law is designed to ensure the whole closed-loop’s stability. The simulation results for a chemical process show the validity of the controller proposed in this paper.

An improved constrained model predictive control approach for Hammerstein-Wiener nonlinear systems

Many industry processes can be described as Hammerstein-Wiener nonlinear systems. In this work, an improved constrained model predictive control algorithm is presented for Hammerstein-Wiener systems. In the new approach, the maximum and minimum of partial derivative for input and output nonlinearities are solved in the neighbourhood of the equilibrium. And several parameter-dependent Lyapunov functions, each one corresponding to a different vertex of polytopic descriptions models, are introduced to analyze the stability of Hammerstein-Wiener systems, but only one Lyapunov function is utilized to analyze system stability like the traditional method. Consequently, the conservation of the traditional quadratic stability is removed, and the terminal regions are enlarged. Simulation and field trial results show that the proposed algorithm is valid. It has higher control precision and shorter blowing time than the traditional approach.

Networked Cooperative Distributed Model Predictive Control Based on State Observer

Although distributed model predictive control has caused significant attention and received many good results, the results are mostly under the assumption that the system states can be observed. However, the states are difficult to be observed in practice. In this paper, a novel distributed model predictive control is proposed based on state observer for a kind of linear discrete-time systems where states are not measured. Firstly, an output feedback control law is designed based on Lyapunov function and state observer. And the stability domain is described. Furthermore, the stability domain as a terminal constraint is added into the constraint conditions of the algorithm to make systems stable outside the stability domain. The simulation results show the effectiveness of the proposed method.

基于Lyapunov-MPC方法的非合作目标近距离抵近控制

针对航天器近距离视线抵近同时存在轨道与姿态机动的非合作目标特定方位控制问题,提出了一种基于控制Lyapunov函数(CLF)的模型预测控制方法 (LMPC)。首先,根据视线坐标系下的轨道动力学方程,建立了满足视线指向要求的航天器相对轨道动力学模型,并推导了期望轨道的解析表达式。其次,利用MPC方法设计控制器进行在线优化控制,并通过纳入基于李雅普洛夫方法的非线性反步控制的显式特征,构建收缩约束式,以确保闭环稳定性。接着,对基于LMPC的控制方法的递归可行性和闭环稳定性进行了证明。最后,仿真结果证明了所设计的LMPC轨迹跟踪方法的有效性和鲁棒性。

CBF-Based Distributed Model Predictive Control for Safe Formation of Autonomous Mobile Robots

A distributed model predictive control(DMPC)method based on robust control barrier function(RCBF)is developed to achieve the safe formation target of multi-autonomous mobile robot systems in an uncertain disturbed environment.The first step is to analyze the safety requirements of the system during safe formation and categorize them into collision avoidance and distance connectivity maintenance.RCBF constraints are designed based on collision avoidance and connectivity maintenance requirements,and security constraints are achieved through a combination.Then,the specified safety constraints are integrated with the objective of forming a multi-autonomous mobile robot formation.To ensure safe control,the optimization problem is integrated with the DMPC method.Finally,the RCBF-DMPC algorithm is proposed to ensure iterative feasibility and stability while meeting the constraints and expected objectives.Simulation experiments illustrate that the designed algorithm can achieve cooperative formation and ensure system security.

Multi-objective robust controller synthesis for discrete-time systems with convex polytopic uncertain domain

Multi-objective robust state-feedback controller synthesis problems for linear discrete-time uncertain systems are addressed. Based on parameter-dependent Lyapunov functions, the Gl2 and GH2 norm expressed in terms of LMI (Linear Matrix Inequality) characterizations are further generalized to cope with the robust analysis for convex polytopic uncertain system. Robust state-feedback controller synthesis conditions are also derived for this class of uncertain systems. Using the above results, multi-objective state-feedback controller synthesis procedures which involve the LMI optimization technique are developed and less conservative than the existing one. An illustrative example verified the validity of the approach.

Improved Model Predictive Control with Prescribed Performance for Aggregated Thermostatically Controlled Loads

Aggregate thermostatically controlled loads(AT-CLs)are a suitable candidate for power imbalance on demand side to smooth the power fluctuation of renewable energy.A new control scheme based on an improved bilinear aggregate model of ATCLs is investigated to suppress power imbalance.Firstly,the original bilinear aggregate model of ATCLs is extended by the second-order equivalent thermal parameter model to optimize accumulative error over a long time scale.Then,to ensure the control performance of tracking error,an improved model predictive control algorithm is proposed by integrating the Lyapunov function with the error transformation,and theoretical stability of the proposed control algorithm is proven.Finally,the simulation results demonstrate that the accuracy of the improved bilinear aggregate model is enhanced;the proposed control algorithm has faster convergence speed and better tracking accuracy in contrast with the Lyapunov function-based model predictive control without the prescribed performance.

基于PID代价函数的鲁棒型永磁同步电机模型预测控制

当有限集模型预测控制(Finite Control Set Model Predictive Control,FCS-MPC)应用在永磁同步电机(Permanent Magnet Synchronous Machine,PMSM)弱磁控制时,系统存在参数鲁棒性较差的问题。为了解决此问题,本文提出一种基于比例−积分−微分(Proportional-Integral-Derivative,PID)型代价函数的FCS-MPC永磁同步电机弱磁控制策略。在该策略中,PID型代价函数由3部分组成:跟踪电流的比例误差代价、削弱稳态控制误差的积分误差代价和降低纹波误差的微分误差代价。本文依据永磁同步电机的数学模型建立了预测模型,详细描述了PID型代价函数的FCSMPC在永磁同步电机弱磁控制中的实现过程。同时,为了保证预测的准确性,对系统采用了延时补偿策略。仿真结果证明,当永磁同步电机在弱磁控制中参数失配时,本文提出的基于PID型代价函数的FCS-MPC,不仅可提高控制系统对电机参数和负载转矩扰动的鲁棒性,还保留了FCS-MPC良好的动态性能。

The design of predictive control with characterized set of initial condition for constrained switched nonlinear system

Stabilization of the constrained switched nonlinear systems is an attractive research subject. Predictive control can handle variable constraints well and make the system stable. Its stability is typically based on an assumption of initial feasibility of the optimization problem; however the set of initial conditions, starting from where a given predictive formulation is guaranteed to be feasible, is not explicitly characterized. In this paper, a hybrid predictive control method is proposed for a class of switched nonlinear systems with input constraints and un-measurable states. The main idea is to design a mixed controller using Lyapunov functions and a state observer, which switches appropriately between a bounded feedback controller and a predictive controller, and to give an explicitly characterized set of initial conditions to stabilize each closed-loop subsystem. For the whole switched nonlinear system, a suitable switched law based on the state estimation is designed to orchestrate the transitions between the consistituent modes and their respective controllers, and to ensure the whole closed-loop system's stability. The simulation results for a chemical process show the validity of the controller proposed in this paper.

过热汽温的稳定自适应预测函数控制

针对火电厂锅炉过热蒸汽温度的动特性设计了一种基于Laguerre模型的稳定自适应预测函数控制器。通过对闭环系统状态方程的稳定性分析,依据Lyapunov稳定性定理得到了控制系统稳定的必要条件。对于不同负荷情况下模型发生跳变所引起的不稳定,该文提出一种衰减因子补偿校正方法,并使用混沌算法在线寻优调节衰减因子,提高了控制品质。仿真研究中根据多模型切换性能指标函数来判断模型跳变,当负荷变化时,在线辨识模型参数,得到较好的控制结果,证明该算法的有效性。

无人机编队机动飞行时的队形保持反馈控制

为提高编队大机动时的队形保持能力,采用虚拟结构编队方法,基于李雅普诺夫直接法设计独立的非线性队形保持控制器,并在此基础上采用非线性模型预测控制方法设计含队形反馈的编队轨迹跟踪器。通过在代价函数中引入队形误差代价来实现队形反馈控制策略,并采用动态参数实现编队队形保持和沿参考轨迹飞行之间的自适应切换,各无人机通过滚动求解有限时域优化问题得到虚拟结构的控制指令。仿真结果表明,相较于无队形反馈的情况,所设计的含队形反馈轨迹跟踪器能够显著地降低编队大机动时的队形保持误差。

平抑新能源功率波动的聚合温控负荷改进模型预测控制

利用需求侧聚合温控负荷(ATCLs)提供负荷跟踪辅助服务以平抑新能源功率波动是一种经济、有效的方法,但对ATCLs的控制可能会影响用户的舒适度。为此,提出一种考虑用户舒适度的ATCLs平衡新能源功率波动控制方法。首先,采用人体热舒适性评价指标预测平均投票和预测不满意度得到夏季室内舒适温度范围,结合实验方法进一步确定2次调节间最大温度波动范围;然后,利用ATCLs双线性模型,将舒适温度范围和最大温度波动范围作为约束条件,提出一种基于Lyapunov函数的改进模型预测控制(MPC)方法,该方法减少了传统MPC的计算量并缩短了其执行延时,Lyapunov直接法保证了控制的收敛性,且分布式控制的引入降低了对通信系统的要求。仿真结果表明,所提方法在兼顾用户舒适度的前提下,快速平衡供用电之间的功率偏差,提高了电力系统对间歇式新能源的消纳能力。

双值预测函数控制

针对典型工业过程——一阶加纯滞后对象跟踪设定曲线提出了双值预测函数控制。在给出控制算法的基础上，对系统稳定性和鲁棒性进行了分析，给出了增益失配的鲁棒性条件。

基于混合区域极点配置的航空发动机全包线鲁棒变参数控制器设计

针对航空发动机全包线多变量鲁棒变增益控制器设计问题,提出了一种基于混合区域极点配置的鲁棒变参数控制方法。利用Jacobian方法建立多调度参数下的发动机仿射线性变参数(Linear parameter varying,LPV)模型,用于描述发动机全包线内的非线性动态特性;针对上述LPV模型,采用仿射参数依赖Lyapunov函数设计具有H∞鲁棒性能的状态反馈控制器,给出了控制系统全局稳定性的证明;并利用混合区域极点配置方法,将闭环系统极点配置到左半平面指定位置,以保证控制系统的动态特性及稳定裕度;进而引入凸多胞技术,将参数依赖线性矩阵不等式(Linear matrix inequality,LMI)方程转化为有限维LMI进行控制器求解,并得到了全局解。针对涡扇发动机的仿真结果表明:存在复杂量测噪声干扰条件下,鲁棒变参数控制器可以实现发动机全包线内控制指令的精确跟踪,系统阶跃响应的调节时间不超过1.5s,系统无超调,对控制期望的稳态跟踪误差在0.02%以内,符合发动机控制系统技术要求。

三维编队飞行模型建立及自适应鲁棒控制

以张量分析为工具建立无人机编队飞行相对运动模型,用飞行中外界干扰的估计值构造系统能量函数,根据Lyapunov稳定判据,提出一种无人机编队飞行队形保持的自适应鲁棒控制律。研究表明:无人机编队飞行张量模型具有广泛的适用性;为无人机编队飞行深层问题研究、克服标架奇点引起的计算障碍等提供了新途径;提出的控制律简单,有效。

基于TS模糊模型的稳定预测控制及其在机炉协调系统中的应用

针对TS模糊系统,提出一种基于模糊李亚普诺夫函数的稳定预测控制方法,通过构造模糊李普诺夫函数并最小化预测控制中无穷时域或拟无穷时域性能指标的上界,来设计满足系统闭环稳定、输入约束以及控制性能最优的平行分配补偿控制律。该控制律最终归结为求解一组线性矩阵不等式约束下的凸优化问题。模糊李亚普诺夫函数的使用减少了公共李亚普诺夫函数及分段李亚普诺夫函数的保守性,增加了可行解的范围。数值仿真和火电厂非线性机炉协调系统中的仿真试验,证明了这种方法的优越性和有效性。

参数和时延不确定性离散时间系统的H_∞鲁棒控制

针对含有参数和时延不确定性线性离散时间系统的鲁棒控制问题 ,构造改进的 L yapunov函数 ,并采用 L MI与 H∞ 鲁棒控制相结合的方法 ,使得系统在不含外界未知扰动时 ,只需满足一个矩阵不等式 ,便可通过状态的静态反馈控制使闭环系统达到二次稳定 ;而在系统含有外界未知扰动时 ,结合基于离散时间系统的无源性控制方法 ,同样只需满足一个矩阵不等式 ,便可通过状态的静态反馈控制使得闭环系统达到理想的干扰抑制作用。

约束Hammerstein系统构造性预测控制及其在聚丙烯牌号切换控制中的应用

针对具有状态、输入和中间变量约束的连续时间Hammerstein系统,提出了一种多变量构造性模型预测控制策略。首先,基于Hammerstein系统的特殊结构,利用Raccati方程构造线性环节的控制Lyapunov函数,进而设计其一族可调控制律(即稳定控制类)。其次,对约束Hammerstein系统定义一个有限时域滚动优化控制问题,通过在线优化计算实际预测控制量。利用Lyapunov稳定性定理建立闭环系统渐近稳定的充分条件。最后,以工业聚丙烯装置牌号切换控制为例,仿真验证本文结果的有效性。

一种基于连续特征模型的新型自适应控制方法

针对一类非线性系统,提出一种新型的自适应控制方法。首先通过构造原系统的连续特征模型,使得特征模型与原非线性系统具有等效的输入-输出特性,即当输入相同时,二者的输出完全相同。所以,特征模型可以替代原系统作为被控对象进行输出反馈控制系统设计。由于原非线性系统具有未知参数和不确定性,特征模型的特征参数是未知的、快时变的。然后将连续特征模型与动态面控制技术相结合,形成一种鲁棒自适应控制方法。该方法完全不依赖原系统模型,仅利用其输出信息进行反馈控制,无需设计观测器对原系统的内部状态、未知参数和不确定性进行观测。最后采用Lyapunov理论证明了闭环系统的稳定性,仿真结果验证了方法的有效性。