基于鲁棒一步集的Tube不变集鲁棒模型预测控制

针对一类干扰有界的输入和状态受约束线性离散系统,提出了一种基于鲁棒一步集的Tube不 变集鲁棒模型预测控制方法.首先采用多面体不变集离线设计方法得到基于多面体不变集序列的扩 展终端约束集;然后为了扩大鲁棒模型预测控制的初始状态允许区域,并提高系统的鲁棒性,在扩展终端约束集的基础上,通过引入鲁棒一步集并借助Tube不变集控制策略,设计了基于鲁棒一步集的鲁棒模型预测控制方法,并给出了算法的存在性和稳定性证明. 该方法不仅极大地扩大了初始状态允许区域,而且对有界干扰具有有效的抑制作用,使得受扰系统收敛到以原点为中心的最小鲁棒正不变集内.最后仿真验证了算法的有效性.     

在线优化线性反馈增益的非线性鲁棒预测控制方法

以鲁棒控制不变集作为预测控制的终端约束集,设计了一种新的鲁棒预测控制算法.将预测控制在不同采样点的待优化控制律考虑为线性反馈控制律,并通过在线优化求解线性反馈增益.从理论上证明了若采用所设计的鲁棒预测控制器,则系统是输入状态稳定的.最后通过计算机仿真验证了所提出设计方法的可行性.     

具有自适应噪声边界的Tube可达集鲁棒预测控制

针对过程噪声设定边界与真实噪声边界失配的有界干扰离散线性不确定系统,提出一种具有自适应噪声边界的Tube可达集鲁棒模型预测控制方法.首先,该算法引入基于MIT规则的自适应集员滤波在线估计系统状态和噪声边界.其次,基于估计值,通过迭代自适应集员滤波的时间更新部分计算出预测时域内闭环不确定系统状态的可达集.最后,用可达集代替不变集并根据Tube鲁棒模型预测控制策略,给出了实际不确定系统的控制律,确保系统状态鲁棒渐近稳定,并收敛于终端干扰不变集.仿真结果验证了该控制方法的有效性.     

基于多面体不变集的变终端约束集RMPC

针对一类状态和输入受约束的多胞不确定线性时变系统,提出了一种基于多面体不变集的变终端约束集鲁棒模型预测控制算法.首先采用基于状态反馈增益的多面体不变集计算方法,给出了一种新的控制不变集序列构造方法,然后以控制不变集序列的并集作为终端约束集,结合在线优化和增益切换,实施变终端约束集双模鲁棒预测控制.该算法不仅有效地扩大了...     

采用鲁棒容许集对有约束的不确定系统作鲁棒模型预测控制

针对输入和状态受约束的干扰有界多胞不确定线性系统,提出了基于鲁棒容许集的扩大吸引域鲁棒模型预测控制(RMPC)方法.首先给出了多面体不变集的鲁棒容许集计算方法,并推导了鲁棒容许集存在的充分必要条件.其次,为了拓展Tube不变集鲁棒模型预测控制算法的适用范围,讨论了干扰有界多胞不确定线性系统的Tube不变集控制策略.之后为了扩大约束系统吸引域,提出了干扰有界多胞不确定系统的鲁棒容许集模型预测控制策略.通过采用鲁棒容许集和Tube不变集RMPC,该方法不仅扩大了吸引域,而且降低了在线计算量;同时,采用基于最小鲁棒正不变集的Tube不变集策略保证了算法的鲁棒性.最后仿真结果验证了算法的有效性.     

输入状态稳定的鲁棒预测控制

以有界干扰非线性系统为研究对象,设计一种基于近似可达集的鲁棒预测控制方法。该方法以鲁棒控制不变集作为终端约束集,采用一种简单的三次多项式逼近预测控制的待优化控制律,通过在线优化求解三次多项式的各项系数,并从理论上证明了所设计的鲁棒预测控制律可以使系统输入状态稳定。最后通过仿真实例验证了所提出的鲁棒预测控制方法的可行性和有效性。     

一类离散不确定系统的Tube不变集离线鲁棒模型预测控制

针对一类输入和状态受限的离散线性不确定系统,提出了一种基于Tube不变集的离线鲁棒模型预测控制方法.首先针对输入和状态约束线性时不变标准系统,设计了改进的基于多面体不变集的离线模型预测控制算法,并证明了稳定性.其次对于存在未知有界干扰的实际不确定系统,引入了Tube不变集策略,通过设计对应标准模型的最优控制序列和状态轨迹,给出了实际不确定系统的离线Tube不变集控制策略,保证系统状态鲁棒渐近稳定,并收敛于终端干扰不变集.仿真结果验证了该控制方法的有效性.     

运用区间算法的约束非线性系统鲁棒模型预测控制

针对一类具有输入和状态约束的干扰有界非线性系统,提出了基于区间分析的约束非线性鲁棒模型预测控制,以降低计算量并扩大系统吸引域.首先,在集合运算的基础上,利用区间运算和函数区间扩展,给出了一种计算效能更好、保守性更低的非线性系统鲁棒一步集计算方法;其次,构造重叠的多面体控制不变集序列并以此计算约束非线性系统的鲁棒多步集,并通过设计基于集合的在线优化策略,提出了基于鲁棒一步集的单步优化非线性模型预测控制,有效降低了非线性优化的在线计算量;最后,仿真实例验证了算法的有效性.     

一种改进的鲁棒约束预测控制器的综合设计方法

针对多包描述的不确定系统,提出一种新的鲁棒约束预测控制器.高线设计多包系统worst-case情况下性能最优的不变集,在线求解多包系统无穷时域性能指标的rain-max优化问题.设计方法采用了时变的终端约束集,扩大了初始可行域,并能获得较优的控制性能.仿真结果验证了该方法的有效性.     

基于容许集的多胞不确定系统三模RMPC

针对输入和状态受约束的多胞不确定线性系统,提出了基于容许集的扩大吸引域三模鲁棒模型预测控制方法.在多面体不变集离线模型预测控制算法的基础上引入容许集,以多面体不变集序列的并集作为模态1,基于N步容许集的控制容许集作为模态2,并利用离线设计和在线优化的控制策略,设计了三模变终端约束鲁棒模型预测控制算法,以实现系统渐近稳定.该算法不仅降低了在线运算量,而且扩大了吸引域.最后的仿真结果验证了所提出算法的有效性.     

Design of an RMPC with a time‐varying terminal constraint set for tracking problem

This paper presents a robust model predictive control algorithm with a time‐varying terminal constraint set for systems with model uncertainty and input constraints. In this algorithm, the nonlinear system is approximated by a linear model where the approximation error is considered as an unstructured uncertainty that can be represented by a Lipschitz nonlinear function. A continuum of terminal constraint sets is constructed off‐line, and robust stability is achieved on‐line by using a variable control horizon. This approach significantly reduces the computational complexity. The proposed robust model predictive controller with a terminal constraint set is used in tracking set‐points for nonlinear systems. The effectiveness of the proposed method is illustrated with a numerical example. Copyright © 2015 John Wiley & Sons, Ltd.     

Enlarging the domain of attraction of MPC controllers

This paper presents a method for enlarging the domain of attraction of nonlinear model predictive control (MPC). The usual way of guaranteeing stability of nonlinear MPC is to add a terminal constraint and a terminal cost to the optimization problem such that the terminal region is a positively invariant set for the system and the terminal cost is an associated Lyapunov function. The domain of attraction of the controller depends on the size of the terminal region and the control horizon. By increasing the control horizon, the domain of attraction is enlarged but at the expense of a greater computational burden, while increasing the terminal region produces an enlargement without an extra cost.In this paper, the MPC formulation with terminal cost and constraint is modified, replacing the terminal constraint by a contractive terminal constraint. This constraint is given by a sequence of sets computed off-line that is based on the positively invariant set. Each set of this sequence does not need to be an invariant set and can be computed by a procedure which provides an inner approximation to the one-step set. This property allows us to use one-step approximations with a trade off between accuracy and computational burden for the computation of the sequence. This strategy guarantees closed loop-stability ensuring the enlargement of the domain of attraction and the local optimality of the controller. Moreover, this idea can be directly translated to robust MPC.     

Robust nonlinear MPC without terminal constraint for tracking changing setpoints in the presence of non-additive unknown disturbance

This paper develops a novel robust tracking model predictive control (MPC) without terminal constraint for discrete-time nonlinear systems capable to deal with changing setpoints and unknown non-additive bounded disturbances. The MPC scheme without terminal constraint avoids difficult computations for the terminal region and is thus simpler to design and implement. However, the existence of disturbances and/or sudden changes in a setpoint may lead to feasibility and stability issues in this method. In contrast to previous works that considered changing setpoints and/or additive slowly varying disturbance, the proposed method is able to deal with changing setpoints and non-additive non-slowly varying disturbance. The key idea is the addition of tightened input and state (tracking error) constraints as new constraints to the tracking MPC scheme without terminal constraints based on artificial references. In the proposed method, the optimal tracking error converges asymptotically to the invariant set for tracking, and the perturbed system tracking error remains in a variable size tube around the optimal tracking error. Closed-loop input-to-state stability and recursive feasibility of the optimization problem for any piece-wise constant setpoint and non-additive disturbance are guaranteed by tightening input and state constraints as well as weighting the terminal cost function by an appropriate stabilizing weighting factor. The simulation results of the satellite attitude control system are provided to demonstrate the efficiency of the proposed predictive controller.     

基于容许集的变终端约束MPC控制

针对一类输入和状态受约束的离散线性系统,提出一种基于Ⅳ步容许集的变终端约束集模型预测控制方法.首先给出多面体不变集序列作为终端约束集的离线模型预测控制算法,扩大了终端约束集.为进一步扩大初始状态可镇定区域,引入N步容许集,设计了基于容许集的变终端约束集模型预测控制方法.该算法采用离线设计、在线优化方法,实现了系统渐近稳定,不仅降低了在线运算量,而且扩大了初始状态可镇定区域.仿真结果表明了算法的有效性.