Min-Max MPC based on a computationally efficient upper bound of the worst case cost

Min-Max MPC (MMMPC) controllers [P.J. Campo, M. Morari, Robust model predictive control, in: Proc. American Control Conference, June 10–12, 1987, pp. 1021–1026] suffer from a great computational burden which limits their applicability in the industry. Sometimes upper bounds of the worst possible case of a performance index have been used to reduce the computational burden. This paper proposes a computationally efficient MMMPC control strategy in which the worst case cost is approximated by an upper bound based on a diagonalization scheme. The upper bound can be computed with O(n³) operations and using only simple matrix operations. This implies that the algorithm can be coded easily even in non-mathematical oriented programming languages such as those found in industrial embedded control hardware. A simulation example is given in the paper.     

Robust pole clustering in a good ride quality region of aircraft for matrices with structured uncertainties

This paper presents a general analysis of robust pole clustering in a good ride quality region (GRQR) of aircraft for matrices with structured uncertainties. This region is an intersection of a ring and a horizontal strip, located in the left half-plane, which is a specific non-Ω-transformable region providing good ride quality of aircraft. The paper applies the Rayleigh principle along the norm theory to analyze robust pole clustering within this region since the generalized Lyapunov theory is not valid for non-Ω-transformable regions. Concerned uncertainties are structured/parametric uncertainties, including interval matrices. The results are useful for robust control analysis and design, especially, of robust good ride quality of aircraft, shuttles, vehicles and space station, as well as some industrial systems. An example of the F-16 dynamics for which GRQR is suitable is included to illustrate the results.     

Feedback predictive control for constrained fuzzy systems with Markovian jumps

In this paper, a feedback model predictive control method is presented to tackle control problems with constrained multivariables for uncertain discrete‐time nonlinear Markovian jump systems. An uncertain Markovian jump fuzzy system (MJFS) is obtained by employing the Takagi‐Sugeno (T‐S) fuzzy model to represent a discrete‐time nonlinear system with norm bounded uncertainties and Markovain jump parameters. To achieve more generality, the transition probabilities of the Markov chain are assumed to be partly unknown and partly accessible. The predictive formulation adopts an on‐line optimization paradigm that utilizes the closed‐loop state feedback controller and is solved using the standard semi‐definite programming (SDP). To reduce the on‐line computational burden, a mode independent control move is calculated at every sampling time based on a stochastic fuzzy Lyapunov function (FLF) and a parallel distributed compensation (PDC) scheme. The robust mean square stability, performance minimization and constraint satisfaction properties are guaranteed under the control move for all admissible uncertainties. A numerical example is given to show the efficiency of the developed approach. Copyright © 2011 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

柔性结构系统的观测器型鲁棒最优保性能控制

通过简要分析柔性直线系统结构,给出3自由度高阶直线柔性系统的数学模型。根据实际直线柔性控制过程滑动质量块位置状态信息易得、但速度状态信息不易得的特点,构造了速度状态观测器。同时针对柔性结构系统对于干扰激发的振动具有难以迅速稳定的特点,设计了基于观测器的直线柔性系统的鲁棒最优保性能控制。实验结果表明:对于直线柔性系统,所设计的观测器型鲁棒最优保性能控制是有效的。     

Robust and stable flow shop scheduling with unexpected arrivals of new jobs and uncertain processing times

In real scheduling problems, some disruptions and unexpected events may occur. These disruptions cause the initial schedule to quickly become infeasible and non-optimal. In this situation, an appropriate rescheduling method should be used. In this paper, a new approach has been proposed to achieve stable and robust schedule despite uncertain processing times and unexpected arrivals of new jobs. This approach is a proactive–reactive method which uses a two-step procedure. In the first step an initial robust solution is produced proactively against uncertain processing times using robust optimization approach. This initial robust solution is more insensitive against the fluctuations of processing times in future. In the next step, when an unexpected disruption occurs, an appropriate reactive method is adopted to deal with this unexpected event. In fact, in the second step, the reactive approach determines the best modified sequence after any unexpected disruption based on the classical objective and performance measures. The robustness measure is implemented in the reactive approach to increase the performance of the real schedule after disruption. Computational results indicate that this method produces better solutions in comparison with four classical heuristic approaches according to effectiveness and performance of solutions.     

无线传感网中基于成对节点探测不确定性的目标容错跟踪方法

针对无线传感器网络(Wireless Sensor Networks,WSN)中的节点在真实环境中的不可靠感知现象及其对目标跟踪精度的影响,首先分析计算了成对传感器节点感知存在的不确定区域及其边界,在此基础上,提出了一种基于成对节点探测不确定性的目标容错跟踪方法(Tracking with Pairwise Uncertainty of RSSI,TPU-RSSI),即通过匹配分组感知采样得到的感知向量(sampling vector)和跟踪区域划分面(face)的特征向量(signature vector)来进行移动目标容错跟踪。该方法在保持跟踪方法灵活性的基础上,能够减小由环境因素带来的跟踪误差。为了降低计算复杂度,提出了一种基于邻居面连接的启发式匹配算法。大量的仿真实验结果均表明,所提方法相比同类的其他方法具有更强的灵活性和更高的定位精度。     

Min–Max MPC based on a network problem

In general, min–max model predictive controllers have a high computational burden. In this work, an efficient implementation of this class of controllers that can be applied to linear plants with additive uncertainties and quadratic cost functions is presented. The new approach relies on the equivalence of the maximization problem with a network problem. If a given condition is satisfied, the computational burden of the proposed implementation grows polynomially with the prediction horizon. In particular, the resulting optimization problem can be posed as a quadratic programming problem with a number of constraints and variables that grows in a quadratic manner with the prediction horizon. An alternative controller has been proposed for those systems that do not satisfy this condition. This alternative controller approximates the original one with a given bound on the error.