PID Control of Planar Nonlinear Uncertain Systems in the Presence of Actuator Saturation

This paper investigates PID control design for a class of planar nonlinear uncertain systems in the presence of actuator saturation. Based on the bounds on the growth rates of the nonlinear uncertain function in the system model, the system is placed in a linear differential inclusion. Each vertex system of the linear differential inclusion is a linear system subject to actuator saturation. By placing the saturated PID control into a convex hull formed by the PID controller and an auxiliary linear feedback law, we establish conditions under which an ellipsoid is contractively invariant and hence is an estimate of the domain of attraction of the equilibrium point of the closed-loop system. The equilibrium point corresponds to the desired set point for the system output. Thus, the location of the equilibrium point and the size of the domain of attraction determine, respectively, the set point that the output can achieve and the range of initial conditions from which this set point can be reached. Based on these conditions, the feasible set points can be determined and the design of the PID control law that stabilizes the nonlinear uncertain system at a feasible set point with a large domain of attraction can then be formulated and solved as a constrained optimization problem with constraints in the form of linear matrix inequalities (LMIs). Application of the proposed design to a magnetic suspension system illustrates the design process and the performance of the resulting PID control law.      

Distributionally robust optimization of home energy management system based on receding horizon optimization

This paper investigates the scheduling strategy of schedulable load in home energy management system (HEMS) under uncertain environment by proposing a distributionally robust optimization (DRO) method based on receding horizon optimization (RHO-DRO). First, the optimization model of HEMS, which contains uncertain variable outdoor temperature and hot water demand, is established and the scheduling problem is developed into a mixed integer linear programming (MILP) by using the DRO method based on the ambiguity sets of the probability distribution of uncertain variables. Combined with RHO, the MILP is solved in a rolling fashion using the latest update data related to uncertain variables. The simulation results demonstrate that the scheduling results are robust under uncertain environment while satisfying all operating constraints with little violation of user thermal comfort. Furthermore, compared with the robust optimization (RO) method, the RHO-DRO method proposed in this paper has a lower conservation and can save more electricity for users.     

基于改进交叉熵算法的电力系统随机生产模拟

蒙特卡洛模拟的计算效率与系统的可靠性密切相关，在其用于高可靠性系统的随机模拟时存在计算效率偏低的问题。为此，提出了一种基于多层交叉熵与对偶变数抽样技术相结合的随机模拟算法。首先使用多层交叉熵构造零方差概率密度函数的近似函数，提高小概率失效事件的抽取概率；其次基于已构造的近似概率函数，采用对偶变数抽样法进行抽样，进一步提高抽样的收敛速度。以IEEE RTS修改系统为例进行了算例分析，算例结果验证了所提出的基于改进交叉熵的电力系统随机生产模拟算法的有效性。     

Filtered adaptive constrained sampled-data control for uncertain multivariable nonlinear systems

A filtered adaptive constrained sampled-data controller for uncertain multivariable nonlinear systems in the presence of various constraints is synthesized in this paper. A piecewise constant adaptive law drives that estimation error dynamics to zero at each sampling time instant yields adaptive parameters. The filtered control scheme consists of two components. Based on an estimation/cancellation strategy, a disturbance rejection control law is designed to compensate the nonlinear uncertainties within the bandwidth of low-pass filters, whereas a constraint violation avoidance control law is designed to solve an online constrained optimization problem. Although a reduced sampling time helps to minimize the estimation error caused by the neglect of unknowns, the resulting aggressive signals put more restrictions on the control law. Greater sacrifice of tracking performance is required to satisfy the constraints. The constraints violation avoidance control law is in favor of a larger sampling time. Sufficient conditions are given to guarantee the stability of the closed-loop system with the sampled-data controller, where the input/output signals are held constant over the sampling period. Numerical examples are provided to validate the theoretical results, comparisons between the constrained sampled-data controller and unconstrained adaptive controller with the implementation of different sampling times are carried out.     

Estimating posterior inference quality of the relational infinite latent feature model for overlapping community detection

Overlapping community detection has become a very hot research topic in recent decades, and a plethora of methods have been proposed. But, a common challenge in many existing overlapping community detection approaches is that the number of communities K must be predefinedmanually. We propose a flexible nonparametric Bayesian generative model for count-value networks, which can allow K to increase as more and more data are encountered instead of to be fixed in advance. The Indian buffet process was used to model the community assignment matrix Z, and an uncollapsed Gibbs sampler has been derived.However, as the community assignment matrix Z is a structured multi-variable parameter, how to summarize the posterior inference results and estimate the inference quality about Z, is still a considerable challenge in the literature. In this paper, a graph convolutional neural network based graph classifier was utilized to help to summarize the results and to estimate the inference quality about Z. We conduct extensive experiments on synthetic data and real data, and find that empirically, the traditional posterior summarization strategy is reliable.     

A general class of nonparametric control charts

In this article, we introduce a new general class of nonparametric Shewhart‐type control charts using the lengths of runs of test sample observations between successive observations of a reference sample. Several control charts that have appeared in the literature are members of the new family. In addition, 3 new nonparametric control charts that belong to the class are introduced and studied. Numerical results depict that the proposed charts attain competitive in‐control and out‐of‐control performance as compared with existing nonparametric charts.     

Adaptive robust control of fully-constrained cable driven parallel robots

In this paper, adaptive robust control (ARC) of fully-constrained cable driven parallel robots is studied in detail. Since kinematic and dynamic models of the robot are partly structurally unknown in practice, in this paper an adaptive robust sliding mode controller is proposed based on the adaptation of the upper bound of the uncertainties. This approach does not require pre-knowledge of the uncertainties upper bounds and linear regression form of kinematic and dynamic models. Moreover, to ensure that all cables remain in tension, proposed control algorithm benefit the internal force concept in its structure. The proposed controller not only keeps all cables under tension for the whole workspace of the robot, it is chattering-free, computationally simple and it does not require measurement of the end-effector acceleration. The stability of the closed-loop system with proposed control algorithm is analyzed through Lyapunov second method and it is shown that the tracking error will remain uniformly ultimately bounded (UUB). Finally, the effectiveness of the proposed control algorithm is examined through some experiments on a planar cable driven parallel robot and it is shown that the proposed controller is able to provide suitable tracking performance in practice.     

An EWMA signed ranks control chart with reliable run length performances

During the design phase of a control chart, the determination of its exact run length properties plays a vital role for its optimal operation. Markov chain or integral equation methods have been extensively applied in the design phase of conventional control charts. However, for distribution-free schemes, due to the discrete nature of the statistics being used (such as the sign or the Wilcoxon signed rank statistics, for instance), it is impossible to accurately compute their run length properties. In this work, a modified distribution-free phase II exponentially weighted moving average (EWMA)-type chart based on the Wilcoxon signed rank statistic is considered and its exact run length properties are discussed. A continuous transformation of the Wilcoxon signed rank statistic, combined with the classical Markov chain method, is used for the determination of the average run length in the in- and out-of control cases. Moreover, its exact performance is derived without any knowledge of the distribution of sample observations. Finally, an illustrative example is provided showing the practical implementation of our proposed chart.     

Adaptive backstepping repetitive learning control design for nonlinear discrete‐time systems with periodic uncertainties

This paper addresses a tracking problem for uncertain nonlinear discrete‐time systems in which the uncertainties, including parametric uncertainty and external disturbance, are periodic with known periodicity. Repetitive learning control (RLC) is an effective tool to deal with periodic unknown components. By using the backstepping procedures, an adaptive RLC law with periodic parameter estimation is designed. The overparameterization problem is overcome by postponing the parameter estimation to the last backstepping step, which could not be easily solved in robust adaptive control. It is shown that the proposed adaptive RLC law without overparameterization can guarantee the perfect tracking and boundedness of the states of the whole closed‐loop systems in presence of periodic uncertainties. In addition, the effectiveness of the developed controller is demonstrated by an implementation example on a single‐link flexible‐joint robot. Copyright © 2014 John Wiley & Sons, Ltd.