Natural gradient algorithm for stochastic distribution systems with output feedback

In this paper, we use natural gradient algorithm to control the shape of the conditional output probability density function for the stochastic distribution systems from the viewpoint of information geometry. The considered system here is of multi-input and single output with an output feedback and a stochastic noise. Based on the assumption that the probability density function of the stochastic noise is known, we obtain the conditional output probability density function whose shape is only determined by the control input vector under the condition that the output feedback is known at any sample time. The set of all the conditional output probability density functions forms a statistical manifold (M), and the control input vector and the output feedback are considered as the coordinate system. The Kullback divergence acts as the distance between the conditional output probability density function and the target probability density function. Thus, an iterative formula for the control input vector is proposed in the sense of information geometry. Meanwhile, we consider the convergence of the presented algorithm. At last, an illustrative example is utilized to demonstrate the effectiveness of the algorithm.     

Adaptive fuzzy backstepping control design for a class of pure-feedback switched nonlinear systems

In this paper, an adaptive fuzzy output tracking control approach is proposed for a class of single input and single output (SISO) uncertain pure-feedback switched nonlinear systems under arbitrary switchings. Fuzzy logic systems are used to identify the unknown nonlinear system. Under the framework of the backstepping control design and fuzzy adaptive control, a new adaptive fuzzy output tracking control method is developed. It is proved that the proposed control approach can guarantee that all the signals in the closed-loop system are semi-globally uniformly ultimately bounded (SGUUB) and the tracking error remains an adjustable neighborhood of the origin. A numerical example is provided to illustrate the effectiveness of the proposed approach.     

纯量反馈系统同时强镇定的充分条件

一个稳定的补偿器可同时镇定n个对象(同时强镇定)等价于一个补偿器(不一定稳定)同时镇定n 1个对象(同时镇定)．两个以上对象的同时强镇定和三个以上对象的伺时镇定是线性系统中一个急待解决的公开问题．文中所作的基本假定是所有的对象具有相同的简单不稳定零点，在此条件下给出了n个对象同时强镇定的一个充分条件．当仅有一个不稳定零点时．容易检验是否同时强镇定，否则仅需确定n个对象的不稳定零点并且判定由不稳定零点导出一个相应矩阵是正定的，就能判定n个对象同时强镇定．因此是一个易于检验的充分条件．文章同时给出了n个对象同时强镇定的算法，丰富了同时强镇定的充分条件．     

基于样条插值的模糊控制算法

利用三次样条插值函数,直接由控制输入输出数据对建立了控制输入与控制输出之间的映射关系,得到了一元三次样条插值控制算法和二元双三次样条插值控制算法,并将二者分别用于单输入单输出系统和双输入单输出系统的仿真控制.仿真结果表明,上述方法是可行的,并且基于三次样条函数的模糊插值控制,具有响应快,无超调,稳态误差极小等很好的控制效果.其设计简单,不需要过多规则,对稀疏规则库条件下的控制器设计尤为适用.     

On the combination of kernel principal component analysis and neural networks for process indirect control

ABSTRACT

A new adaptive kernel principal component analysis (KPCA) for non-linear discrete system control is proposed. The proposed approach can be treated as a new proposition for data pre-processing techniques. Indeed, the input vector of neural network controller is pre-processed by the KPCA method. Then, the obtained reduced neural network controller is applied in the indirect adaptive control. The influence of the input data pre-processing on the accuracy of neural network controller results is discussed by using numerical examples of the cases of time-varying parameters of single-input single-output non-linear discrete system and multi-input multi-output system. It is concluded that, using the KPCA method, a significant reduction in the control error and the identification error is obtained. The lowest mean squared error and mean absolute error are shown that the KPCA neural network with the sigmoid kernel function is the best.     

Robust inversion algorithms for vector linear systems

We consider the inversion problem for linear systems, which involves estimation of the unknown input vector. The inversion problem is considered for a system with a vector output and a vector input assuming that the observed output is of higher dimension than the unknown input. The problem is solved by using a controlled model in which the control stabilizes the deviations of the model output from the system output. The stabilizing model control or its averaged form may be used as the estimate of the unknown system input. __________ Translated from Nelineinaya Dinamika i Upravlenie, No. 4, pp. 17–22, 2004.     

切换系统的自适应广义预测控制

针对一类切换系统研究了含有输出预测误差的自适应广义预测控制问题．切换律由有限个子系统的输出预测误差确定．对于单个子系统和多个子系统两种情况,证明了所提出的广义预测控制直接算法能够保证系统的全局收敛性．该算法克服了传统自适应控制固有的收敛速度慢且暂态误差较大的缺点．     

Robust ISS-satisficing variable universe indirect fuzzy control for chaotic systems

In the conventional robust input to state stable (ISS)-satisficing control system, all parameters of the system must be known beforehand, so the application area is limited. In this paper, an attempt is made to create a bridge between two important design techniques, i.e., the robust ISS-satisficing control strategy and the fuzzy control strategy, and the new control method we first proposed has both the inverse optimality of robust ISS-satisficing control and the robust and predictive performance of fuzzy control. By control Lyapunov method, the overall closed-loop system is shown to be stable. In this work, we combine these two control methods, make them learn from the other’s strong points, offset its weakness. The simulation results are given to confirm the control algorithm is feasible and performances well.     

一类时滞非线性系统的自适应模糊控制

对于一类SISO输入时滞已知,状态时滞不确定但有上界的能采用后推设计方法的非线性系统提出一种基于后推设计、自适应模糊控制和滑模控制的控制方案.通过状态变换,把输入时滞系统转化为无输入时滞的系统.用模糊系统来估计系统的未知连续函数,对转化后的新系统设计自适应滑模控制器,使得新系统的状态有界,通过递推证得原系统的状态半全局一致有界.     

An algorithm for multivariable-system closed-loop performance assessment using step data

Among approximate-model techniques, assessment of the closed-loopperformance deterioration arising from the approximate modelplays an important role in control-system design. The earlywork of Owens & Chotai (1983) proposed a method to boundthe closed-loop output transient performance deterioration.But in practice it has been found that the assessment for multivariable(MIMO) systems is not good as the one for single-input single-output(SISO) systems. The obstacle comes from the non-commutationof multivariable convolution operators (Owens & Chotai 1983).This paper proposes a one-step method to assess the closed-loopresponse of a MIMO system. The algorithm to implement the assessmentis discussed. Because the new algorithm assesses the outputtransient performance without the need to assess input performance,the uncertainty in closed-loop output predictions has been reducedgreatly. On leave from Department of Electrical Engineering, ZhejiangUniversity Hangzhou, China.     

System identification and control using adaptive particle swarm optimization

This paper presents a methodology for finding optimal system parameters and optimal control parameters using a novel adaptive particle swarm optimization (APSO) algorithm. In the proposed APSO, every particle dynamically adjusts inertia weight according to feedback taken from particles’ best memories. The main advantages of the proposed APSO are to achieve faster convergence speed and better solution accuracy with minimum incremental computational burden. In the beginning we attempt to utilize the proposed algorithm to identify the unknown system parameters the structure of which is assumed to be known previously. Next, according to the identified system, PID gains are optimally found by also using the proposed algorithm. Two simulated examples are finally given to demonstrate the effectiveness of the proposed algorithm. The comparison to PSO with linearly decreasing inertia weight (LDW-PSO) and genetic algorithm (GA) exhibits the APSO-based system’s superiority.     

H2 optimal model order reduction on the Stiefel manifold for the MIMO discrete system by the cross Gramian

ABSTRACT

In this paper, the H₂ optimal model order reduction method for the large-scale multiple-input multiple-output (MIMO) discrete system is investigated. First, the MIMO discrete system is resolved into a number of single-input single-output (SISO) subsystems, and the H₂ norm of the original MIMO discrete system is expressed by the cross Gramian of each subsystem. Then, the retraction and the vector transport on the Stiefel manifold are introduced, and the geometric conjugate gradient model order reduction method is proposed. The reduced system of the original MIMO discrete system is generated by using the proposed method. Finally, two numerical examples show the efficiency of the proposed method.     

用奇异值分解求解的PI型有约束广义预测控制算法

本文推得了一种比例积分型广义预测控制算法，在算法中加入了对系统的输入和输出信号的约束以加强算法应用能力，在控制值的优化示解中使用了矩阵奇异值分解以增加算法的精度和数值稳定性。     

Variable structure control systems: synthesis of scalar and vector systems by state and output feedback

Modern views are applied to examine synthesis of variable structure systems (VSS) for SISO and MIMO systems of general position in the presence of information on the full phase vector or only on the output vector. In the latter case we consider separately the cases of organizing a sliding mode in plant output coordinates and in arbitrary coordinates. The latter case requires the construction of asymptotic observers for linear systems with uncertainty in the parameters or in inputs, and the corresponding observation theory is sketched. Special attention is given to the case of so-called hyperoutput systems, i.e., multiply connected systems in which the number of outputs exceeds the number of inputs. For hyperoutput systems under fairly general conditions we can arbitrarily choose the observer dynamics, which is important for improving the performance of the control system as a whole. We show that the observer dynamics does not change the VSS stability.     

基于LS-SVM的管道腐蚀速率灰色组合预测模型

为提高管道腐蚀速率预测精度,建立了一种基于最小二乘支持向量机的灰色组合预测模型.以各种灰色模型对管道腐蚀速率的预测结果作为支持向量机的输入,以管道腐蚀速率的实测值作为支持向量机的输出,采用最小二乘支持向量机回归算法和高斯核函数对支持向量机进行训练,利用训练好的支持向量机进行组合预测.预测模型兼具灰色模型所需原始数据少、建模简单、运算方便的优势和最小二乘支持向量机具有泛化能力强、非线性拟合性好、小样本等特性,弥补了单一预测模型的不足,避免了神经网络组合预测易于陷入局部最优的弱点.模型结构简单、实用,仿真结果验证了其有效性.     

A least squares identification algorithm for a state space model with multi-state delays

A parameter estimator is presented for a state space model with time delay based on the given input–output data. The basic idea is to expand the state equations and to eliminate some state variables, and to substitute the state equation into the output equation to obtain the identification model which contains the information vector and parameter vector. A least squares algorithm is developed to estimate the system parameter vectors. Finally, an illustrative example is provided to verify the effectiveness of the proposed algorithm.     

Terminal constrained robust hybrid iterative learning model predictive control for complex time-delayed batch processes

This work mainly addresses terminal constrained robust hybrid iterative learning model predictive control against time delay and uncertainties in a class of complex batch processes with input and output constraints. In this work, an equivalently novel extended two-dimensional switched system is first constructed to represent the process model by introducing state difference, output error and new relaxation variable information. Then, a hybrid predictive updating controller is proposed and an optimal performance index function including terminal constraints is designed. Under the condition that the switching signal meets certain conditions, the solvable problem of model predictive control is realized by Lyapunov stability theory. Meanwhile, the design scheme of controller parameters is also given. In addition, the robust constraint set is adopted to overcome the disadvantage that the traditional asymptotic stability cannot converge to the origin when it involves disturbances, such that the system state converges to the constraint set and meets its expected value. Finally, the effectiveness of the proposed algorithm is verified by controlling the speed and pressure parameters of the injection molding process.     

Robustness analysis and tuning of generalized predictive control using frequency domain approaches

The paper presents a new frequency-domain methodology to explicitly address the robustness margins for analysis and tuning of generalized predictive control (GPC). The GPC is formulated in two-degree-of-freedom configuration to allow for simultaneous execution of robustness analysis and frequency characteristic shaping. The underlying idea is to present a robust tuning scheme for GPC scheme by synthesizing some sensitivity functions in discrete-time domain, quantifying the relevant cause-and-effect perturbations, in order to shape them so that the effects of influences can be reduced in a specific frequency range. Several frequency-domain templates have been introduced to practically demonstrate usefulness of output, noise, and input sensitivity functions as complementing analysis tools for robust tuning of GPC. The proposed method ensures robust adjustments of the non-trivial tuning of GPC free parameter knobs through simultaneous realization of robustness analysis and frequency characteristic shaping. The method can hence be utilized as a powerful method for tuning of GPC for a wide range of single-input single-output (SISO) linear systems. Illustrative simulation examples have been conducted to explore the effectiveness of the proposed method.     

线性定常系统特征模型的特征参量辨识

说明线性定常系统特征模型的特征参量是一组由高阶线性定常系统的相关信息压缩而成,于是不能简单的作为与状态无关的慢时变参数来处理. 基于特征建模思想,建立了线性定常系统特征模型的特征参量与子空间方法之间的联系,给出了一种该特征模型的特征参量 的合成辨识算法.同时证明了在用于子空间辨识的样本量充分大和用于状态估计的时间充分长的情况下, 特征参量的估计值与真值之间的误差达到充分小. 最后,对于一个六阶的单输入单输出线性定常系统的仿真例子,对投影的带遗忘因子最小二乘算法和合成辨识算法进行了比较,验证了合成辨识算法的有效性.     

Minimal stabilization of vector (MISO and SIMO) systems

We consider the problem of constructing a stabilizer described by a system of linear differential equations and such that a given dynamical system becomes stable after being closed by the feedback produced by the stabilizer. Moreover, we require that the dimension of the stabilizer, that is, the dimension of its state vector, be minimal. We assume that the given system has either a single input and multiple outputs (a SIMO system) or, on the opposite, multiple inputs and a single output (a MISO system).