基于定性状态模型的定性控制方法研究

针对某些复杂系统难以获得精确数学模型来实现有效控制这一问题,采用定性状态模型来描述含有不确定性的非线性系统,提出了一种定性控制方法。首先通过对系统状态的定性划分,采用基于定性推理的自动机建立被控系统定性状态模型,然后设计基于系统定性状态模型的定性控制器,并给出了控制器设计的一般步骤。最后以液位控制系统为例,建立了液位对象的定性状态模型并设计了定性控制器,仿真结果表明该方法的有效性及其理论价值和应用前景。     

重复购买产品的竞争与市场扩散行为分析

市场竞争的加剧缩短了产品生命周期,并催生了知识化制造.基于对知识化制造环境中产品扩散行为的分析,给出重复购买竞争产品扩散行为的非线性模型.以经常购买产品为例对模型进行研究,给出定性分析结果：重复购买条件下两竞争产品在同一市场内扩散,一产品占领稳定的市场份额,另一产品终遭淘汰.最后通过对模型进行仿真得到了与定性分析一致的结果.     

Adaptive control of Hammerstein–Wiener nonlinear systems

The Hammerstein–Wiener model is a block-oriented model, having a linear dynamic block sandwiched by two static nonlinear blocks. This note develops an adaptive controller for a special form of Hammerstein–Wiener nonlinear systems which are parameterized by the key-term separation principle. The adaptive control law and recursive parameter estimation are updated by the use of internal variable estimations. By modeling the errors due to the estimation of internal variables, we establish convergence and stability properties. Theoretical results show that parameter estimation convergence and closed-loop system stability can be guaranteed under sufficient condition. From a qualitative analysis of the sufficient condition, we introduce an adaptive weighted factor to improve the performance of the adaptive controller. Numerical examples are given to confirm the results in this paper.     

An integrated synthetic value of fuzzy judgments and nonlinear programming methodology for ranking the facility layout patterns

In this paper, the goal is to incorporate qualitative criteria in addition to quantitative criteria to facility layout design (FLD) problem. To this end, we present an integrated methodology based on the synthetic value of fuzzy judgments and nonlinear programming (SVFJ-NLP). The facility layout patterns (FLPs) together with their performance measures of total cost of material handling are generated by a computer-aided layout-design tool, CRAFT. Also, the performance measures of second quantitative criterion (construction cost of width walls) are calculated by appraising these FLPs. The SVFJ is then applied to collect the performance measures related to qualitative criteria and finally, a non-linear programming (NLP) model is proposed to solve the FLD. Results obtained from a real case study validate the effectiveness of the proposed model.     

一种定性和定量信息混合控制法

基于精确数学模型的定量控制,虽精度高,但控制质量受限于对象参数的变化;定性控制具有较强的鲁棒性,但精确性稍差.结合两者优点,本文提出了一种无需对象精确数学模型的定性、定量信息混合控制新算法.该算法首先建立无因果划的键图模型,使用改进的键图理论,分析并给出键图模型中知识的定性表达方程,并对该定性表达方程进行适当的化简导出控制方程.对比PID控制的仿真结果证实:该算法具有较好的鲁棒性和动态性能,尤其在对象参数时变和含有非线性环节时.     

Knowledge-based parameter identification of TSK fuzzy models

Linear/1st order Takagi–Sugeno–Kang (TSK) fuzzy models are widely used to identify static nonlinear systems from a set of input–output pairs. The synergetic integration of TSK fuzzy models with artificial neural networks (ANN) has led to the emergence of hybrid neuro-fuzzy models that can have excellent adaptability and interpretability at the same time. One drawback of these hybrid models is that they tend to have more black-box characteristics of ANN than the transparency of fuzzy systems. If the quality of training data is questionable then it may lead to a fuzzy model with poor interpretability. In an attempt to remediate this problem, we propose a parameter identification technique for TSK models that relies on a-priori available qualitative domain knowledge. The technique is devised for rule-centered TSK models in which the consequent polynomial can be interpreted as the 1st order Taylor series approximation of the underlying nonlinear function that is being modeled. The resulting neuro-fuzzy model is named as a-priori knowledge-based fuzzy model (APKFM). We have shown that besides being reasonably accurate, APKFM has excellent interpretability and extrapolation capability. The effectiveness of APKFM is shown using two examples of static systems. In the first example, a toy nonlinear function is chosen for approximation by an APKFM. In the second example, a real world problem pertaining to the maintenance cost estimation of electricity distribution networks is addressed.     

Responses to transients in living and simulated neurons

This paper is concerned with synaptic coding when inputs to a neuron change over time. Experiments were performed on a living and simulated embodiment of a prototypical inhibitory synapse. These were used to test a simple model composed of a fixed delay preceding a nonlinear encoder. Based on these results, we present a qualitative model for phenomena previously observed in the living preparation, including hysteresis and dependence of discharge regularity on rate of change of presynaptic spike rate. As change is the rule rather than the exception in nature, understanding neurons responses to nonstationarity is essential for understanding their function.     

On the simulation of the energy transmission in the forbidden band-gap of a spatially discrete double sine-Gordon system

In this work, we present a numerical method to consistently approximate solutions of a spatially discrete, double sine-Gordon chain which considers the presence of external damping. In addition to the finite-difference scheme employed to approximate the solution of the difference-differential equations of the model under investigation, our method provides positivity-preserving schemes to approximate the local and the total energy of the system, in such a way that the discrete rate of change of the total energy with respect to time provides a consistent approximation of the corresponding continuous rate of change. Simulations are performed, first of all, to assess the validity of the computational technique against known qualitative solutions of coupled sine-Gordon and coupled double sine-Gordon chains. Secondly, the method is used in the investigation of the phenomenon of nonlinear transmission of energy in double sine-Gordon systems; the qualitative effects of the damping coefficient on the occurrence of the nonlinear process of supratransmission are briefly determined in this work, too.     

A hybrid fuzzy goal programming approach with different goal priorities to aggregate production planning

In this study a hybrid (including qualitative and quantitative objectives) fuzzy multi objective nonlinear programming (H-FMONLP) model with different goal priorities will be developed for aggregate production planning (APP) problem in a fuzzy environment. Using an interactive decision making process the proposed model tries to minimize total production costs, carrying and back ordering costs and costs of changes in workforce level (quantitative objectives) and maximize total customer satisfaction (qualitative objective) with regarding the inventory level, demand, labor level, machines capacity and warehouse space. A real-world industrial case study demonstrates applicability of proposed model to practical APP decision problems. GENOCOP III (Genetic Algorithm for Numerical Optimization of Constrained Problems) has been used to solve final crisp nonlinear programming problem.     

Reconstructing specimens using DIC microscope images

Differential interference contrast (DIC) microscopy is a powerful visualization tool used to study live biological cells. Its use, however, has been limited to qualitative observations. The inherent nonlinear relationship between the object properties and the image intensity makes quantitative analysis difficult. Toward quantitatively measuring optical properties of objects from DIC images, we develop a method to reconstruct the specimen's optical properties over a three-dimensional (3-D) volume. The method is a nonlinear optimization which uses hierarchical representations of the specimen and data. As a necessary tool, we have developed and validated a computational model for the DIC image formation process. We test our algorithm by reconstructing the optical properties of known specimens.     

Learning‐Based Animation of Clothing for Virtual Try‐On

This paper presents a learning‐based clothing animation method for highly efficient virtual try‐on simulation. Given a garment, we preprocess a rich database of physically‐based dressed character simulations, for multiple body shapes and animations. Then, using this database, we train a learning‐based model of cloth drape and wrinkles, as a function of body shape and dynamics. We propose a model that separates global garment fit, due to body shape, from local garment wrinkles, due to both pose dynamics and body shape. We use a recurrent neural network to regress garment wrinkles, and we achieve highly plausible nonlinear effects, in contrast to the blending artifacts suffered by previous methods. At runtime, dynamic virtual try‐on animations are produced in just a few milliseconds for garments with thousands of triangles. We show qualitative and quantitative analysis of results.     

Global solutions for nonlinear systems using qualitative reasoning

This paper explores how qualitative information can be used to improve the performance of global optimization procedures. Specifically, we have constructed a nonlinear parameter estimation reasoner (NPER) for finding parameter values that match an ordinary differential equation (ODE) model to observed data. Qualitative reasoning is used within the NPER, for instance, to intelligently choose starting values for the unknown parameters and to empirically determine when the system appears to be chaotic. This enables odrpack, the nonlinear least-squares solver that lies at the heart of this NPER, to avoid terminating at local extrema in the regression landscape. odrpack is uniquely suited to this task because of its efficiency and stability. The NPER's robustness is demonstrated via a Monte Carlo analysis of simulated examples drawn from across the domain of dynamics, including systems that are nonlinear, chaotic, and noisy. It is shown to locate solutions for noisy, incomplete real-world sensor data from radio-controlled cars used in the University of British Columbia's soccer-playing robot project. The parameter estimation scheme described in this paper is a component of pret, an implemented computer program that uses a variety of artificial intelligence techniques to automate system identification— the process of inferring an internal ODE model from external observations of a system — a routine and difficult problem faced by engineers from various disciplines. This revised version was published online in June 2006 with corrections to the Cover Date.     

Fitting nonlinear low-order models for combustion instability control

Tools for fitting low-complexity nonlinear models based on experimental data are examined through the example problem of finding a reduced-order model suitable for control of a combustion instability operating in a limit cycle. This proceeds in four parts; physical modeling, linear system identification, nonlinear analysis, and validation test design. It is shown how the nonlinear tools of describing functions, bifurcation methods and manifold analysis assist in developing a simple nonlinear model capable of describing the data and consistent with physical understanding. The system being modeled is a lean gas turbine combustor which exhibits a sustained mid-range (100–1000 Hz) limit cycle instability. The closed-loop experimental data does not contain a sufficiently rich spectrum for confident modeling in the first linear system identification phase. Despite the paucity of information quality, a grey-box nonlinear model is created and parametrized which provides an explanation both of the limit-cycle fundamental oscillation and of a high frequency nonharmonic signal also present. The model structure is explored and various operating conditions simulated to understand the model better.

The validation and/or refinement of this model is then considered. The model validation problem is important because of the poor information content of the periodic limit cycle data. The challenge is to provide a practically feasible, small excitation to the loop to improve identifiability and to provide qualitative tests of model performance. We examine this problem by considering the nonlinear dynamics of the model class and feasible excitation mechanisms.     

一类定性控制系统的稳定性分析

对一类非线性对象提出了定性稳定性的定义,并对其闭环自治系统的定性稳定性提出一个充分性判据,然后给出一种用变量梯度法构造李亚普诺夫函 步骤,最后以一个二阶非线性对象为例,给出了一种以全部定性状态分析为反馈的定性控制,讨论了闭环控制系统的定性稳定性。     

Robust model-order reduction of complex biological processes

This paper addresses robust model-order reduction of a high dimensional nonlinear partial differential equation (PDE) model of a complex biological process. Based on a nonlinear, distributed parameter model of the same process which was validated against experimental data of an existing, pilot-scale BNR activated sludge plant, we developed a state-space model with 154 state variables in this work. A general algorithm for robustly reducing the nonlinear PDE model is presented and based on an investigation of five state-of-the-art model-order reduction techniques, we are able to reduce the original model to a model with only 30 states without incurring pronounced modelling errors. The Singular perturbation approximation balanced truncating technique is found to give the lowest modelling errors in low frequency ranges and hence is deemed most suitable for controller design and other real-time applications.     

小型无人直升机控制律设计与仿真

依据摄动线化原理,本文对模型直升机非线性模型在平衡点进行了小摄动线性化处理,得出了线性化动力学模型,并对它进行了PID控制律设计,应用MATLAB/Simulink对控制律作用于线性化模型和非线性模型分别进行了仿真验证,结果表明作用于线性化模型具有良好控制效果的控制律尚不能有效控制非线性模型.使用backstepping方法对非线性模型子系统选择相应的李雅普诺夫候选函数,应用递归方法设计了使型直升机动力学非线性模型镇定的控制律,确保李雅普诺夫候选函数的导数为负定.经仿真验证表明利用该设计方法得到的控制律能对非线性模型进行有效控制.     

A recurrent neural network for nonlinear continuouslydifferentiable optimization over a compact convex subset

We propose a general recurrent neural-network (RNN) model for nonlinear optimization over a nonempty compact convex subset which includes the bound subset and spheroid subset as special cases. It is shown that the compact convex subset is a positive invariant and attractive set of the RNN system and that all the network trajectories starting from the compact convex subset converge to the equilibrium set of the RNN system. The above equilibrium set of the RNN system coincides with the optimum set of the minimization problem over the compact convex subset when the objective function is convex. The analysis of these qualitative properties for the RNN model is conducted by employing the properties of the projection operator of Euclidean space onto the general nonempty closed convex subset. A numerical simulation example is also given to illustrate the qualitative properties of the proposed general RNN model for solving an optimization problem over various compact convex subsets.     

Model Predictive Control of Nonlinear Discrete Time Systems with Guaranteed Stability

This paper presents the design of a new robust model predictive control algorithm for nonlinear systems represented by a linear model with unstructured uncertainty. The linear model is obtained by linearizing the nonlinear system at an operating point and the difference between the nonlinear and linear model is considered as a Lipschitz nonlinear function. The controller is designed for the linear model, which fulfills the stabilization condition for the nonlinear term. Unlike previous studies that have not considered a valid Lipschitz matrix of nonlinear term in the design process, we propose an algorithm in this paper in which it is considered. Therefore, the closed loop stability of the nonlinear system is guaranteed. A novel SOS optimization problem to determine design parameters is introduced, which leads to improved closed‐loop performance in comparison to a trial and error tuning procedure. Furthermore, an algorithm is presented to enlarge the region of attraction for the nonlinear closed‐loop system. Stability is improved by checking some additional conditions if which the system may be unstable if not considered. The validity of the proposed algorithm is confirmed by examples.