分布参数过程的特征线变换仿真

利用特征线集总化将双曲型偏微分方程组变换为在一定方向上的常微分方程组。基于较简单的数值算法,如预报——校正数值积分算法,所设计的软件就能有效地解决类似回旋窑具有两端突变分裂边值的复杂分布参数工业系统动态仿真中遇到的问题,结果稳定、精确。     

基于小波变换的二阶线性分布参数系统预测控制

分布参数系统由于其复杂性,控制系统设计一直是控制理论的难点.寻求解决分布参数系统控制的新思路,本文提出了基于正交小波变换的线性离散时间分布参数系统预测控制概念,应用正交小波变换将二阶线性分布参数系统预测控制命题变换为集总参数系统预测控制问题,并设计预测控制器,将控制律进行反演获得原系统的具有分布特性的控制律.仿真研究表明,本文提出的分布参数系统预测控制算法取得了理想的控制效果,对系统模型失配和扰动具有较好的鲁棒性,验证了算法的有效性.     

一阶强双曲分布参数系统的迭代学习控制

研究了一阶强双曲分布参数系统的迭代学习控制问题.首先利用Fourier变换和半群方法导出了系统状态的适应解.进而基于强双曲条件和Plancheral定理,在允许迭代过程中初值存在一定偏差条件下,给出并证明了系统在P型迭代学习控制算法下的收敛条件.最后应用实例说明了所提方法的有效性.     

分布参数系统的时空ARX建模及预测控制

本文针对一类可由抛物型偏微分方程描述的分布参数系统,研究了一种基于输入输出数据的建模与控制方法.首先利用Karhunen-Loève（K-L）分解提取系统的一组主导空间基函数,并以此对系统输出进行时空分解,随后由时空分解得到的时间系数部分以及系统激励构成输入输出信息,利用最小二乘法辨识出时域ARX模型,最后针对该模型设计了广义预测控制器.仿真结果表明,上述控制方法能够对分布参数系统取得良好的控制效果.     

全方位机器人的重心位置预测与轨迹跟踪控制

针对全方向移动机器人存在非线性动态强耦合、实时重心偏移及难以实现高精度跟踪控制的问题, 本文提 出一种基于长短期记忆(LSTM)神经网络的重心位置在线预测的轨迹跟踪控制法. 首先, 建立考虑重心偏移的动力 学模型并基于LSTM神经网络训练构建其对比模型; 其次, 基于模型对比法实时估计重心偏移参数, 再基于张神经 网络(ZNN)对估计的重心偏移参数进行预测以减小估计过程引起的滞后; 最后, 基于非线性动态反馈解耦法设计数 值加速度控制算法, 且基于离散系统极点配置法分析了系统的稳定性. 仿真结果验证了所提方法相对于数值加速 度控制器与自适应控制器因能在线预测重心偏移参数完成高精度动态解耦实现控制精度的提高. 实际实验中, 所 提控制算法相比数值加速度控制及模型预测控制, 其跟踪精度明显提高, 这表明所提控制算法可显著减小重心偏移 对跟踪控制精度的影响.     

广义预测自适应控制的双重控制算法

提出了一种基于双重控制思想的广义预测自适应控制算法,该算法在模型辨识和控制的过程中,采用谨慎控制和探测控制相结合的双重控制,充分考虑估计参数的误差,在使系统状态最优地沿预定轨线运动的同时最大限度的积累被估计参数的信息,以便最快地降低系统的不确定性。仿真结果表明,该控制算法比普通的广义预测自适应控制具有更好的控制品质。     

分布参数系统边界控制的Haar小波算法

由于分布参数系统通常由偏微分方程描述,采用解析法求解分布参数系统最优边界控制问题,是非常难以解决的.正交函数逼近的方法在分布参数系统控制方面,已经取得了较好的效果.Haar小波作为正交基函数,利用小波的一些运算及变换矩阵,将分布参数系统转化为集总参数系统,再求其逼近解.仿真示例验证了所提出的算法是非常有效的.该方法为分布参数系统的控制算法提出了一条新的解决方案.     

一种基于未知模型的广义预测控制算法

研究未知被控对象具有动态调整、参数时变以及受到外界干扰时,采用广义自适应预测控制算法(GPC)对系统进行控制。运用基于CARMA模型的参数在线动态辨识,在线时实算出未知对象的参数模型,再运用预测控制算法,计算出当前的控制量;再滚动优化,使未知系统具有良好的控制性能。并且通过Matlab分析仿真证明了广义预测控制的全局稳定性、收敛性和鲁棒性。     

1987年中国自动化学会控制理论及其应用年会论文集中部分国家和科学院自然科学基金资助项目论文题录

作者工作单位特征结构配皿能力的一致性参数有容差的鲁棒性补德器的设计交换环上线性系统及应用粗壮特征结构最优调节器设计分散信息结构分析与优化大系统的分散预测控制一类非线性离散系统的分析算法与稳定判据双曲型点控制系统的逼近分布参数脉冲调宽采样控制系统线性奇异系统的最优滤波..线性二次型调节问题的一种实用综合方法自适应DaUin数字控制器递推综合广义预测自校正控制器阶次未知:系统的递推算法和自校正控制一‘_具有降价模型的MRAC系统的餐棒控制器设计‘下实用的自’校正器仿真与实时{控制软件‘包”机器人动态模型参数估…     

基于输入约束一致性算法的多无人机编队控制

针对多无人机系统的编队控制问题,提出了一种基于级联系统理论及输入约束一致性算法的控制方法。首先,给出了垂直起降无人机系统的一般性模型。然后,基于级联系统理论将复杂的一般性模型化简成级联形式,针对级联形式模型,利用双曲正切函数的有界性质,在控制器设计时引入双曲正切函数设计了一致性控制算法。最后基于所设计的输入约束一致性控制算法,设计编队控制算法研究了多无人机编队控制问题。基于Matlab仿真平台对所提控制方法进行验证,仿真结果表明在所设计的一致性控制算法作用下,系统中所有的状态都能够趋于一致。基于所设计的输入约束一致性算法,所提编队控制算法可以实现空间中的无人机保持指定的编队队形飞行。     

Non-fragile guaranteed cost fuzzy control for nonlinear first-order hyperbolic partial differential equation systems

This paper concerns the non-fragile guaranteed cost control for nonlinear first-order hyperbolic partial differential equations (PDEs), and the case of hyperbolic PDE systems with parameter uncertainties is also addressed. A Takagi–Sugeno (T–S) fuzzy hyperbolic PDE model is presented to exactly represent the nonlinear hyperbolic PDE system. Then, the state-feedback non-fragile controller distributed in space is designed by the parallel distributed compensation (PDC) method, and some sufficient conditions are derived in terms of spatial differential linear matrix inequalities (SDLMIs) such that the T–S fuzzy hyperbolic PDE system is asymptotically stable and the cost function keeps an upper bound. Moreover, for the nonlinear hyperbolic PDE system with parameter uncertainties, using the above-design approach, the robust non-fragile guaranteed cost control scheme is obtained. Furthermore, the finite-difference method is employed to solve the SDLMIs. Finally, a nonlinear hyperbolic PDE system is presented to illustrate the effectiveness and advantage of the developed design methodology.     

A galerkin/neural-network-based design of guaranteed cost control for nonlinear distributed parameter systems.

This paper presents a Galerkin/neural-network- based guaranteed cost control (GCC) design for a class of parabolic partial differential equation (PDE) systems with unknown nonlinearities. A parabolic PDE system typically involves a spatial differential operator with eigenspectrum that can be partitioned into a finite-dimensional slow one and an infinite-dimensional stable fast complement. Motivated by this, in the proposed control scheme, Galerkin method is initially applied to the PDE system to derive an ordinary differential equation (ODE) system with unknown nonlinearities, which accurately describes the dynamics of the dominant (slow) modes of the PDE system. The resulting nonlinear ODE system is subsequently parameterized by a multilayer neural network (MNN) with one-hidden layer and zero bias terms. Then, based on the neural model and a Lure-type Lyapunov function, a linear modal feedback controller is developed to stabilize the closed-loop PDE system and provide an upper bound for the quadratic cost function associated with the finite-dimensional slow system for all admissible approximation errors of the network. The outcome of the GCC problem is formulated as a linear matrix inequality (LMI) problem. Moreover, by using the existing LMI optimization technique, a suboptimal guaranteed cost controller in the sense of minimizing the cost bound is obtained. Finally, the proposed design method is applied to the control of the temperature profile of a catalytic rod.     

Analysis and control of parabolic PDE systems with input constraints

This paper develops a general framework for the analysis and control of parabolic partial differential equations (PDE) systems with input constraints. Initially, Galerkin's method is used for the derivation of ordinary differential equation (ODE) system that capture the dominant dynamics of the PDE system. This ODE systems are then used as the basis for the synthesis, via Lyapunov techniques, of stabilizing bounded nonlinear state and output feedback control laws that provide an explicit characterization of the sets of admissible initial conditions and admissible control actuator locations that can be used to guarantee closed-loop stability in the presence of constraints. Precise conditions that guarantee stability of the constrained closed-loop parabolic PDE system are provided in terms of the separation between the fast and slow eigenmodes of the spatial differential operator. The theoretical results are used to stabilize an unstable steady-state of a diffusion-reaction process using constrained control action.     

Predictive control for a class of distributed delay systems using Chebyshev polynomials

In this paper, the model predictive control (MPC) is developed for linear time-varying systems with distributed time delay in state. The Chebyshev operational matrices of product, integration and delay are utilized to transform the solution of distributed delay differential equation to the solution of algebraic equations. The Chebyshev functions are also applied to derive approximate solution of finite horizon optimal control problem involved in MPC. The proposed method is simple and computationally advantageous. Illustrative example demonstrates the validity and applicability of the technique.     

Modeling and vibration control for a flexible pendulum inverted system based on a PDE observer

This study addresses the problem of trajectory control of a flexible pendulum inverted system on the basis of the partial differential equation (PDE) and ordinary differential equation (ODE) dynamic model. One of the key contributions of this study is that a new model is proposed to simplify the complex system. In addition, this study proposed a nonlinear PDE observer to estimate distributed positions and velocities along flexible pendulum. Singular perturbation method is proposed to solve the coupling system of nonlinear PDE observer. The nonlinear PDE observer is divided into a fast subsystem and a slow subsystem by the use of the singular perturbation method. To stabilise this fast subsystem, a boundary controller is proposed at the free end of the beam. The sliding-mode control method is proposed to design controller for slow subsystems. The asymptotic stability of both the proposed nonlinear PDE observer and controller is validated by theoretical analysis. The results are illustrated by simulation.     

Online policy iteration algorithm for optimal control of linear hyperbolic PDE systems

In this paper, the linear quadratic (LQ) optimal control problem is considered for a class of linear distributed parameter systems described by first-order hyperbolic partial differential equations (PDEs). Reinforcement learning (RL) technique is introduced for adaptive optimal control design from the design-then-reduce (DTR) framework. Initially, a policy iteration (PI) algorithm is proposed, which learns the solution of the space-dependent Riccati differential equation (SDRDE) online without requiring the internal system dynamics of the PDE system. To prove its convergence, the PI algorithm is shown to be equivalent to an iterative procedure of a sequence of space-dependent Lyapunov differential equations (SDLDEs). Then, the convergence is established by showing that the solutions of SDLDEs are a monotone non-increasing sequence that converges to the solution of the SDRDE. For implementation purpose, an online least-square method is developed for the approximation of the solutions of the SDLDEs. Finally, the proposed design method is applied to the distributed control of a steam-jacketed tubular heat exchanger to illustrate its effectiveness.     

Finite-dimensional constrained fuzzy control for a class of nonlinear distributed process systems.

This correspondence studies the problem of finite-dimensional constrained fuzzy control for a class of systems described by nonlinear parabolic partial differential equations (PDEs). Initially, Galerkin's method is applied to the PDE system to derive a nonlinear ordinary differential equation (ODE) system that accurately describes the dynamics of the dominant (slow) modes of the PDE system. Subsequently, a systematic modeling procedure is given to construct exactly a Takagi-Sugeno (T-S) fuzzy model for the finite-dimensional ODE system under state constraints. Then, based on the T-S fuzzy model, a sufficient condition for the existence of a stabilizing fuzzy controller is derived, which guarantees that the state constraints are satisfied and provides an upper bound on the quadratic performance function for the finite-dimensional slow system. The resulting fuzzy controllers can also guarantee the exponential stability of the closed-loop PDE system. Moreover, a local optimization algorithm based on the linear matrix inequalities is proposed to compute the feedback gain matrices of a suboptimal fuzzy controller in the sense of minimizing the quadratic performance bound. Finally, the proposed design method is applied to the control of the temperature profile of a catalytic rod.     

Parameter identification of aggregated thermostatically controlled loads for smart grids using PDE techniques

This paper develops methods for model identification of aggregated thermostatically controlled loads (TCLs) in smart grids, via partial differential equation (PDE) techniques. Control of aggregated TCLs provides a promising opportunity to mitigate the mismatch between power generation and demand, thus enhancing grid reliability and enabling renewable energy penetration. To this end, this paper focuses on developing parameter identification algorithms for a PDE-based model of aggregated TCLs. First, a two-state boundary-coupled hyperbolic PDE model for homogenous TCL populations is derived. This model is extended to heterogeneous populations by including a diffusive term, which provides an elegant control-oriented model. Next, a passive parameter identification scheme and a swapping-based identification scheme are derived for the PDE model structure. Simulation results demonstrate the efficacy of each method under various autonomous and non-autonomous scenarios. The proposed models can subsequently be employed to provide system critical information for power system monitoring and control.     

一类具有复杂执行器动态的双曲线型偏微分方程输出调节

本文研究了一类具有边界执行器动态特性的双曲线型偏微分方程(Partial differential equation, PDE)系统的输出调节问题. 特别地, 执行器由一组非线性常微分方程(Ordinary differential equation, ODE)描述, 控制输入出现在执行器的一端而非直接作用在PDE系统上, 这使得控制任务变得相当困难. 基于几何设计方法和有限维与无限维反步法, 本文提出了显式表达的输出调节器, 实现了该类系统的扰动补偿及跟踪控制. 并且我们采用Lyapunov稳定性理论严格证明了闭环系统及跟踪误差在范数意义上的指数稳定性. 仿真实例对比验证了所提出控制方法的有效性.     

Boundary control for a constrained two-link rigid–flexible manipulator with prescribed performance

In this paper, we consider a boundary control problem for a constrained two-link rigid–flexible manipulator. The nonlinear system is described by hybrid ordinary differential equation–partial differential equation (ODE–PDE) dynamic model. Based on the coupled ODE–PDE model, boundary control is proposed to regulate the joint positions and eliminate the elastic vibration simultaneously. With the help of prescribed performance functions, the tracking error can converge to an arbitrarily small residual set and the convergence rate is no less than a certain pre-specified value. Asymptotic stability of the closed-loop system is rigorously proved by the LaSalle's Invariance Principle extended to infinite-dimensional system. Numerical simulations are provided to demonstrate the effectiveness of the proposed controller.