基于神经网络的一类非线性系统的稳定自适应控制器设计方法*

针对一类非线性连续时间系统,其中非线性函数未知,提出了一种基于神经网络的稳定自适应控制方案,由于控制律的选择基于Ｌｙａｐｕｎｏｖ稳定性理论,因此,该控制方案不仅能够解决这类非线性系统的跟踪问题。     

多变量非方系统多环PI控制器设计

基于等价传递函数（ETF）理论,提出含有多时滞的高维多变量非方系统多环PI（preportional-integral）控制器设计方法．首先,利用等价传递函数与被控过程传递函数的广义逆之间关系推导出ETF的求解通式．接着,基于已获得的ETF,利用IMC-PID（internal model control-proportional integral derivation）原理设计控制器,再利用Maclaurin级数展开获得多环PI控制器参数．所提ETF算法不仅具有更高的精度且适应于高维非方系统．最后通过仿真实例验证了所提算法的简单性和有效性．     

Observer-based adaptive control for uncertain time-delay systems

In this paper, we will focus on investigating the observer-based controlling problem of time-delay systems. First, we investigate a class of simple time-delay systems. The corresponding adaptive observer and controller are designed, which are both independent of the time-delays. Based on Lyapunov stability theory, we prove that the closed-loop system is asymptotically stable. Next we further consider the interconnected time-delay system case. The corresponding adaptive observer and controller are designed, we prove that the resulting closed-loop system is also asymptotically stable. Simulations on controlling time-delay systems and interconnected systems are investigated, and the results show that the designed controllers are feasible and efficient.     

Structure and stability analysis of a Takagi–Sugeno fuzzy PI controller with application to tissue hyperthermia therapy

 In this paper, we first reveal the analytical structure of a simple Takagi–Sugeno (TS) fuzzy PI controller relative to the linear PI controller. The fuzzy controller consists of two linear input fuzzy sets, four TS fuzzy rules with linear consequent, Zadeh fuzzy logic AND and the centroid defuzzifier. We prove that the fuzzy controller is actually a nonlinear PI controller with the gains changing with process output. Utilizing the well-known small Gain Theorem in control theory, we then derive sufficient conditions for global stability of the fuzzy control systems involving the TS fuzzy PI controller. Finally, as an application demonstration, we apply the fuzzy PI controller to control issue temperature, in computer simulation, during hyperthermia therapy. The relationship between heat energy and tissue temperature is represented by a linear time-varying model with a time delay. The sufficient conditions for global stability are used to design a stable fuzzy control system. Our simulation results show that the fuzzy PI control system achieves satisfactory temperature control performance. The control system is robust and stable even when the model parameters are changed suddenly and significantly.     

一类非线性系统的自适应预测函数控制

针对一类具有输出反馈耦合的离散非线性系统,将过程的非线性状态空间模型等效为线性时变状态空间模型;然后利用最小二乘法辨识系统参数,并通过在目标函数中引入系统状态的变化给出一种具有类似离散PI最优调节器结构的新型自适应预测函数控制器．由于引入了新的优化目标函数,该控制器控制效果与鲁棒性要优于仅考虑预测输出误差的传统预测函数控制器．仿真结果表明,该控制器优于经典离散PI最优调节器．     

Tracking and disturbance rejection of MIMO nonlinear systems with PI controller

We study tracking and disturbance rejection of a class of MIMO nonlinear systems with linear proportional plus integral (PI) compensator. Roughly speaking, we show that if the given nonlinear plant is exponentially stable and has a strictly increasing dc steady-state I/O map, then a simple PI compensator can be used to yield a stable unity-feedback closed-loop system which asymptotically tracks reference inputs that tend to constant vectors and asymptotically rejects disturbances that tend to constant vectors.     

Parameter estimation and compensation in systems with nonlinearly parameterized perturbations

We consider a class of systems influenced by perturbations that are nonlinearly parameterized by unknown constant parameters, and develop a method for estimating the unknown parameters. The method applies to systems where the states are available for measurement, and perturbations with the property that an exponentially stable estimate of the unknown parameters can be obtained if the whole perturbation is known. The main contribution is to introduce a conceptually simple, modular design that gives freedom to the designer in accomplishing the main task, which is to construct an update law to asymptotically invert a nonlinear equation. Compensation for the perturbations in the system equations is considered for a class of systems with uniformly globally bounded solutions, for which the origin is uniformly globally asymptotically stable when no perturbations are present. We also consider the case when the parameters can only be estimated when the controlled state is bounded away from the origin, and show that we may still be able to achieve convergence of the controlled state. We illustrate the method through examples, and apply it to the problem of downhole pressure estimation during oil well drilling.     

一类多变量非线性动态系统的模糊自适应控制

对一类非线性多变量未知动态系统，提出了一种模糊处在适应控制策略。证明了该控制算法能保证闭环系统稳定，跟踪误差收敛。     

一类非线性系统的自适应模糊滑模控制

对一类具有不确定性的非线性系统,根据滑模控制原理并利用模糊系统的逼近能 力,提出了一种自适应模糊滑模控制系统的设计方法.控制结构中采用模糊系统自适应朴偿 过程的不确定性.利用李雅普诺夫理论,证明了控制算法是全局稳定的,跟踪误差可收敛到 零的一个邻域内.     

H∞ control for a class of cascade switched nonlinear systems

In this paper, we investigate the H_∞ control problem for a class of cascade switched nonlinear systems consisting of two nonlinear parts which are also switched systems using the multiple Lyapunov function method. Firstly, we design the state feedback controller and the switching law, which guarantees that the corresponding closed‐loop system is globally asymptotically stable and has a prescribed H_∞ performance level. This method is suitable for a case where none of the switched subsystems is asymptotically stable. Then, as an application, we study the hybrid H_∞ control problem for a class of nonlinear cascade systems. Finally, an example is given to illustrate the feasibility of our results. Copyright © 2008 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Global asymptotic stabilisation in probability of nonlinear stochastic systems via passivity

The purpose of this paper is to develop a systematic method for global asymptotic stabilisation in probability of nonlinear control stochastic systems with stable in probability unforced dynamics. The method is based on the theory of passivity for nonaffine stochastic differential systems combined with the technique of Lyapunov asymptotic stability in probability for stochastic differential equations. In particular, we prove that a nonlinear stochastic differential system whose unforced dynamics are Lyapunov stable in probability is globally asymptotically stabilisable in probability provided some rank conditions involving the affine part of the system coefficients are satisfied. In this framework, we show that a stabilising smooth state feedback law can be designed explicitly. A dynamic output feedback compensator for a class of nonaffine stochastic systems is constructed as an application of our analysis.     

PI tracking control for nonlinear time-varying delay Markov jump systems

This paper considers robust stochastic stability and PI tracking control problem for Markov jump systems with both input delay and an unknown nonlinear function. Based on the traditional PI control strategy, a new controller design scheme is proposed for nonlinear time-delay Markov jump systems which can realize multiple control objectives including robust stochastic stability and tracking performance. By using the Lyapunov stability theory and LMI algorithms, a sufficient condition for the solution to robust stochastic stability and tracking control problem is obtained. Then, the desired controller with PI structure is designed, which ensures the resulting closed-loop system is robust stochastically stable and the system state has favorable tracking performance. Finally, a numerical example is provided to illustrate the effectiveness of the proposed results.     

Energy methods for stability of bilinear systems with oscillatory inputs

A large body of recent literature has been devoted to the topic of motions of mechanical systems forced by oscillatory inputs (see, for example, References 7, 12, 15, 17 and 29). A common feature in most of this work (with Reference 7 being the exception) is that the results apply principally to kinematic problems, and the equations of motion do not involve drift terms. The main object of study in this paper is the class of bilinear control systems with oscillatory (periodic) inputs. We shall show that included in this class are models of mechanical system dynamics which are obtained through a process of reduction and linearization about operating points. In particular, we study the stability of such systems under high-frequency, periodic forcing. The averaged potential is defined for linearizations of the systems on the (reduced) configuration space, and it is shown that stable motions of the forced system are associated with minimum values of this quantity. We use both classical averaging theory as well as a novel geometric argument to provide parallel but independent assessments of the use of the averaged potential in carrying out a stability analysis. A salient feature of the geometric approach is that we are able to justify the use of an energy-like quantity to determine Lyapunov stability in conservative mechanical systems. This makes contact with a growing body of literature on the use of energy methods for stability and control design (e.g. References 7, 8, 18, 24, 26 and 27). We briefly describe the connection with previous work on the averaged potential.     

r阶鲁棒稳定性与零动态非渐稳单人单出系统的静态分叉控制镇定

研究零动态非渐稳的单输入单输出控制系统的局部近镇定问题,讨论了对这种系统镇定的设计方法,并对一类满足条件（Ｓ）的系统,利用静态分叉控制结果,提供了构造反馈控制函数使上述系统局部渐近镇定的方法。该方法也可看作是静态分叉控制在某些情况下的一种简化。     

Event-triggered synchronization control for complex networks with uncertain inner coupling

This paper is concerned with the event-triggered synchronization control problem for a class of complex networks with uncertain inner couplings. The uncertain inner coupling under consideration is characterized in terms of the interval matrix. In order to save the communication and computation resources, the event-based mechanism is adopted and the event-triggered synchronization control scheme is proposed for the complex networks. First, we transform the event-triggered synchronization control problem into the exponential stabilization problem for a new class of dynamical systems with multiple delays. Then, by employing the Lyapunov stability theory, we derive a sufficient condition under which the multi-delayed system is exponentially stable. Subsequently, a set of event-triggered synchronization controllers is designed in terms of the solution to a linear matrix inequality that can be solved effectively by using available software. Finally, a numerical simulation example is presented to show the effectiveness of the proposed event-triggered control scheme.     

不确定组合大系统的自适应分散镇定控制

考虑具有非线性关联作用的不确定时变线性组合大系统的自适应分散镇定问题.针对 系统不确定界完全未知的情形,首先从理论上证明了可设计自适应鲁棒分散控制器确保受控系 统渐近稳定;进而从工程实际应用的角度,给出了确保受控系统实用稳定的自适应鲁棒分散控 制器的设计方案.仿真说明该设计方案是有效的.     

城市交通网络正系统模型与稳态信号控制

城市路网内车流分布不均衡为交通拥堵原因之一,且交通控制系统为典型正系统．为此,本文采用Compartment正系统对网络交通流演化建模,以网络均衡为控制目标,提出稳态信号控制方法．首先,建立网络交通流Compartment正系统模型,可描述具有任意控制结构网络的过饱和特征;进一步,给定网络车流输入,由非负矩阵理论可得网络存在唯一稳定平衡点,给出平衡点解析计算公式．由此,提出网络稳态信号控制律,为路段状态反馈控制律．最后,以北京市奥林匹克公园区域拓扑路网为例,在VISSIM软件中建立仿真环境,比较稳态信号控制方法与定时控制方法,仿真结果表明在高需求网络条件下,稳态信号控制方法可改善网络整体性能和缓解局部拥堵．     

Nonlinear PI control of uncertain systems: an alternative to parameter adaptation

A novel approach to stabilization and trajectory tracking for nonlinear systems with unknown parameters and uncertain disturbances is developed. We take a drastic departure from the classical adaptive control approach consisting of a parameterized feedback law and an identifier, which tries to minimize a tracking (or prediction) error. Instead, we propose a simple nonlinear PI structure that generates a stable error equation with a perturbation function that exhibits at least one root. Trajectories are forced to converge to this root by suitably adjusting the nonlinear PI gains. We consider the two basic problems of: (i) matched uncertainties, when the uncertain terms are in the image of the input matrix, and (ii) unknown control directions, when the control signal is multiplied by a gain of unknown sign. We show that, without knowing the system parameters, and with only basic information on the uncertainties we can achieve global asymptotic stability and global tracking, without injecting high gains into the loop. Interestingly, we prove that we can take as our nonlinear PI structure an activation function reminiscent of that used in neural networks. Although most of the results are derived assuming full state measurement, we also present an observer-based solution for a chain of integrators with unknown control direction. The procedure is shown to provide simple solutions to the classical problems of neural network function approximation, as well as eccentricity control and friction compensation of mechanical systems.     

随机时滞马尔可夫跳跃系统的比例-积分跟踪控制

针对具有时变时滞和未知非线性的随机马尔可夫跳变系统,基于传统的PI控制策略和线性矩阵不等式算法,提出一种具有随机稳定性能、跟踪性能和鲁棒性能的多目标控制器设计方案.运用Lyapunov稳定性理论并引入L<,1>性能指标,构造出具有PI结构的跟踪控制器,保证了随机马尔可大跳跃系统的稳定性和跟踪性能,实现了系统跟踪性能的优...