不确定线性时滞系统的一种混杂状态反馈保成本控制及优化设计方法

本文研究一类不确定线性时滞系统的混杂状态反馈保成本控制及优化设计问题.假设存在有限个备选的控制增益已知的控制器,并且其中任何单一的状态反馈控制器都不能镇定系统,基于单Lyapunov函数的方法,给出了混杂状态反馈保成本控制的充分条件及优化设计方案.当备选的控制增益未知时,利用多Lyapunov函数法,同样给出混杂状态反馈保成本控制的充分条件及相应的优化设计方法.最后用仿真验证了文中方法的有效性.     

一类不确定线性系统的混杂状态反馈保成本控制

研究一类不确定线性系统的混杂状态反馈保成本控制问题．系统矩阵和输入矩阵中含有时变不确定性，假设存在有限个备选的控制增益已知的控制器，并且任何单一的状态反馈控制器都不能镇定系统，基于单Lyapunov函数的方法，给出了混杂状态反馈保成本控制的充分条件及切换律的设计方案．当切换系统的控制增益未知时，利用多Lyapunov函数法，给出混杂状态反馈保成本控制的充分条件，并通过仿真验证了该方法的有效性。     

基于全调节RBF神经网络的远程网络控制器设计

针对一类具有参数不确定项的非线性网络控制系统,提出一种基于全调节RBF神经网络的反馈线性化与远程状态反馈控制方法相结合的控制策略.该控制策略首先通过设计全调节RBF神经网络的权值W,中心值φ和影响范围σ的调节律,在线补偿系统的非线性及参数不确定项;然后利用状态反馈控制解决时延条件下的网络控制问题.通过Lyapunov稳定性理论给出了系统的稳定性定理,并通过仿真实验验证了该方法的有效性.     

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．     

线性不确定系统的给定阶最优控制器设计

为避免间接法设计降阶控制器的模型近似引起的性能下降,本文在静态输出反馈控制器设计的基础上,直接设计了线性不确定系统的给定阶混合H2/H∞动态反馈控制器.利用系统内外分解方法,得到了最优降阶状态观测器.通过求解降维状态观测器的静态输出反馈,可得到降阶控制的最优反馈增益阵.给定阶控制器由两个Ric cati方程和一个Lyapunov方程参数化表示.最后,通过一个例子,说明了本文提出的给定阶控制器设计方法.     

Markov跳跃非线性系统逆最优增益设计

证明了一类严格反馈Markov跳跃系统是依概率输入–状态可稳定的.其次,证明了逆最优增益设计问题可解的一个充分条件是存在一组满足小控制量的依概率输入–状态稳定控制李雅普诺夫函数.最后,利用积分反推方法,给出了严格反馈Markov跳跃系统逆最优增益设计问题的一个构造性解.其中,为了克服由于Markov跳跃引起的耦合项所带来的困难,所设计的李雅普诺夫函数以及控制器是与模态无关的.     

参数不确定统一混沌系统鲁棒最优控制

针对含有参数不确定性的统一混沌系统,基于鲁棒最优控制理论,提出了一种简单的线性状态反馈控制策略.该策略给出了系统渐进稳定的充分条件,并可以通过求解线性矩阵不等式(LMI),快速有效地求得系统反馈的控制增益,利用Lyapunov方法证明了闭环系统的稳定性.仿真结果验证了所提出的控制策略的有效性.     

一种非线性观测器和能量结合的反馈控制系统

文中利用高增益观测器和状态反馈控制器设计的分离性原理,提出了一种结合非线性观测器和能量的基于估计状态的反馈控制系统.针对垂直欠驱动具有旋转激励的平移振荡器非线性系统,首先,利用高增益观测器,选取合适的增益,使得观测值迅速收敛到系统的状态,其次,从系统能量的角度出发,选取一个恰当的李雅普诺夫函数,证明了所得到的反馈控制系统的渐进稳定性,系统分析及仿真结果表明该方法在动态性方面优于采用高增益观测器和滑模相结合的控制方法,便于工程实现.     

一类不确定模糊系统的二次稳定性的研究

利用T-S模糊模型对一类非线性连续不确定时滞系统进行建模,通过对时变时滞不确定T-S模糊系统基于状态反馈控制器二次稳定性问题的分析,给出了使系统二次稳定具有增益变化的模糊状态反馈控制器存在的充分条件,该充分条件以线性矩阵不等式的形式给出,因其所有参数都是线性的,所以具有数值易解性.设计实例表明了该设计方法的可行性和有效性.     

基于支持向量机的一类非线性系统预测控制

针对一类具有输出反馈耦合的离散非线性系统,将过程的非线性部分通过支持向量机转化为全局线性状态空间模型,并在目标函数中引入系统状态的变化,给出一种类似于离散PI最优调节器的新型预测控制器.该方法不需要在线辨识系统参数,因为系统的内模已转换成全局离线模型.由于引入了新的优化目标函数,该控制器的控制效果和鲁棒性优于仅考虑预测输出误差的传统预测控制器.仿真结果表明,它也优于经典离散PI最优调节器.     

A deterministic theory of estimation and control

A feedback control system can be structured for linear nonstationary process and measurement systems comprising a deterministic filter whose output is the independent variable of a linear control law. Subject to uniform controllability and observability, the filter and control gains can be specified to provide arbitrary and separable stability properties. If the filter gain is selected to produce a stabilizing effect on the state estimate, and the control gain is selected to produce a stabilizing effect on the process, the filter and control gains are shown to satisfy matrix Riccati differential equations. This suggests the use of stochastic optimal control theory when there is no quantitative measure of optimality, but it is desirable to assure the qualitative property that feedback be stabilizing. A concise derivation of the Kalman-Bucy filter is included in an appendix to illustrate the facility of approaching optimal estimation problems with the methods of stability theory.     

Variable feedback gain control design based on particle swarm optimizer for automatic fighter tracking problems

The main focus of this paper is to develop an optimization method for the automatic fighter tracking (AFT) problem. The AFT problem is similar to a general evader–pursuer maneuvering automation problem between the dynamic systems of two highly interactive objects. This paper proposes a particle swarm optimizer-based variable feedback gain controller (PSO-based VFGC) for dealing with AFT problems. The PSO-based VFGC is designed to obtain the control value of a pursuer through an error-feedback gain controller. Once conditions of system closed-loop stability have been satisfied, the optimal feedback gains can be obtained through PSO, and the actual control values can be derived from the obtained values. Simulation results confirm the capabilities of the proposed method by comparing the results against two other methods in the field: the weight matrix value defined Ricatti equation, and the linear matrix inequality (LMI) based linear quadratic regulator (LQR). The performance of the proposed method is superior to that of its alternatives.     

Computer-aided design of P or PI plus rate feedback compensators for linear systems

A computer-aided solution for the gains of P or PI plus rate feedback compensators based on an exact model-matching criterion is developed. The corresponding Matlab functions are developed, and the software listings are given. Using the developed design tool, control engineers are able to obtain P or PI plus rate feedback gains much more quickly than traditional methods of design. Demonstration example problems for control of linear plants are presented, and results are compared with those obtained by other approaches reported in the open literature.     

On a piecewise-constant feedback control for the linear regulator problem†

The design of a piecewise constant feedback control for the linear regulator problem from the standpoint of fixing the gains a priori and optimizing the system with respect to the location of the discontinuities in control is considered. The gains, available as an extra set of parameters, may be chosen to ‘approximate’ the optimal Riccati gain matrix or by some other criterion. The discontinuities induced by the assumed form of the control are treated using the theory of distributions, and the optimal set of discontinuities is found by a second-variation algorithm. In addition, the Cayley-Hamilton technique is found to be a viable computational alternative for arbitrary time-invariant systems.     

Robust near-optimal output feedback control of non-linear systems

This work proposes a robust near-optimal non-linear output feedback controller design for a broad class of non-linear systems with time-varying bounded uncertain variables. Both vanishing and non-vanishing uncertainties are considered. Under the assumptions of input-to-state stable (ISS) inverse dynamics and vanishing uncertainty, a robust dynamic output feedback controller is constructed through combination of a high-gain observer with a robust optimal state feedback controller synthesized via Lyapunov's direct method and the inverse optimal approach. The controller enforces exponential stability and robust asymptotic output tracking with arbitrary degree of attenuation of the effect of the uncertain variables on the output of the closed-loop system, for initial conditions and uncertainty in arbitrarily large compact sets, provided that the observer gain is sufficiently large. Utilizing the inverse optimal control approach and singular perturbation techniques, the controller is shown to be near-optimal in the sense that its performance can be made arbitrarily close to the optimal performance of the robust optimal state feedback controller on the infinite time-interval by selecting the observer gain to be sufficiently large. For systems with non-vanishing uncertainties, the same controller is shown to ensure boundedness of the states, uncertainty attenuation and near-optimality on a finite time-interval. The developed controller is successfully applied to a chemical reactor example.     

Continuous-discrete gain transformation methods for linear feedback control

The problem of transforming between continuoustime state variable feedback gains and equivalent discrete gains suitable for digital implementation is considered. The concepts of state and control equivalence yield two simple transformation rules, a pseudo-inverse method and an average gain method, respectively. As the sampling interval δ→0, these methods are contrasted with existing Taylor series based approaches. The new transformation rules are also studied numerically using a ship course-keeping example. Transformed optimal continuous gains are compared with optimal discrete gains over a wide range of sampling intervals.     

Structural design of composite nonlinear feedback control for linear systems with actuator constraint

The performance of the composite nonlinear feedback (CNF) control law relies on the selection of the linear feedback gain and the nonlinear function. However, it is a tough task to select an appropriate linear feedback gain and appropriate parameters of the nonlinear function because the general design procedure of CNF control just gives some simple guidelines for the selections. This paper proposes an operational design procedure based on the structural decomposition of the linear systems with input saturation. The linear feedback gain is constructed by two linear gains which are designed independently to stabilize the unstable zero dynamics part and the pure integration part of the system respectively. By investigating the influence of these two linear gains on transient performance, it is flexible and efficient to design a satisfactory linear feedback gain for the CNF control law. Moreover, the parameters of the nonlinear function are tuned automatically by solving a minimization problem. The proposed design procedure is illustrated by applying it to design a tracking control law for the inverted pendulum on a cart system. Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Adaptive output feedback stabilization for a class of nonlinear systems with inherent nonlinearities and uncertainties

This paper investigates the problem of adaptive stabilization by output feedback for a class of uncertain nonlinear systems. The distinguishing feature of such a class of systems is the presence of uncertain control coefficient and unmeasured states dependent growth with growth rate of polynomial‐of‐output multiplying an unknown constant. First, new high‐gain K‐filters with two dynamic gains are introduced, and an appropriate state observer is constructed based on the K‐filters. Then, motivated by the universal control idea, the backstepping scheme is successfully developed for the adaptive output feedback control design. By appropriate choice of the design parameters, the global stability of the closed‐loop system can be guaranteed. Finally, numerical simulations are provided to illustrate the correctness of the theoretical results. Copyright © 2010 John Wiley & Sons, Ltd.     

Finite-time stabilization by state feedback control for a class of time-varying nonlinear systems

In this paper, finite-time stabilization is considered for a class of nonlinear systems dominated by a lower-triangular model with a time-varying gain. Based on the finite-time Lyapunov stability theorem and dynamic gain control design approach, state feedback finite-time stabilization controllers are proposed with gains being tuned online by two dynamic equations. Different from many existing finite-time control designs for lower-triangular nonlinear systems, the celebrated backstepping method is not utilized here. It is observed that our design procedure is much simpler, and the resulting control gains are in general not as high as those provided by the backstepping method. A simulation example is given to demonstrate the effectiveness of the proposed design procedure.     

Hybrid fuzzy control of robotics systems

This paper presents a new approach towards optimal design of a hybrid fuzzy controller for robotics systems. The salient feature of the proposed approach is that it combines the fuzzy gain scheduling method and a fuzzy proportional-integral-derivative (PID) controller to solve the nonlinear control problem. The resultant fuzzy rule base of the proposed controller can be decomposed into two layers. In the upper layer, the gain scheduling method is incorporated with a Takagi-Sugeno (TS) fuzzy logic controller to linearize the robotics system for a given reference trajectory. In the lower layer, a fuzzy PID controller is derived for all the locally linearized systems by replacing the conventional PI controller by a linear fuzzy logic controller, which has different gains for different linearization conditions. Within the guaranteed stability region, the controller gains can be optimally tuned by genetic algorithms. Simulation studies on a pole balancing robot and a multilink robot manipulator demonstrate the effectiveness and robustness of the proposed approach.