非线性时滞系统的周期自适应学习跟踪控制

针对一类参数未知的周期非线性时滞系统的输出跟踪控制问题,设计了一种周期自适应迭代学习跟踪控制算法,该方法利用信号置换的思想重组系统,并在假设未知时变参数和参考输出的周期具有已知最小公倍数的情况下,将时滞以及其他不确定的时变项合并为一个周期性的辅助时变参数新变量,进而用周期自适应算法来估计该辅助量.通过构造一个Lyapunov-Krasovskii型复合能量函数,分析了系统的收敛性,证明了经过多次重复迭代学习,所有闭环信号有界且输出跟踪误差收敛,最后通过构造数值实例进行了仿真验证.理论分析和仿真结果表明,该算法简单有效,对于非线性时滞系统的跟踪问题具有很好的控制效果.     

含有参数化和非参数化不确定性系统重复学习控制

针对含有参数化和非参数化的高阶非线性系统,设计了一种重复学习控制方案.假设未知时变参数和参考信号的共同周期是已知的,通过参数重组技巧,将所有未知时变项合并为一个周期时变向量.将改进Backstepping方法与分段积分机制相结合,构造了微分-差分参数自适应律和重复学习控制律,使跟踪误差在误差平方范数意义下渐近收敛于零.利用Lyapunov泛函,给出了闭环系统收敛的充分条件.仿真结果验证了该方法的有效性.     

未知时变时滞非线性参数化系统自适应迭代学习控制

针对含有未知时变参数和时变时滞的非线性参数化系统,提出了一种新的自适应迭代学习控制方法.该方法将参数分离技术与信号置换思想相结合,可以处理含有时变参数和时滞相关不确定性的非线性系统.设计了一种自适应控制策略,使跟踪误差的平方在一个有限区间上的积分渐近收敛于零.通过构造Lyapunov-Krasovskii型复合能量函数,给出了闭环系统收敛的一个充分条件.给出两个仿真例子验证了控制方法的有效性.     

非线性参数化系统自适应迭代学习控制

研究一类含有未知时变参数的非线性参数化系统的学习控制问题.利用参数分离技术和信号置换思想,通过置换系统方程,合并所有时变参数为一个未知时变参数,用迭代自适应方法估计该未知参数,设计了一种自适应迭代学习控制方法,使得跟踪误差的平方在一个有限区间上的积分渐近收敛于零.通过构造一个类Lyapunov函数,给出了跟踪误差收敛和所有闭环系统信号有界的一个充分条件.仿真结果验证了该方法的有效性.     

基于观测器的非线性时变时滞系统自适应重复控制

针对一类未知时变时滞非线性系统,提出一种基于观测器的重复控制方案．采用线性矩阵不等式设计非线性观测器,所设计的控制律含有ＰＩＤ 反馈项,常值参数自适应律是微分差分型的,时变参数学习律是差分型的．在假设未知时变时滞、时变参数和参考输出的周期有已知的最小公倍数下,通过构造一个Ｌｙaｐｕｎｏｖ-Ｋｒａｓｏｖｓｋｉｉ型复合能量函数,证明了所有闭环信号有界且输出跟踪误差收敛．仿真实例表明了算法的有效性．     

含有未知控制方向的非线性时滞系统学习控制

本文对于一类含有未知控制方向及时滞的非线性参数化系统,设计了自适应迭代学习控制算法.在设计控制算法过程中采用了参数分离技术和信号置换思想来处理系统中出现的时滞项,Nussbaum增益技术解决未知控制方向等问题.为了对系统中出现的未知时变参数和时不变参数进行估计,分别设计了差分及微分参数学习律.然后通过构造的Lyapunov-Krasovskii复合能量函数给出了系统跟踪误差渐近收敛及闭环系统中所有信号有界的条件.最后通过一个仿真例子说明了控制器设计的有效性.     

基于观测器的非线性时变时滞系统自适应重复控制

针对一类未知时变时滞非线性系统,提出一种基于观测器的重复控制方案．采用线性矩阵不等式设计非线性观测器,所设计的控制律含有ＰＩＤ 反馈项,常值参数自适应律是微分 差分型的,时变参数学习律是差分型的．在假设未知时变时滞、时变参数和参考输出的周期有已知的最小公倍数下,通过构造一个Ｌｙaｐｕｎｏｖ-Ｋｒａｓｏｖｓｋｉｉ型复合能量函数,证明了所有闭环信号有界且输出跟踪误差收敛．仿真实例表明了算法的有效性．

     

时变时滞非线性系统自适应神经网络控制

对于一类具有未知时变时滞和虚拟控制系数的不确定严格反馈非线性系统,基于后推设计提出一种自适应神经网络控制方案.选取适当的Lyapunov-Krasovskii泛函补偿未知时变时滞不确定项.通过构造连续的待逼近函数来解决利用神经网络对未知非线性函数进行逼近时出现的奇异问题.通过引入一个新的中间变量,保证了虚拟控制求导的正确性.仿真算例表明,所设计的控制器能保证闭环系统所有信号是半全局一致终结有界的,且跟踪误差收敛到零的一个邻域内.     

一种简化的自适应模糊动态面控制

针对一类不确定非线性时变时滞系统,提出了一种简化的自适应模糊动态面控制方法.该方法取消了对系统时滞常做的假设.仅采用一个模糊逼近器便使所有的未知函数得到补偿,简化了控制器的结构.通过构造合适的Lyapunov-Krasovskii泛函,闭环系统的所有信号被证明为半全局一致最终有界.仿真实例进一步验证了控制方案的有效性.     

输入具有齿隙非线性特性的周期系统的自适应控制

针对一类输入含齿隙非线性动态特性的周期时变系统, 在周期不确定性可时变参数化的条件下设计自适应控制器. 对周期时变参数进行傅里叶级数展开, 并采用微分自适应律估计未知傅里叶系数和齿隙动态特性参数, 通过鲁棒方法消除截断误差和齿隙模型的有界误差项对系统性能的影响. 采用双曲函数替代符号函数确保控制器可微, 同时能有效抑制颤振. 引入Δ函数, 避免参数估计发散, 并保证系统输出渐近跟踪理想轨迹. 理论分析与仿真结果表明, 闭环系统所有信号有界.     

Adaptive iterative learning control for nonlinearly parameterized systems with unknown time-varying delay and unknown control direction

This paper proposes a new adaptive iterative learning control approach for a class of nonlinearly parameterized systems with unknown time-varying delay and unknown control direction.By employing the parameter separation technique and signal replacement mechanism,the approach can overcome unknown time-varying parameters and unknown time-varying delay of the nonlinear systems.By incorporating a Nussbaum-type function,the proposed approach can deal with the unknown control direction of the nonlinear systems.Based on a Lyapunov-Krasovskii-like composite energy function,the convergence of tracking error sequence is achieved in the iteration domain.Finally,two simulation examples are provided to illustrate the feasibility of the proposed control method.     

Observer-based adaptive control for nonlinear input-delay systems with unknown control directions

This paper investigates the problem of adaptive control for strict-feedback nonlinear systems with input delay and unknown control directions. The Nussbaum function is utilised to deal with the unknown control directions and a novel compensation system is introduced to handle the time-varying input delay. By using neural network(NN) approximation and backstepping approaches, an adaptive NN controller is designed which can guarantee the semi-global boundedness of all the signals in the closed-loop system. Two simulation examples are also given to illustrate the effectiveness of the proposed method.     

Adaptive iterative learning control for nonlinearly parameterized systems with unknown time-varying delays

First of all, an adaptive iterative learning control strategy is developed for a class of nonlinearly parameterized systems with two unknown time-varying parameters and one unknown time-varying delay. The proposed control law includes a PID-type feedback term in time domain and an adaptive learning term used to estimate the unknown time-varying vector in iteration domain. By constructing a Lyapunov-Krasovskii-like composite energy function, we prove the stability of the closed-loop system and the convergence of the tracking error. Then, the design idea is further extended to a broader class of systems with mixed parameters in which the unknown time-invariant vector is estimated by a PI-type learning law in time domain. The simulation results, for a time-delay chaotic system, confirm the effectiveness of the proposed control scheme.     

Global stabilisation for a class of upper-triangular nonlinear systems with unmodelled dynamics and time-delay

This paper considers the stabilisation control problem of upper-triangular nonlinear time-delay systems. One distinct characteristic of this work is that the systems contain unmodelled dynamics, unknown control coefficients and time-varying delay, which make the control design much more difficult. By modifying the homogeneous domination approach and introducing a gain-scaling method, a new controller is constructed such that all the states of the closed-loop systems are bounded and convergent to the origin. Simulation examples are given to illustrate the validity of the theory.     

Adaptive tracking control of uncertain MIMO nonlinear systems with time-varying delays and unmodeled dynamics

In this paper, adaptive neural tracking control is proposed based on radial basis function neural networks (RBFNNs) for a class of multi-input multi-output (MIMO) nonlinear systems with completely unknown control directions, unknown dynamic disturbances, unmodeled dynamics, and uncertainties with time-varying delay. Using the Nussbaum function properties, the unknown control directions are dealt with. By constructing appropriate Lyapunov-Krasovskii functionals, the unknown upper bound functions of the time-varying delay uncertainties are compensated. The proposed control scheme does not need to calculate the integral of the delayed state functions. Using Young s inequality and RBFNNs, the assumption of unmodeled dynamics is relaxed. By theoretical analysis, the closed-loop control system is proved to be semi-globally uniformly ultimately bounded.     

控制增益符号未知的MIMO时滞系统自适应控制

针对一类带有死区模型并具有未知函数控制增益的不确定MIMO非线性时滞系统,基于滑模控制原理和Nussbaum函数的性质,提出了一种稳定的自适应神经网络控制方案.该方案放宽了对函数控制增益上界为未知常数的假设,并通过使用Lyapunov-Krasovskii泛函抵消了因未知时变时滞带来的系统不确定性.理论分析证明,闭环系统是半全局一致终结有界.仿真结果表明了该方法的有效性.