非线性随机系统的概率密度追踪控制

针对目前非线性随机系统控制方法的设计复杂、 计算成本高以及缺乏稳定性或收敛性证明等缺点, 提出了一种全新的基于等效非线性系统法求近似稳态解的思想设计的非线性随机系统的反馈控制, 使受控系统输出的稳态概率密度函数逼近事先给定的目标概率密度函数. 利用 Lyapunov 函数法证明了受控系统的收敛性. 数学仿真结果证明了这种方法的可行性和正确性.     

随机激励下非线性水轮机系统的控制设计

针对一类随机非线性哈密顿系统提出了一种全新的反馈跟踪控制方法.该控制策略可以准确地控制系统输出的概率密度分布特性.闭环系统的稳定性也通过李雅普诺夫函数法得到严格的数学证明.最后,以随机非线性水轮机系统为例,详细演示了控制设计过程及其有效性.仿真结果表明,新的反馈控制策略可以使水轮机系统的输出满足预先指定的平稳概率密度函数.     

基于偏格式线性化的MIMO系统无模型自适应控制

针对常规PID控制器不能很好兼顾抗干扰性与鲁棒性以及基于模型的控制算法过于依赖受控系统数学模型的缺点,提出一种适用于离散时间多输入多输出(MIMO)非线性系统的无模型自适应控制算法.该算法首先通过偏格式线性化方法将非线性系统线性化,再利用一种新型的投影算法在线辨识受控系统参数,根据辨识得到的受控系统参数直接递推计算无模...     

二维直线电机的多入多出无模型自适应轮廓控制

针对传统的单入单出控制器无法解决二维直线电机存在的非线性,不确定性以及强耦合作用等问题,依据无模型自适应控制不依赖于被控系统精确数学模型,仅需受控系统输入输出数据便能实现自适应控制这一特点,采用多入多出的紧格式动态线性化无模型自适应控制算法对二维直线电机XY轴进行整体控制器设计.同时,针对二维直线电机这种含有纯二阶积分环节的非自平衡系统,提出了多入多出无模型自适应控制改良方法,并进行严格的稳定性和收敛性证明.为了提高二维直线电机的轮廓精度,在多入多出无模型自适应控制改良方法的基础上,加入交叉耦合控制器,与传统的交叉耦合控制方法相比较,提高了跟踪精度和轮廓精度.最后通过仿真和实物实验证明了所提方案的有效性.     

神经网络在线投影算法及非线性建模应用

针对神经网络难以在线学习的缺点,把神经网络当作结构已知的非线性系统,权系数的学习看成非线性系统的参数估计,基于新估计准则的非线性系统在线参数估计投影算法,给出前馈神经网络的一种在线运行投影学习算法.理论上证明该算法的全局收敛性,讨论算法参数的物理意义和取值范围.通过2个非线性时变系统的神经网络建模应用的仿真,验证算法的全局收敛性和在线运行能力.     

采样非线性系统的神经网络稳定自适应控制

针对一类动力学未知或难以建模的采样非线性系统,提出了一种基于神经网络的跟随控 制器稳定自适应控制方法.控制器采用径向基函数神经网络近似对象的动力学非线性,神经 网络参数的自适应规律由稳定理论得到.文中给出了系统稳定性和跟随误差收敛性的证明, 并通过仿真实例揭示了所提方法的性能.     

基于神经网络的非线性系统稳定自适应控制

本文针对一类具有未知非线性函数和未知虚拟系数非线性函数的二阶非线性系统 ,提出了一种基于神经网络的稳定自适应输出跟踪控制方法 .用李雅普诺夫稳定性分析方法证明了本文的神经网络自适应控制器能够使受控系统稳定 ,并使输出跟踪误差随时间趋于无穷而收敛到零 .仿真算例证明了该算法的有效性     

非线性系统的神经网络鲁棒自适应跟踪控制

针对一类具有未知非线性函数和未知虚拟系数非线性函数的二阶非线性系统,提出了一种神经网络鲁棒自适应输出跟踪控制方法.用李雅普诺夫稳定性分析方法证明了本文的神经网络自适应控制器能够使受控系统内的所有信号均为有界.选择的神经网络权值调整规律可以防止自适应控制中的参数漂移.     

测量数据丢失的一类非线性系统迭代学习控制

迭代学习控制方法应用于网络控制系统时,由于通信网络的约束导致数据包丢失现象经常发生.针对存在输出测量数据丢失的一类非线性系统,研究P型迭代学习控制算法的收敛性问题.将数据丢失描述为一个概率已知的随机伯努利过程,在此基础上给出P型迭代学习控制算法的收敛条件,理论上证明了算法的收敛性,并通过仿真验证理论结果.研究表明,当非线性系统存在输出测量数据丢失时,迭代学习控制算法仍然可以保证跟踪误差的收敛性.     

拒绝服务攻击下的多输入多输出非线性系统无模型自适应控制

针对多输入多输出(MIMO)非线性离散时间系统,研究系统遭受拒绝服务(DoS)攻击和随机发生数据包丢失下的控制问题.首先采用两个独立的伯努利分布对周期性DoS攻击和随机发生的数据包丢失进行建模.其次结合DoS攻击设计无模型自适应控制(MFAC)算法,进而通过理论分析和数学推导证明所提算法的收敛性.并且通过结合先前时刻数...     

Feedback control of nonlinear stochastic systems for targeting a specified stationary probability density

In the present paper, an innovative procedure for designing the feedback control of multi-degree-of-freedom (MDOF) nonlinear stochastic systems to target a specified stationary probability density function (SPDF) is proposed based on the technique for obtaining the exact stationary solutions of the dissipated Hamiltonian systems. First, the control problem is formulated as a controlled, dissipated Hamiltonian system together with a target SPDF. Then the controlled forces are split into a conservative part and a dissipative part. The conservative control forces are designed to make the controlled system and the target SPDF have the same Hamiltonian structure (mainly the integrability and resonance). The dissipative control forces are determined so that the target SPDF is the exact stationary solution of the controlled system. Five cases, i.e., non-integrable Hamiltonian systems, integrable and non-resonant Hamiltonian systems, integrable and resonant Hamiltonian systems, partially integrable and non-resonant Hamiltonian systems, and partially integrable and resonant Hamiltonian systems, are treated respectively. A method for proving that the transient solution of the controlled system approaches the target SPDF as t→∞ is introduced. Finally, an example is given to illustrate the efficacy of the proposed design procedure.     

Control of quasi non-integrable Hamiltonian systems for targeting a specified stationary probability density

An innovative design procedure for the feedback control of quasi non-integrable Hamiltonian systems to target a specified stationary probability density function (SPDF) is proposed based on the averaged Fokker–Planck–Kolmogorov equation. The control force is split into a conservative part and a dissipative part. The conservative part is designed to make the controlled system and the target SPDF having the same Hamiltonian structure. The dissipative part is then determined to make the target SPDF to be the stationary solution of the controlled system. Then, a Lyapunov function method is adopted for proving that the transient solution of the controlled system approaches to the target SPDF as time t → ∞. The simulation result for an example shows the effectiveness of the proposed control strategy.     

Adaptive finite-time neural network control for nonlinear stochastic systems with state constraints

This paper focuses on the adaptive finite-time neural network control problem for nonlinear stochastic systems with full state constraints. Adaptive controller and adaptive law are designed by backstepping design with log-type barrier Lyapunov function. Radial basis function neural networks are employed to approximate unknown system parameters. It is proved that the tracking error can achieve finite-time convergence to a small region of the origin in probability and the state constraints are confirmed in probability. Different from deterministic nonlinear systems, here the stochastic system is affected by two random terms including continuous Brownian motion and discontinuous Poisson jump process. Therefore, it will bring difficulties to the controller design and the estimations of unknown parameters. A simulation example is given to illustrate the effectiveness of the designed control method.     

Robust approximation-free prescribed performance control for nonlinear systems and its application

This paper presents a robust prescribed performance control approach and its application to nonlinear tail-controlled missile systems with unknown dynamics and uncertainties. The idea of prescribed performance function (PPF) is incorporated into the control design, such that both the steady-state and transient control performance can be strictly guaranteed. Unlike conventional PPF-based control methods, we further tailor a recently proposed systematic control design procedure (i.e. approximation-free control) using the transformed tracking error dynamics, which provides a proportional-like control action. Hence, the function approximators (e.g. neural networks, fuzzy systems) that are widely used to address the unknown nonlinearities in the nonlinear control designs are not needed. The proposed control design leads to a robust yet simplified function approximation-free control for nonlinear systems. The closed-loop system stability and the control error convergence are all rigorously proved. Finally, comparative simulations are conducted based on nonlinear missile systems to validate the improved response and the robustness of the proposed control method.     

Model‐Reference Adaptive Moment Control of Uncertain Nonlinear Stochastic Systems

In this paper, a new model‐reference adaptive moment control method is proposed to control the first and second moments of an uncertain nonlinear system with additive external stochastic excitation. This method has established a closed‐loop control system that calculates an adaptive stochastic nonlinear input by introducing a Lyapunov function and adaptive update law. The proposed adaptive structure is innovative in trying to minimize two errors simultaneously: the moments tracking error and the error between the nonlinear system output and reference model. Furthermore, the proposed method can control the expected and covariance matrices of the states without needing to solve the complicated Fokker‐Planck‐Kolmogorov differential equation or using the approximate methods. Simulation has been performed on two practical examples, which show a good performance for the designed controller.     

Robust neural network tracking controller using simultaneous perturbation stochastic approximation

This paper considers the design of robust neural network tracking controllers for nonlinear systems. The neural network is used in the closed-loop system to estimate the nonlinear system function. We introduce the conic sector theory to establish a robust neural control system, with guaranteed boundedness for both the input/output (I/O) signals and the weights of the neural network. The neural network is trained by the simultaneous perturbation stochastic approximation (SPSA) method instead of the standard backpropagation (BP) algorithm. The proposed neural control system guarantees closed-loop stability of the estimation system, and a good tracking performance. The performance improvement of the proposed system over existing systems can be quantified in terms of preventing weight shifts, fast convergence, and robustness against system disturbance.     

Robust state observer and control design using command-to-state mapping

In this paper, by introducing the concept of command-to-state/output mapping, it is shown that the state of an uncertain nonlinear system can robustly be estimated if command-to-state mapping of the system and that of an uncertainty-free observer converge to each other. Then, a global Jacobian system is defined to capture this convergence property for the dynamics of estimation error, and a set of general stability and convergence conditions are derived using Lyapunov direct method. It is also shown that the conditions are constructive and can be reduced to an algebraic Lyapunov matrix equation by which nonlinear feedback in the observer and its corresponding Lyapunov function can be searched in a way parallel to those of nonlinear control design. Case studies and examples are used to illustrate the proposed observer design method. Finally, observer-based control is designed for systems whose uncertainties are generated by unknown exogenous dynamics.     

Adaptive fuzzy sliding mode control for electro-hydraulic servo mechanism

An innovative approach to adaptive fuzzy sliding mode control for a class of SISO continuous nonlinear systems with unknown dynamics and bounded disturbances is introduced in this paper. The main idea of the presented method consists in the introduction of the fuzzy self-tuning mechanism for adaptation of the sliding mode control parameters – extended feedback and switching gains. Such modification reduces the well-known chattering problem in classical sliding mode control. In comparison with the other algorithms eliminating this problem the proposed method results in faster convergence and more transparent and interpretable design of self-tuning mechanism. Moreover, the proposed method guaranteing the asymptotic reference signal tracking with bounded system signals can be easily implemented to high order systems. The performance of the presented control design is demonstrated on control of a nonlinear electro-hydraulic servo mechanism.