Neural network solution for finite-horizon H-infinity constrained optimal control of nonlinear systems

In this paper, neural networks are used to approximately solve the finite-horizon constrained input H-infinity state feedback control problem. The method is based on solving a related Hamilton-Jacobi-Isaacs equation of the corresponding finite-horizon zero-sum game. The game value function is approximated by a neural network with time- varying weights. It is shown that the neural network approximation converges uniformly to the game-value function and the resulting almost optimal constrained feedback controller provides closed-loop stability and bounded L2 gain. The result is an almost optimal H-infinity feedback controller with time-varying coefficients that is solved a priori off-line. The effectiveness of the method is shown on the Rotational/Translational Actuator benchmark nonlinear control problem.     

Nonlinear H∞-control and estimation of optimal H∞-gain

The structure of nonlinear H_∞-controller and the estimation of optimal H_∞-gain are investigated in this paper. The essential problem boils down to the existence of semipositive solution to the Hamilton-Jacobi-Isaacs inequality. Further, the solvability of this first-order fully nonlinear differential inequality is discussed. We look for one kind of special semipositive radial solution to the Hamilton-Jacobi-Isaacs inequality. An explicit estimation of optimal H_∞-gain and explicit formulas of semipositive radial solutions to the Hamilton-Jacobi-Isaacs inequality are obtained. The results are quite simple and intuitive. They even shed a new insight on the linear H_∞-theory.     

高超声速飞行器非线性H_∞姿态控制设计

针对高超声速飞行器倾斜转弯姿态跟踪控制问题,将非线性耦合系统的姿态跟踪控制表述为非线性H∞控制的指令误差状态空间实现形式.基于非线性系统γ-耗散性及L2增益设计准则,设计满足Hamil-ton-Jacobi-Isaacs不等式的光滑可微储能函数.在一定假设条件下,利用非线性系统在局部空间内线性伴随系统的Riccati微...     

执行器故障下不确定非线性系统的鲁棒保成本控制

对一类执行器故障的非线性不确定系统,研究了具有L2增益扰动衰减性能指标约束的鲁棒保成本控制器的设计问题.提出了更实际、更一般的执行器故障模型；给出了具有L2增益扰动衰减性能的鲁棒保成本控制系统的概念和属性.采用HJI不等式方法,导出了故障闭环系统渐近稳定、具有给定的抗干扰能力和成本函数有上界的充分条件.仿真实例验证了结论的有效性.     

Robust performance control of uncertain nonlinear systems: A self-tuning approach

The problem of output regulation with a guaranteed H^∞ performance, besides robust stability, for a class of feedback linearizable nonlinear systems via self-tuning controllers is investigated. The H^∞ performance consists of the desired disturbance attenuation and internal finite L²-gain stability. We show that, under the perturbations of matched parametric uncertainties, the sufficient condition for the existence of a self-tuning controller reduces to the solvability of a single Hamilton-Jacobi-Isaacs inequality (or algebraic Riccati equation) which indicates that the design can be performed as if the system uncertainties were absent. Under certain situations, the sufficient condition is also necessary. Once a solution of this nonlinear differential inequality (or algebraic equation) is available, a desired self-tuning controller with gradient-type parameter estimator can easily be constructed. The present work falls into the category of singular nonlinear H^∞ control since the desired H^∞ performance does not require any penalty on control input variables. The results also provide an immediate application to H^∞ self-tuning model reference control in linear systems under full state measurement.     

无轴承异步电动机悬浮子系统独立鲁棒控制方法研究

为实现无轴承异步电动机(BIM)的动态解耦控制,基于径向基函数神经网络(RBFNN),提出一种悬浮子系统独立鲁棒控制方法。应用RBFNN辨识系统模型不确定因素和外界干扰,基于HJI不等式原理设计RBFNN鲁棒控制器,实现悬浮子系统的动态独立解耦控制,并提高系统的稳定性和抗干扰性能。仿真和实验结果表明所提出的BIM控制系统具有良好的动静态性能。