一种基于Lyapunov约束的学习控制方法及应用

针对非线性系统的稳定控制器直接设计问题,提出一种基于Lyapunov稳定性条件的学习控制器设计方法框架,将传统的控制器设计与稳定性证明分析问题转化为以控制器为求解项,Lyapunov稳定条件为约束的最优化问题,提供了一种直接求解全局稳定的最优控制器的新途径。首先建立了以系统跟踪误为目标函数与以Lyapunov稳定条件为约束的最优化问题,接着给出了一类基于神经网络实现的PID结合前馈控制器设计形式,最后分析并设计了学习控制器求解方法,采用相关深度学习技术以提升求解能力。二阶线性与非线性系统仿真测试与一级旋转倒立摆模拟实验表明所提方法具有快速收敛、低误差、控制输出平滑且低幅值等特点;在加入扰动、噪声、参数不确定性和不同的测试期望输出条件下的反步法对比测试结果表明所提方法对扰动与噪声具有强抑制能力,同时学习控制器具有高泛化能力。基于V-Rep的一级旋转倒立摆模拟与四旋翼单轴控制实物实验结果验证了所提方法对物理系统控制问题具有高控制精度与强抗扰能力。

A framework of learning controller with Lyapunov based constraint and application

In this paper, the direct way of designing a stable controller for nonlinear system is studied. A framework of learning controller with Lyapunov based constraint is proposed, which transforms design and analysis of a controller to straightforward way by solving an optimization item with the Lyapunov constraint. A novel way of the global stability guaranteed controller is realized directly. Firstly, the optimization problem subject to Lyapunov based constraints is formulated, in which the tracking error is the objective function to be minimized. Secondly, the controller combines with PID and feedforward is given in form of neural networks. Finally, the optimization solution of the controller method is analyzed and solved, in which some deep learning technologies are used to enhance the capability of solution. Test results of two simulations of 2 order linear and nonlinear systems demonstrate that the proposed method has high performance in speed of convergence, tracking error and smoothness and amplitude of control output. Results of comparison simulation with backstepping control to the nonlinear system with disturbance, noise, uncertainty of parameters and the difference of reference output demonstrate that the proposed method has high performance in terms of robustness and generalization. Results of simulated physical experiment of one stage rotary inverted pendulum based on V Rep and physical testing of single axis controlling for quadrotor prove that the method proposed is capable of high precision control and strong disturbance rejection.