Local Stability and Convergence Analysis of Neural Network Controllers With Error Integral Inputs
Local Stability and Convergence Analysis of Neural Network Controllers With Error Integral Inputs
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DOI：
10.1109/tnnls.2021.3116189
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发表时间：
2021-10
影响因子：
10.4
通讯作者：
Xingang Fu;Shuhui Li;D. Wunsch;Eduardo Alonso
中科院分区：
文献类型：
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作者：
Xingang Fu;Shuhui Li;D. Wunsch;Eduardo Alonso
研究了一类以误差积分为输入的神经网络控制器的局部稳定性和局部收敛性。它是正式证明，如果神经网络控制器的输入只包括误差项，控制系统显示了一个非零的稳态误差的任何常数参考除了一个特定的点，单层和多层神经网络控制器。进一步证明了在单层和多层神经网络控制器的输入中加入误差积分是一种有效的方法，可以消除任何常值参考的稳态误差。由于神经网络控制器的非线性，神经网络控制系统在平衡点处被线性化。证明了如果线性化后的神经网络控制系统的特征值都有负的真实的部分，则保证了系统的局部渐近稳定性和局部指数收敛性。两个案例研究进行了探索，以验证理论结果：单层神经网络控制器在1-D系统和4层神经网络控制器在2-D系统应用于可再生能源集成。仿真结果表明，当神经网络控制器和相应的广义比例积分（PI）控制器具有相同的特征值时，所有的控制系统表现出几乎相同的响应在一个小的邻域各自的平衡点。
This article investigates the local stability and local convergence of a class of neural network (NN) controllers with error integrals as inputs for reference tracking. It is formally proved that if the input of the NN controller consists exclusively of error terms, the control system shows a non-zero steady-state error for any constant reference except for one specific point, for both single-layer and multi-layer NN controllers. It is further proved that adding error integrals to the input of the (single- and multi-layers) NN controller is one sufficient way to remove the steady-state error for any constant reference. Due to the nonlinearity of the NN controllers, the NN control systems are linearized at the equilibrium points. We provide proof that if all the eigenvalues of the linearized NN control system have negative real parts, local asymptotic stability and local exponential convergence are guaranteed. Two case studies were explored to verify the theoretical results: a single-layer NN controller in a 1-D system and a four-layer NN controller in a 2-D system applied to renewable energy integration. Simulations demonstrate that when NN controllers and the corresponding generalized proportional-integral (PI) controllers have the same eigenvalues, all control systems exhibit almost the same responses in a small neighborhood of their respective equilibrium points.