In this paper, a method is presented to synthesize neural network controllers
such that the feedback system of plant and controller is dissipative,
certifying performance requirements such as L2 gain bounds. The class of plants
considered is that of linear time-invariant (LTI) systems interconnected with
an uncertainty, including nonlinearities treated as an uncertainty for
convenience of analysis. The uncertainty of the plant and the nonlinearities of
the neural network are both described using integral quadratic constraints
(IQCs). First, a dissipativity condition is derived for uncertain LTI systems.
Second, this condition is used to construct a linear matrix inequality (LMI)
which can be used to synthesize neural network controllers. Finally, this
convex condition is used in a projection-based training method to synthesize
neural network controllers with dissipativity guarantees. Numerical examples on
an inverted pendulum and a flexible rod on a cart are provided to demonstrate
the effectiveness of this approach.

通过基于积分二次约束的方法，本文提出一种合成神经网络控制器的方法，使得植物和控制器的反馈系统具有耗散性，并证明 L2 增益的性能要求。通过不确定性来描述植物的不确定性和神经网络的非线性，使用耗散条件导出了不确定线性时不变系统的耗散性条件，并使用线性矩阵不等式来合成神经网络控制器。最后，将该凸条件用于基于投影的训练方法来合成具有耗散性保证的神经网络控制器。通过倒立摆和弹性杆车的数值例子来证明这种方法的有效性。