基于深度学习感知的动力系统在线优化
Online Optimization of Dynamical Systems with Deep Learning Perception
AI总结：
本文针对状态不可测且控制代价未知的动力系统，提出基于投影梯度流和神经网络的数据驱动反馈控制器，并利用扰动系统稳定性理论证明其指数输入到状态稳定性，在机器人和流行病控制中验证了有效性。
摘要：
本文考虑了当状态无法直接测量且控制性能指标未知或部分已知时，控制动力系统的问题。具体而言，我们专注于设计数据驱动的控制器，以将动力系统调节到受约束凸优化问题的解，其中：i) 必须从非线性且可能高维的数据中估计状态；ii) 优化问题的代价——该代价模拟与系统输入和状态相关的控制目标——不可用，必须从数据中学习。我们提出了一种基于投影梯度流方法改编的数据驱动反馈控制器；该控制器将神经网络作为估计未知函数的组成部分。利用扰动系统的稳定性理论，我们推导了保证控制回路指数输入到状态稳定性（ISS）的充分条件。特别是，我们证明了互连系统相对于神经网络的逼近误差和影响系统的未知扰动是ISS的。瞬态界结合了深度神经网络的通用逼近性质与ISS表征。在机器人控制和流行病控制的背景下，给出了说明性的数值结果。
英文摘要：
This paper considers the problem of controlling a dynamical system when the state cannot be directly measured and the control performance metrics are unknown or partially known. In particular, we focus on the design of data-driven controllers to regulate a dynamical system to the solution of a constrained convex optimization problem where: i) the state must be estimated from nonlinear and possibly high-dimensional data; and, ii) the cost of the optimization problem -- which models control objectives associated with inputs and states of the system -- is not available and must be learned from data. We propose a data-driven feedback controller that is based on adaptations of a projected gradient-flow method; the controller includes neural networks as integral components for the estimation of the unknown functions. Leveraging stability theory for perturbed systems, we derive sufficient conditions to guarantee exponential input-to-state stability (ISS) of the control loop. In particular, we show that the interconnected system is ISS with respect to the approximation errors of the neural network and unknown disturbances affecting the system. The transient bounds combine the universal approximation property of deep neural networks with the ISS characterization. Illustrative numerical results are presented in the context of control of robotics and epidemics.
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