论文标题
具有深度学习感知的动态系统的在线优化
Online Optimization of Dynamical Systems with Deep Learning Perception
论文作者
论文摘要
本文考虑了无法直接测量状态并且控制性能指标是未知或部分已知的,控制动态系统的问题。特别是,我们专注于数据驱动的控制器的设计,以调节动态系统,以解决约束凸优化问题的解决方案:i)必须从非线性和可能的高维数据中估算状态; ii)优化问题的成本 - 模型控制与系统的输入和状态相关的目标 - 不可用,必须从数据中学到。我们提出了一个基于投影梯度流方法的适应性数据驱动的反馈控制器;控制器包括神经网络作为估计未知函数的积分组件。利用稳定性理论为扰动系统,我们得出了足够的条件,以保证控制回路的指数对国家稳定性(ISS)。特别是,我们表明互连系统是关于神经网络的近似错误以及影响系统的未知干扰的ISS。瞬态边界将深神经网络的通用近似特性与ISS表征结合在一起。说明性的数值结果在机器人技术和流行病的控制背景下呈现。
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.