This paper considers a set of multiple independent control systems that are
each connected over a non-stationary wireless channel. The goal is to maximize
control performance over all the systems through the allocation of transmitting
power within a fixed budget. This can be formulated as a constrained
optimization problem examined using Lagrangian duality. By taking samples of
the unknown wireless channel at every time instance, the resulting problem
takes on the form of empirical risk minimization, a well-studied problem in
machine learning. Due to the non-stationarity of wireless channels, optimal
allocations must be continuously learned and updated as the channel evolves.
The quadratic convergence property of Newton's method motivates its use in
learning approximately optimal power allocation policies over the sampled dual
function as the channel evolves over time. Conditions are established under
which Newton's method learns approximate solutions with a single update, and
the subsequent sub-optimality of the control problem is further characterized.
Numerical simulations illustrate the near-optimal performance of the method and
resulting stability on a wireless control problem.

该文考虑了一组通过非稳态无线信道相互连接的多个独立控制系统，通过在固定预算内分配发送功率，最大化所有系统的控制性能。通过对未知无线信道进行采样，可以将问题转化为经验风险最小化问题，并使用 Lagrangian dual 问题进行约束优化。由于无线信道的非稳态性，最优的功率分配必须随着信道的演化而持续学习和更新。通过使用牛顿法以随时间演化为样本的对偶函数，学习接近最优的功率分配策略并取得二次收敛特性。数值模拟阐明了该方法的近最优性能和在无线控制问题上的稳定性。