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This paper considers a set of multiple independent control systems that are each connected over a nonstationary 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 nonstationarity 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 suboptimality 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.
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AoI-optimal Scheduling for Arbitrary K-channel Update-Through-Queue Systems
This work generalizes the Age-of-Information (AoI) minimization problem of update-through-queue systems such that in addition to deciding the waiting time, the sender also chooses over which “channel” each update packet will be served. Different channels have different costs, delays, and quality characteristics that reflect the scheduler’s selections of routing, communications, and update modes. Instead of considering only two channels with restricted parameters as in the existing works, this work studies the general K-channel problem with arbitrary parameters. The results show that both the optimal waiting time and the optimal channel-selection policies admit an elegant water-filling structure, and can be efficiently computed by the proposed low-complexity fixed-point-based numerical method.
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- PAR ID:
- 10526137
- Publisher / Repository:
- IEEE
- Date Published:
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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