The Discrete-time Internal Model Principle of Time-varying Optimization: Limitations and Algorithm Design
(2025) 2025 IEEE 64th Conference on Decision and Control (CDC) — Location: Rio de Janeiro, Brazil (9.December.2025)
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- Abstract
- Time-varying optimization problems arise in a va riety of engineering applications. The available information about how the problem changes in time dictates the types of algorithms that are applicable to a particular problem as well as the types of convergence guarantees that may be proven. In this paper, we study dynamic gradient-feedback algorithms for time-varying optimization in discrete time. By casting the design of such algorithms as an output regulation problem for dynamical systems, we provide necessary and sufficient conditions for the existence of a gradient-feedback algorithm that asymptotically tracks a critical trajectory of the optimization problem. When these conditions hold, we provide a design procedure to construct such an algorithm. As a fundamental limitation, we show that any algorithm that asymptotically tracks a critical trajectory needs to contain an internal model of the temporal variation, which we refer to as the internal model principle of time-varying optimization.
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Citations
Bianchin, G., & van Scoy, B. (2025). The Discrete-time Internal Model Principle of Time-varying Optimization: Limitations and Algorithm Design. 2025 IEEE 64th Conference on Decision and Control (CDC), Rio de Janeiro, Brazil. https://hdl.handle.net/2078.5/266829