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This paper proposes a set of novel optimization algorithms for solving a class of convex optimization problems with time-varying streaming cost functions. We develop an approach to track the optimal solution with a bounded error. Unlike prior work, our algorithm is executed only by using the first-order derivatives of the cost function, which makes it computationally efficient for optimization with time-varying cost function. We compare our algorithms to the gradient descent algorithm and show why gradient descent is not an effective solution for optimization problems with time-varying cost. Several examples, including solving a model predictive control problem cast as a convex optimization problem with a streaming time-varying cost function, demonstrate our results.
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Data-driven synthesis of optimization-based controllers for regulation of unknown linear systems
This paper proposes a data-driven framework to solve time-varying optimization problems associated with unknown linear dynamical systems. Making online control decisions to steer a system to the solution trajectory of a time-varying optimization problem is a central goal in many modern engineering applications. Yet, the available methods critically rely on a precise knowledge of the system dynamics, thus requiring ad-hoc system identification and model refinement phases. In this work, we leverage tools from behavioral theory to show that the steady-state transfer function of a system can be computed from control experiments without knowledge or estimation of the system model. Such direct computation allows us to avoid the explicit model identification phase, and is significantly more tractable than the direct model-based computation. We leverage the data-driven representation to design a controller inspired from a gradient-descent method that drives the system to the solution of an unconstrained optimization problem, without any knowledge of time-varying disturbances affecting the model equation. Results are tailored to cost functions that are smooth and satisfy the Polyak-Lojasiewicz inequality. Simulation results illustrate the technical findings.
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- PAR ID:
- 10312630
- Date Published:
- Journal Name:
- Proceedings of the IEEE Conference on Decision Control
- ISSN:
- 0743-1546
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1109/CDC45484.2021.9682795
