Online Gradient Descent for Linear Dynamical Systems
arXiv:1912.09311 · doi:10.1016/j.ifacol.2020.12.1258
Abstract
In this paper, online convex optimization is applied to the problem of controlling linear dynamical systems. An algorithm similar to online gradient descent, which can handle time-varying and unknown cost functions, is proposed. Then, performance guarantees are derived in terms of regret analysis. We show that the proposed control scheme achieves sublinear regret if the variation of the cost functions is sublinear. In addition, as a special case, the system converges to the optimal equilibrium if the cost functions are invariant after some finite time. Finally, the performance of the resulting closed loop is illustrated by numerical simulations.
Accepted for publication in the proceedings of the 2020 IFAC World Congress. 8 pages, 3 figures
References in corpus (3)
Cited by in corpus (6)
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- Online Stochastic Optimization for Unknown Linear Systems: Data-Driven Synthesis and Controller Analysis