Details
| Original language | English |
|---|---|
| Pages (from-to) | 945-952 |
| Number of pages | 8 |
| Journal | IFAC-PapersOnLine |
| Volume | 53 |
| Issue number | 2 |
| Publication status | Published - 2020 |
| Event | 21st IFAC World Congress 2020 - Berlin, Germany Duration: 12 Jul 2020 → 17 Jul 2020 |
Abstract
Keywords
- math.OC, Linear systems, Real-time optimal control, Online convex optimization, Online gradient descent, Online learning, Predictive control
ASJC Scopus subject areas
- Engineering(all)
- Control and Systems Engineering
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In: IFAC-PapersOnLine, Vol. 53, No. 2, 2020, p. 945-952.
Research output: Contribution to journal › Conference article › Research › peer review
}
TY - JOUR
T1 - Online Gradient Descent for Linear Dynamical Systems
AU - Nonhoff, Marko
AU - Müller, Matthias A.
PY - 2020
Y1 - 2020
N2 - 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.
AB - 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.
KW - math.OC
KW - Linear systems
KW - Real-time optimal control
KW - Online convex optimization
KW - Online gradient descent
KW - Online learning
KW - Predictive control
UR - http://www.scopus.com/inward/record.url?scp=85093311163&partnerID=8YFLogxK
U2 - 10.1016/j.ifacol.2020.12.1258
DO - 10.1016/j.ifacol.2020.12.1258
M3 - Conference article
VL - 53
SP - 945
EP - 952
JO - IFAC-PapersOnLine
JF - IFAC-PapersOnLine
SN - 2405-8963
IS - 2
T2 - 21st IFAC World Congress 2020
Y2 - 12 July 2020 through 17 July 2020
ER -