Online Optimal Control with Linear Dynamics and Predictions: Algorithms and Regret Analysis

By Yingying Li, Xin Chen, Na Li. 2019

115 citations recorded by the source corpus.

This paper studies the online optimal control problem with time-varying convex stage costs for a time-invariant linear dynamical system, where a finite lookahead window of accurate predictions of the stage costs are available at each time. We design online algorithms, Receding Horizon Gradient-based Control (RHGC), that utilize the predictions through finite steps of gradient computations. We study the algorithm performance measured by dynamic regret: the online performance minus the optimal performance in hindsight. It is shown that the dynamic regret of RHGC decays exponentially with the size of the lookahead window. In addition, we provide a fundamental limit of the dynamic regret for any online algorithms by considering linear quadratic tracking problems. The regret upper bound of one RHGC method almost reaches the fundamental limit, demonstrating the effectiveness of the algorithm. Finally, we numerically test our algorithms for both linear and nonlinear systems to show the effectiveness and generality of our RHGC.

Subfields: Computational Theory and Mathematics, Computer Networks and Communications, Management Science and Operations Research

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Theory and Mathematics

1. Anan Liu
2. Yuting Su
3. Yaoyao Liu
4. Qianru Sun
5. Bernt Schiele

In Computer Networks and Communications

1. Yaoyao Liu
2. Qianru Sun
3. Bernt Schiele

In Management Science and Operations Research

1. Yaoyao Liu
2. Qianru Sun
3. Bernt Schiele

Citations in the corpus

• RMM: Reinforced Memory Management for Class-Incremental Learning (2023, methodology): “To this end, we leverage reinforcement learning [26, 49, 57] and design a new policy function to contain two sub-functions that propagate two levels of actions in a hierarchical way.”
• Adaptive Aggregation Networks for Class-Incremental Learning (2020, background): “Closely related topics are referred to as continual learning [10, 26] and lifelong learning [2, 7, 22].”
• Mnemonics Training: Multi-Class Incremental Learning Without Forgetting (2020, background): “Motivated by this, a number of works have recently emerged [2, 9, 16, 17, 25, 36].”