Calculus of Variations and Optimal Control Theory: A Concise Introduction

By Daniel Liberzon. 2012

851 citations recorded by the source corpus.

Subfields: Control and Systems Engineering, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/c5495df22c2dd9a58bc11fcc8d638c3c502ce32d

How researchers see this paper

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

In Control and Systems Engineering

1. Tim de Bruin
2. Jens Kober
3. Lucian Busoniu
4. Laurent Lessard
5. Shimon Whiteson
6. E. Weinan
7. Xiaojin Zhu
8. Tim G. J. Rudner

In Numerical Analysis

1. Tim de Bruin
2. Cheng Tai
3. Jens Kober
4. Lucian Busoniu
5. Laurent Lessard
6. E. Weinan
7. Xiaojin Zhu
8. Qianxiao Li

Citations in the corpus

• Stochastic Modified Equations and Adaptive Stochastic Gradient Algorithms (2015, background): “82) This is known as the Hamilton-Jacobi-Bellman equation (HJB). Note that this PDE is solved backwards in time. The derivation of this PDE can be found in most references on optimal control, e.g. in Liberzon (2012). The main idea is the dynamic programming principle: for any tthe [t;T]-portion of t”
• Reinforcement learning for control: Performance, stability, and deep approximators (2018, methodology): “Optimal control meth-ods typically seek control laws in an o ffl ine manner assuming availability of the underlying dynamic models (Liberzon, 2011; Borrelli et al., 2017).”
• VIREL: A Variational Inference Framework for Reinforcement Learning (2018, background): “From the second order sufficient conditions for f(x∗) to be a maximum, we have u>∇2f(x∗)u ≤ 0 ∀ u ∈ U with equality only when u = 0 [36].”
• Learning Model Predictive Control for Iterative Tasks. A Data-Driven Control Framework (2016, neutral): “The controller accelerates until it reaches the midpoint between the initial and final position and it decelerates afterward, as we would expect from the optimal solution to a minimum time problem [28].”
• An Optimal Control Approach to Sequential Machine Teaching (2018, methodology): “and computational tools that have been developed over the past 60 years to address it. For a more detailed exposition on the theory, we refer the reader to modern references on the topic (Kirk, 2012; Liberzon, 2011; Athans and Falb, 2013). This section is self-contained and we will use notation cons”