# Certainty Equivalent Quadratic Control for Markov Jump Systems

arXiv: https://arxiv.org/abs/2105.12358 · HTML: https://mlsanity.com/paper/2105.12358/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 25 references that are in the map.
- First posted on arXiv 26 May 2021.

## Builds on (most cited first, 8 of 8)

- [On the Sample Complexity of the Linear Quadratic Regulator](https://mlsanity.com/paper/1710.01688/) (2017)
- [Naive Exploration is Optimal for Online LQR](https://mlsanity.com/paper/2001.09576/) (2020)
- [Near optimal finite time identification of arbitrary linear dynamical systems](https://mlsanity.com/paper/1812.01251/) (2018)
- [Non-asymptotic Identification of LTI Systems from a Single Trajectory](https://mlsanity.com/paper/1806.05722/) (2018)
- [Spectral State Compression of Markov Processes](https://mlsanity.com/paper/1802.02920/) (2018)
- [Efficient Optimistic Exploration in Linear-Quadratic Regulators via Lagrangian Relaxation](https://mlsanity.com/paper/2007.06482/) (2020)
- [Non-Asymptotic Analysis of Robust Control from Coarse-Grained Identification](https://mlsanity.com/paper/1707.04791/) (2017)
- [Policy Optimization for Markovian Jump Linear Quadratic Control: Gradient-Based Methods and Global Convergence](https://mlsanity.com/paper/2011.11852/) (2020)

## Built on by (most cited first, 3 of 3)

- [Identification and Adaptive Control of Markov Jump Systems: Sample Complexity and Regret Bounds](https://mlsanity.com/paper/2111.07018/) (2021)
- [System Identification via Nuclear Norm Regularization](https://mlsanity.com/paper/2203.16673/) (2022)
- [Mode Reduction for Markov Jump Systems](https://mlsanity.com/paper/2205.02697/) (2022)

## Abstract (arXiv)

Real-world control applications often involve complex dynamics subject to abrupt changes or variations. Markov jump linear systems (MJS) provide a rich framework for modeling such dynamics. Despite an extensive history, theoretical understanding of parameter sensitivities of MJS control is somewhat lacking. Motivated by this, we investigate robustness aspects of certainty equivalent model-based optimal control for MJS with quadratic cost function. Given the uncertainty in the system matrices and in the Markov transition matrix is bounded by ε and η respectively, robustness results are established for (i) the solution to coupled Riccati equations and (ii) the optimal cost, by providing explicit perturbation bounds which decay as O(ε + η) and O((ε + η)2) respectively.