# Suboptimality analysis of receding horizon quadratic control with unknown linear systems and its applications in learning-based control

arXiv: https://arxiv.org/abs/2301.07876 · HTML: https://mlsanity.com/paper/2301.07876/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 26 of its 65 references that are in the map.
- First posted on arXiv 19 Jan 2023.

## Builds on (most cited first, 26 of 26)

- [Global Convergence of Policy Gradient Methods for the Linear Quadratic Regulator](https://mlsanity.com/paper/1801.05039/) (2018)
- [On the Sample Complexity of the Linear Quadratic Regulator](https://mlsanity.com/paper/1710.01688/) (2017)
- [Learning Without Mixing: Towards A Sharp Analysis of Linear System Identification](https://mlsanity.com/paper/1802.08334/) (2018)
- [A Tour of Reinforcement Learning: The View from Continuous Control](https://mlsanity.com/paper/1806.09460/) (2018)
- [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)
- [Regret Bounds for Robust Adaptive Control of the Linear Quadratic Regulator](https://mlsanity.com/paper/1805.09388/) (2018)
- [Online Linear Quadratic Control](https://mlsanity.com/paper/1806.07104/) (2018)
- [Statistical Learning Theory for Control: A Finite Sample Perspective](https://mlsanity.com/paper/2209.05423/) (2022)
- [Convergence and sample complexity of gradient methods for the model-free linear quadratic regulator problem](https://mlsanity.com/paper/1912.11899/) (2019)
- [Online Optimal Control with Linear Dynamics and Predictions: Algorithms and Regret Analysis](https://mlsanity.com/paper/1906.11378/) (2019)
- [Safely Learning to Control the Constrained Linear Quadratic Regulator](https://mlsanity.com/paper/1809.10121/) (2018)
- [The Power of Predictions in Online Control](https://mlsanity.com/paper/2006.07569/) (2020)
- [On the Regret Analysis of Online LQR Control with Predictions](https://mlsanity.com/paper/2102.01309/) (2021)
- [From self-tuning regulators to reinforcement learning and back again](https://mlsanity.com/paper/1906.11392/) (2019)
- [Sample Complexity of Linear Quadratic Gaussian (LQG) Control for Output Feedback Systems](https://mlsanity.com/paper/2011.09929/) (2020)
- [Learning to Control Linear Systems can be Hard](https://mlsanity.com/paper/2205.14035/) (2022)
- [Optimization of the Model Predictive Control Meta-Parameters Through Reinforcement Learning](https://mlsanity.com/paper/2111.04146/) (2021)
- [Regret Analysis of Learning-Based MPC with Partially-Unknown Cost Function](https://mlsanity.com/paper/2108.02307/) (2021)
- [Predictive Control with Learning-Based Terminal Costs Using Approximate Value Iteration](https://mlsanity.com/paper/2212.00361/) (2022)
- [Adaptive Horizon Model Predictive Control](https://mlsanity.com/paper/1602.08619/) (2016)
- [Real-time Model Predictive Control and System Identification Using Differentiable Physics Simulation](https://mlsanity.com/paper/2202.09834/) (2022)
- [Online Learning for Predictive Control with Provable Regret Guarantees](https://mlsanity.com/paper/2111.15041/) (2021)
- [Performance Bounds of Model Predictive Control for Unconstrained and Constrained Linear Quadratic Problems and Beyond](https://mlsanity.com/paper/2211.06187/) (2022)
- [Stability and performance analysis of NMPC: Detectable stage costs and general terminal costs](https://mlsanity.com/paper/2110.11021/) (2021)
- [Performance bounds of adaptive MPC with bounded parameter uncertainties](https://mlsanity.com/paper/2111.07896/) (2021)

## Built on by (most cited first, 1 of 1)

- [Nonmyopic Global Optimisation via Approximate Dynamic Programming](https://mlsanity.com/paper/2412.04882/) (2024)

## Abstract (arXiv)

This work analyzes how the trade-off between the modeling error, the terminal value function error, and the prediction horizon affects the performance of a nominal receding-horizon linear quadratic (LQ) controller. By developing a novel perturbation result of the Riccati difference equation, a novel performance upper bound is obtained and suggests that for many cases, the prediction horizon can be either one or infinity to improve the control performance, depending on the relative difference between the modeling error and the terminal value function error. The result also shows that when an infinite horizon is desired, a finite prediction horizon that is larger than the controllability index can be sufficient for achieving a near-optimal performance, revealing a close relation between the prediction horizon and controllability. The obtained suboptimality performance upper bound is applied to provide novel sample complexity and regret guarantees for nominal receding-horizon LQ controllers in a learning-based setting. We show that an adaptive prediction horizon that increases as a logarithmic function of time is beneficial for regret minimization.