# Learning-Based Optimal Control with Performance Guarantees for Unknown Systems with Latent States

arXiv: https://arxiv.org/abs/2303.17963 · HTML: https://mlsanity.com/paper/2303.17963/

## 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 31 Mar 2023.

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

- [Hilbert Space Methods for Reduced-Rank Gaussian Process Regression](https://mlsanity.com/paper/1401.5508/) (2014)
- [Nonlinear System Identification: A User-Oriented Roadmap](https://mlsanity.com/paper/1902.00683/) (2019)
- [Bayesian Inference and Learning in Gaussian Process State-Space Models with Particle MCMC](https://mlsanity.com/paper/1306.2861/) (2013)
- [Feedback Linearization based on Gaussian Processes with event-triggered Online Learning](https://mlsanity.com/paper/1911.06565/) (2019)
- [A flexible state space model for learning nonlinear dynamical systems](https://mlsanity.com/paper/1603.05486/) (2016)
- [Prediction with Approximated Gaussian Process Dynamical Models](https://mlsanity.com/paper/2006.14551/) (2020)
- [Stable Gaussian Process based Tracking Control of Euler-Lagrange Systems](https://mlsanity.com/paper/1806.07190/) (2018)
- [Distributed Bayesian Online Learning for Cooperative Manipulation](https://mlsanity.com/paper/2104.04342/) (2021)

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

- [Finite-Sample-Based Reachability for Safe Control with Gaussian Process Dynamics](https://mlsanity.com/paper/2505.07594/) (2025)
- [Barrier Certificates for Unknown Systems with Latent States and Polynomial Dynamics using Bayesian Inference](https://mlsanity.com/paper/2504.01807/) (2025)
- [Learning Dynamics from Infrequent Output Measurements for Uncertainty-Aware Optimal Control](https://mlsanity.com/paper/2512.08013/) (2025)

## Abstract (arXiv)

As control engineering methods are applied to increasingly complex systems, data-driven approaches for system identification appear as a promising alternative to physics-based modeling. While the Bayesian approaches prevalent for safety-critical applications usually rely on the availability of state measurements, the states of a complex system are often not directly measurable. It may then be necessary to jointly estimate the dynamics and the latent state, making the quantification of uncertainties and the design of controllers with formal performance guarantees considerably more challenging. This paper proposes a novel method for the computation of an optimal input trajectory for unknown nonlinear systems with latent states based on a combination of particle Markov chain Monte Carlo methods and scenario theory. Probabilistic performance guarantees are derived for the resulting input trajectory, and an approach to validate the performance of arbitrary control laws is presented. The effectiveness of the proposed method is demonstrated in a numerical simulation.