Scalable Safety Maximization of Stochastic Systems
Real-world systems are often subject to uncertainties and disturbances, which may stem from external influences or dynamics which are hard to model. Accordingly, these effects are often difficult to predict and approximated as stochastic perturbations, which can lead to an unsafe control behavior if not properly managed.
I research control approaches for stochastic systems which maximize the probability of safety. My main focus is on the development of scalable algorithms for the analysis and control of high-dimensional systems. Therefore, I developed theory on approximate dynamic programming approaches as well as stochastic control architectures.
Selected publications:
- N. Schmid and J. Lygeros, "Probabilistic Reachability and Invariance Computation of Stochastic Systems using Linear Programming", 22nd IFAC World Congress, Yokohama, Japan, 2023. Arxiv-Link, Publisher-Link.
- N. Schmid, J. Choi, O. So, C. Fan, "Maximizing Reach-Avoid Probabilities for Linear Stochastic Systems via Control Architectures", Arxiv, 2025, Arxiv-Link.
Safety-Constrained Stochastic Systems
Beyond safety, systems are usually subject to performance objectives. However, there might be trade-offs between safety and performance. Designing controllers which trade-off risks against performance are challenging to compute, as they pose non-Markov constraints.
I proved that such problems can be reformulated as Markov Decision Processes on an augmented state space, which allows solving them using (approximate) dynamic programming approaches.
Selected publications:
- N. Schmid and J. Lygeros, "Computing Optimal Joint Chance Constrained Control Policies", Arxiv, 2023, Arxiv-Link, Publisher-Link.
- N. Schmid, M. Fochesato, T. Sutter and J. Lygeros, "Joint Chance Constrained Optimal Control via Linear Programming", IEEE Control Systems Letters, 2024. Arxiv-Link, Publisher-Link.
Stochastic Control for Biological Systems
Related to my theoretical work, I am interested in practical applications involving biological systems, such as medical instruments and precision agriculture. Not only do such systems have highly nonlinear dynamics, making them challenging to control. But they are also subject to biological variability, introducing uncertainties in the evolution of the system state.
I am currently working on the design and control of a hydroponics system, which is a soil-less cultivation method that allows for a precise control over plant growth conditions. The goal is to develop an optimal, learning-based control strategy that maximizes crop yield vs. resource usage (water, electricity). I further study the optimal fertilization of fields. Publications on these topics will become available in 2026.