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Niklas Schmid

Publications and source records attributed to Niklas Schmid.

13 recordsLinked to original sources
arXiv2026

Bounded Linear Programs for Data-Driven Optimal Control via Moment-Matching

Linear programming (LP) formulations offer a conceptually elegant approach to infinite-horizon, model-free nonlinear optimal control in continuous spaces. However, in addition to the curse of dimensionality, their practical use is limited by the difficulty of consistently obtaining bounded solutions. In this work, we use moment-matching techniques to derive sufficient boundedness conditions in terms of the available dataset and the cost vector of the LP. Moreover, we discuss practical design methods for nonlinear systems and polynomial features.

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arXiv2026

Model-Agnostic Meta Learning for Differentiable MPC

Applying policy optimization to Model Predictive Control (MPC) yields high-performance and reliable controllers. However, the resulting controllers often overfit their training conditions and suffer significant performance degradation in unseen tasks. We propose a novel framework combining policy optimization with meta-learning to train highly adaptable MPC controllers. Our approach enables rapid adaptation to unseen tasks, maintaining high performance at a fraction of the computational cost required for full retraining. Furthermore, we integrate system identification into the pipeline to continuously refine both the MPC hyperparameters and the underlying predictive models. We validate our proposed methodology on a Ball-on-Plate system, demonstrating superior adaptability across various parameterized trajectory-tracking tasks.

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arXiv2026

Joint Chance Constrained Safe-Optimal Control

We consider the finite-time optimal control of stochastic systems subject to a probabilistic constraint on the trajectories' safety. Such formulations are known as joint chance constrained optimal control problems. The common practice is to jointly minimise the expected cost of all trajectories, safe and unsafe. This leads to policies which invite constraint violations to exploit low-cost unsafe trajectories. When constraints represent states of critical failure, such behaviour is undesirable. We demonstrate that this behaviour can be overcome by only minimizing the expected cost of safe trajectories. The underlying rationale follows a practical intuition: In many applications, the cost incurred by unsafe trajectories is irrelevant (e.g., the battery usage of a crashed quadcopter), and one is usually interested in minimizing the cost of trajectories that are safe. We show that this problem can be cast as a constrained Markov Decision Process over an augmented state space. This allows solving it via dynamic programming. We derive bounds on the policies' safety under errors resulting from gridding approximations when the system's state space is continuous. Finally, we empirically compare dynamic programming as well as reinforcement learning solutions on a simulated 2D unicycle system in cluttered reach-avoid environments.

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arXiv2026

Meta-Learning for Rapid Adaptation in Reference Tracking of Uncertain Nonlinear Systems

In this paper, we address the problem of reference tracking for uncertain nonlinear systems. Since collecting data from the target system (i.e., the system of interest) is often challenging, our objective is to design optimal controllers using limited target system data. Meta-learning provides a promising paradigm by leveraging offline data from source systems (systems sharing structural similarities with the target system) to accelerate training and enhance control performance. Motivated by this idea, we propose a meta-learning-based control framework that tailors the implicit model-agnostic meta-learning (iMAML) algorithm to the control setting. The framework operates in two phases: an (offline) meta-training phase, where an aggregated representation is learned from source data to capture the shared system dynamics among similar systems, and an (online) meta-adaptation phase, where this representation is fine-tuned on the target system using only a few data samples and limited adaptation steps. We formulate this framework as a bi-level optimization problem and provide an efficient solution with reduced storage complexity and few approximations. The proposed framework is general, allowing various learning algorithms to be integrated. To demonstrate this flexibility, we propose two specific learning algorithms that can be incorporated into our framework based on a neural state-space model and a deep Q-network, respectively. The primary distinction between these approaches is whether explicit system identification is required. Numerical simulations and hardware experiments demonstrate that the proposed methods enhance control performance and consistently outperform baseline approaches.

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arXiv2026

Maximizing Reach-Avoid Probabilities for Linear Stochastic Systems via Control Architectures

The maximization of reach-avoid probabilities for stochastic systems is a central topic in the control literature. Yet, the available methods are either restricted to low-dimensional systems or suffer from conservative approximations. To address these limitations, we propose control architectures that combine the flexibility of Markov Decision Processes with the scalability of Model Predictive Controllers. The Model Predictive Controller tracks reference signals while remaining agnostic to the stochasticity and reach-avoid objective. Instead, the reach-avoid probability is maximized by optimally updating the controller's reference online. To achieve this, the closed-loop system, consisting of the system and Model Predictive Controller, is abstracted as a Markov Decision Process in which a new reference can be chosen at every time-step. A feedback policy generating optimal references is then computed via Dynamic Programming. If the state space of the system is continuous, the Dynamic Programming algorithm must be executed on a finite system approximation. Modifications to the Model Predictive Controller enable a computationally efficient robustification of the Dynamic Programming algorithm to approximation errors, preserving bounds on the achieved reach-avoid probability. The approach is validated on a perturbed 12D quadcopter model in cluttered reach-avoid environments proving its flexibility and scalability.

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arXiv2026

Parameter-Robust MPPI for Safe Online Learning of Unknown Parameters

Robots deployed in dynamic environments must remain safe even when key physical parameters are uncertain or change over time. We propose Parameter-Robust Model Predictive Path Integral (PRMPPI) control, a framework that integrates online parameter learning with probabilistic safety constraints. PRMPPI maintains a particle-based belief over parameters via Stein Variational Gradient Descent, evaluates safety constraints using Conformal Prediction, and optimizes both a nominal performance-driven and a safety-focused backup trajectory in parallel. This yields a controller that is cautious at first, improves performance as parameters are learned, and ensures safety throughout. Simulation and hardware experiments demonstrate higher success rates, lower tracking error, and more accurate parameter estimates than baselines.

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arXiv2025

Distributionally Robust Optimization over Wasserstein Balls with i.i.d. Structure

We consider distributionally robust optimization problems where the uncertainty is modeled via a structured Wasserstein ambiguity set. Specifically, the ambiguity is restricted to product measures $P^{\otimes N}$, where $P$ lies within a Wasserstein ball centered at an empirical distribution $\widehat{P}$. This structure reflects the assumption of independent and identically distributed (i.i.d.) uncertainty components and yields a non-convex ambiguity set that is strictly contained in its unstructured counterpart, thereby reducing conservatism. The resulting optimization problem is generally intractable due to the loss of convexity. We address this by introducing a sequence of tractable convex relaxations, each admitting strong duality, and prove that this sequence converges to the original problem value under suitable conditions. Numerical examples are provided to illustrate the effectiveness of the proposed approach. As a byproduct of our proofs, we establish a novel formula, of independent interest, relating the Wasserstein distance of a mixture of product distributions to the Wasserstein distance between its constituent measures.

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arXiv2024

Peak Time-Windowed Risk Estimation of Stochastic Processes

This paper develops a method to upper-bound extreme-values of time-windowed risks for stochastic processes. Examples of such risks include the maximum average or 90% quantile of the current along a transmission line in any 5-minute window. This work casts the time-windowed risk analysis problem as an infinite-dimensional linear program in occupation measures. In particular, we employ the coherent risk measures of the mean and the expected shortfall (conditional value at risk) to define the maximal time-windowed risk along trajectories. The infinite-dimensional linear program must then be truncated into finite-dimensional optimization problems, such as by using the moment-sum of squares hierarchy of semidefinite programs. The infinite-dimensional linear program will have the same optimal value as the original nonconvex risk estimation task under compactness and regularity assumptions, and the sequence of semidefinite programs will converge to the true value under additional properties of algebraic characterization. The scheme is demonstrated for risk analysis of example stochastic processes.

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arXiv2024

Joint Chance Constrained Optimal Control via Linear Programming

We establish a linear programming formulation for the solution of joint chance constrained optimal control problems over finite time horizons. The joint chance constraint may represent an invariance, reachability or reach-avoid specification that the trajectory must satisfy with a predefined probability. For finite state and action spaces, the solution is exact and our method computationally superior to approaches in the literature. For continuous state or action spaces, our linear programming formulation enables basis function approximations.

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arXiv2023

Computing Optimal Joint Chance Constrained Control Policies

We consider the problem of optimally controlling stochastic, Markovian systems subject to joint chance constraints over a finite-time horizon. For such problems, standard Dynamic Programming is inapplicable due to the time correlation of the joint chance constraints, which calls for non-Markovian, and possibly stochastic, policies. Hence, despite the popularity of this problem, solution approaches capable of providing provably-optimal and easy-to-compute policies are still missing. We fill this gap by augmenting the dynamics via a binary state, allowing us to characterize the optimal policies and develop a Dynamic Programming based solution method.

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arXiv2023

Parallel Model Predictive Control for Deterministic Systems

In this note, we consider infinite horizon optimal control problems with deterministic systems. Since exact solutions to these problems are often intractable, we propose a parallel model predictive control (MPC) method that provides an approximate solution. Our method computes multiple lookahead minimization problems at each time, where each minimization may involve a different number of lookahead steps, and terminal cost and constraint. The policy computed via parallel MPC applies the first control of the lookahead minimization with the lowest cost. We show that the proposed method can harnesses the power of multiple computing units. Moreover, we prove that the policy computed via parallel MPC has better performance guarantee than that computed via the single lookahead minimization involved in parallel MPC.

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arXiv2022

A real-time GP based MPC for quadcopters with unknown disturbances

Gaussian Process (GP) regressions have proven to be a valuable tool to predict disturbances and model mismatches and incorporate this information into a Model Predictive Control (MPC) prediction. Unfortunately, the computational complexity of inference and learning on classical GPs scales cubically, which is intractable for real-time applications. Thus GPs are commonly trained offline, which is not suited for learning disturbances as their dynamics may vary with time. Recently, state-space formulation of GPs has been introduced, allowing inference and learning with linear computational complexity. This paper presents a framework that enables online learning of disturbance dynamics on quadcopters, which can be executed within milliseconds using a state-space formulation of GPs. The obtained disturbance predictions are combined with MPC leading to a significant performance increase in simulations with jMAVSim. The computational burden is evaluated on a Raspberry Pi 4 B to prove the real-time applicability.

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