arXiv subjects

Nicolas Hoischen

Publications and source records attributed to Nicolas Hoischen.

8 recordsLinked to original sources

arXiv2026

On the Existence of Quadratic Control Lyapunov Functions for Koopman-Operator based Bilinear Systems

Koopman operator-based methods enable data-driven bilinear representations of unknown nonlinear control systems. Accurate representations often demand significantly higher dimensions than the original system, making control design challenging. Control Lyapunov Functions (CLFs) are widely used for controller synthesis, with quadratic CLF candidates being the most common due to their simplicity. Yet, we show that this class is highly restrictive, especially when the state dimension is large: under mild conditions, their existence implies stabilizability of the bilinear system by a constant input -- that is, the control remains fixed over time. We establish this result by formulating a quadratically constrained quadratic program (QCQP) that exactly characterizes valid CLFs. Since QCQPs are NP-hard, we propose a convex semidefinite relaxation that offers a sufficient validity condition. For single-input systems, we prove that a quadratic CLF requires constant control stabilizability, and empirically demonstrate that this extends to high-dimensional multi-input systems in many cases.

eess.SY↗

arXiv2025

Operator Models for Continuous-Time Offline Reinforcement Learning

Continuous-time stochastic processes underlie many natural and engineered systems. In healthcare, autonomous driving, and industrial control, direct interaction with the environment is often unsafe or impractical, motivating offline reinforcement learning from historical data. However, there is limited statistical understanding of the approximation errors inherent in learning policies from offline datasets. We address this by linking reinforcement learning to the Hamilton-Jacobi-Bellman equation and proposing an operator-theoretic algorithm based on a simple dynamic programming recursion. Specifically, we represent our world model in terms of the infinitesimal generator of controlled diffusion processes learned in a reproducing kernel Hilbert space. By integrating statistical learning methods and operator theory, we establish global convergence of the value function and derive finite-sample guarantees with bounds tied to system properties such as smoothness and stability. Our theoretical and numerical results indicate that operator-based approaches may hold promise in solving offline reinforcement learning using continuous-time optimal control.

stat.ML↗

arXiv2025

Risk-Aware Trajectory Optimization and Control for an Underwater Suspended Robotic System

This paper focuses on the trajectory optimization of an underwater suspended robotic system comprising an uncrewed surface vessel (USV) and an uncrewed underwater vehicle (UUV) for autonomous litter collection. The key challenge lies in the significant uncertainty in drag and weight parameters introduced by the collected litter. We propose a dynamical model for the coupled UUV-USV system in the primary plane of motion and a risk-aware optimization approach incorporating parameter uncertainty and noise to ensure safe interactions with the environment. A stochastic optimization problem is solved using a conditional value-at-risk framework. Simulations demonstrate that our approach reduces collision risks and energy consumption, highlighting its reliability compared to existing control methods.

eess.SY↗

arXiv2024

Toward Near-Globally Optimal Nonlinear Model Predictive Control via Diffusion Models

Achieving global optimality in nonlinear model predictive control (NMPC) is challenging due to the non-convex nature of the underlying optimization problem. Since commonly employed local optimization techniques depend on carefully chosen initial guesses, this non-convexity often leads to suboptimal performance resulting from local optima. To overcome this limitation, we propose a novel diffusion model-based approach for near-globally optimal NMPC consisting of an offline and an online phase. The offline phase employs a local optimizer to sample from the distribution of optimal NMPC control sequences along generated system trajectories through random initial guesses. Subsequently, the generated diverse dataset is used to train a diffusion model to reflect the multi-modal distribution of optima. In the online phase, the trained model is leveraged to efficiently perform a variant of random shooting optimization to obtain near-globally optimal control sequences without relying on any initial guesses or online NMPC solving. The effectiveness of our approach is illustrated in a numerical simulation indicating high performance benefits compared to direct neural network approximations of NMPC and significantly lower computation times than online solving NMPC using global optimizers.

eess.SY↗

arXiv2024

Kernel-Based Optimal Control: An Infinitesimal Generator Approach

This paper presents a novel operator-theoretic approach for optimal control of nonlinear stochastic systems within reproducing kernel Hilbert spaces. Our learning framework leverages data samples of system dynamics and stage cost functions, with only control penalties and constraints provided. The proposed method directly learns the infinitesimal generator of a controlled stochastic diffusion in an infinite-dimensional hypothesis space. We demonstrate that our approach seamlessly integrates with modern convex operator-theoretic Hamilton-Jacobi-Bellman recursions, enabling a data-driven solution to the optimal control problems. Furthermore, our learning framework includes nonparametric estimators for uncontrolled infinitesimal generators as a special case. Numerical experiments, ranging from synthetic differential equations to simulated robotic systems, showcase the advantages of our approach compared to both modern data-driven and classical nonlinear programming methods for optimal control.

math.OC↗

arXiv2024

Data-Driven Stochastic Optimal Control in Reproducing Kernel Hilbert Spaces

This paper proposes a fully data-driven approach for optimal control of nonlinear control-affine systems represented by a stochastic diffusion. The focus is on the scenario where both the nonlinear dynamics and stage cost functions are unknown, while only a control penalty function and constraints are provided. To this end, we embed state probability densities into a reproducing kernel Hilbert space (RKHS) to leverage recent advances in operator regression, thereby identifying Markov transition operators associated with controlled diffusion processes. This operator learning approach integrates naturally with convex operator-theoretic Hamilton-Jacobi-Bellman recursions that scale linearly with state dimensionality, effectively solving a wide range of nonlinear optimal control problems. Numerical results demonstrate its ability to address diverse nonlinear control tasks, including the depth regulation of an autonomous underwater vehicle.

math.OC↗

arXiv2023

Safe Connectivity Maintenance of Underactuated Multi-Agent Networks in Dynamic Oceanic Environments

Autonomous multi-agent systems are increasingly being deployed in environments where winds and ocean currents have a significant influence. Recent work has developed control policies for single agents that leverage flows to achieve their objectives in dynamic environments. However, in multi-agent systems, these flows can cause agents to collide or drift apart and lose direct inter-agent communications, especially when agents have low propulsion capabilities. To address these challenges, we propose a hierarchical multi-agent control approach that allows arbitrary single-agent performance policies that are unaware of other agents to be used in multi-agent systems while ensuring safe operation. We first develop a safety controller using potential functions, solely dedicated to avoiding collisions and maintaining inter-agent communication. Next, we design a low-interference safe interaction (LISIC) policy that trades off the performance policy and the safety control to ensure safe and performant operation. Specifically, when the agents are at an appropriate distance, LISIC prioritizes the performance policy while smoothly increasing the safety controller when necessary. We prove that under mild assumptions on the flows experienced by the agents, our approach can guarantee safety. Additionally, we demonstrate the effectiveness of our method in realistic settings through an extensive empirical analysis with simulations of fleets of underactuated autonomous surface vehicles operating in dynamic ocean currents where these assumptions do not always hold.

eess.SY↗

arXiv2022

Reconfigurable Plug-and-play Distributed Model Predictive Control for Reference Tracking

A plug-and-play model predictive control (PnP MPC) scheme is proposed for varying-topology networks to track piecewise constant references. The proposed scheme allows subsystems to occasionally join and leave the network while preserving asymptotic stability and recursive feasibility and comprises two main phases. In the redesign phase, passivity-based control is used to ensure that asymptotic stability of the network is preserved. In the transition phase, reconfigurable terminal ingredients are used to ensure that the distributed MPC problem is initially feasible after the PnP operation. The efficacy of the proposed scheme is evaluated by applying it to a network of mass-spring-damper systems and comparing it to a benchmark scheme. It is found that the novel redesign phase results in faster PnP operations, whereas the novel transition phase increases flexibility by accepting more requests.

eess.SY↗