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Torbjørn Cunis

Publications and source records attributed to Torbjørn Cunis.

17 recordsLinked to original sources
arXiv2026

Safe-by-Design: Approximate Nonlinear Model Predictive Control with Real Time Feasibility

This paper proposes a computationally lightweight, continuous-time receding-horizon nonlinear model predictive control (MPC) approach with infinitesimal prediction horizon. Unlike discrete-time one-step MPC schemes, this methodology permits the formulation of small-sized convex quadratic pro- grams (QPs) for feedback yet recovers the theoretical guarantees of quasi-infinite horizon MPC. The convex QP comes with a small computational footprint, which is advantageous for real- time application where runtime guarantees must be given. We demonstrate the effectiveness of the proposed approach when compared to other constrained control techniques through numerical experiments for nonlinear constrained spacecraft control.

math.OC↗
arXiv2026

Worst-Case Probability Bounds for Finite-Horizon Safety under Moment Uncertainty

This paper addresses the problem of estimating upper bounds on the probability that a dynamical system will enter an undesirable region at some point within a finite time horizon. The primary source of uncertainty lies in the system's initial state, for which only a finite set of moments is known or within a prescribed interval. To tackle this problem, we formulate a measure-based program and propose its relaxation using the moment-sum-of-squares (moment-SOS) framework. The corresponding dual problem is introduced as a functional program, which is subsequently strengthened into a sum-of-squares (SOS) program. Notably, this dual formulation bears a structural resemblance to classical barrier function techniques for certifying system safety, with the key distinction that it yields a probabilistic certificate. The effectiveness of the proposed approach is demonstrated through multiple case studies, including a case involving an object in orbit.

math.OC↗
arXiv2026

Input-to-state Stable Approximate Nonlinear Model Predictive Control with Realtime Feasibility

In this paper, a computationally lightweight approximate robust nonlinear model predictive control (NMPC) law is proposed based on a pair of input-to-state control Lyapunov function and robust control barrier function. The result builds upon and augments a recently introduced nominal infinitesimal- horizon NMPC scheme which permits small-sized quadratic programs to compute the feedback law for nonlinear constraint systems on embedded hardware in real time. Numerical experiments for nonlinear constrained spacecraft control and comparison to other robust NMPC schemes from the literature demonstrate the effectiveness of the proposed scheme.

eess.SY↗
arXiv2026

Sum-of-Squares Stability Verification on Manifolds with Applications in Spacecraft Attitude Control

In the context of spacecraft attitude control, parametrizations such as direction vectors or quaternions are often used to avoid singularities in the attitude representation. This, however, complicates the stability analysis of the system since, given the additional unit constraints, the resulting dynamics evolve on non-contractible manifolds. In this paper, we present a framework to verify almost global asymptotic stability of such systems using LaSalle's invariance principle and sum-of-squares programming, simplifying the search for Lyapunov functions. The framework is then applied to two examples: two-axis attitude acquisition utilizing aerodynamics in very low Earth orbits, and three-axis attitude acquisition for a satellite subject to gravity gradient torques in a circular orbit.

math.OC↗
arXiv2026

On the Practical Implementation of a Sequential Quadratic Programming Algorithm for Nonconvex Sum-of-squares Problems

Sum-of-squares (SOS) optimization provides a computationally tractable framework for certifying polynomial nonnegativity. If the considered problem is convex, the SOS problem can be transcribed into and solved by semi-definite programs. However, in case of nonconvex problems iterative procedures are needed. Yet tractable and efficient solution methods are still lacking, limiting their application, for instance, in control engineering. To address this gap, we propose a filter line search algorithm that solves a sequence of quadratic subproblems. Numerical benchmarks demonstrate that the algorithm can significantly reduce the number of iterations, resulting in a substantial decrease in computation time compared to established methods for nonconvex SOS programs

math.OC↗
arXiv2025

Novel Multi-objective Switched Model Predictive Control with Feasibility and Stability Guarantees

As the relevance of control systems capable of dealing with multiple objectives rises (e.g. being economic while maintaining a certain performance), multi-objective Switched Model Predictive Control combines all the advantages of Model Predictive Control while dealing with multiple objectives. We propose two novel frameworks, a nominal and a robust framework to guarantee recursive feasibility of each Model Predictive Controller under arbitrary switching and assure asymptotic stability of the closed-loop system applying the nominal framework and Input-to-State stability using the robust framework. The presented frameworks employ methods from switched systems, enabling the utilization of a supervisor control instance which allows for complex objectives and multi-objective control. Our numerical example confirms the superior performance of our proposed frameworks compared to a standard Model Predictive Control approach.

math.OC↗
arXiv2025

Virtual Target Trajectory Prediction for Stochastic Targets

Trajectory prediction of aerial vehicles is a key requirement in applications ranging from missile guidance to UAV collision avoidance. While most prediction methods assume deterministic target motion, real-world targets often exhibit stochastic behaviors such as evasive maneuvers or random gliding patterns. This paper introduces a probabilistic framework based on Conditional Normalizing Flows (CNFs) to model and predict such stochastic dynamics directly from trajectory data. The learned model generates probability distributions of future target positions conditioned on initial states and dynamic parameters, enabling efficient sampling and exact density evaluation. To provide deterministic surrogates compatible with existing guidance and planning algorithms, sampled trajectories are clustered using a time series k-means approach, yielding a set of representative "virtual target" trajectories. The method is target-agnostic, computationally efficient, and requires only trajectory data for training, making it suitable as a drop-in replacement for deterministic predictors. Simulated scenarios with maneuvering and ballistic targets demonstrate that the proposed approach bridges the gap between deterministic assumptions and stochastic reality, advancing guidance and control algorithms for autonomous vehicles.

cs.RO↗
arXiv2024

CaΣoS: A nonlinear sum-of-squares optimization suite

We present Ca$Σ$oS, the first MATLAB software specifically designed for nonlinear sum-of-squares optimization. A symbolic polynomial algebra system allows to formulate parametrized sum-of-squares optimization problems and facilitates their fast, repeated evaluations. To that extent, we make use of CasADi's symbolic framework and realize concepts of monomial sparsity, linear operators (including duals), and functions between polynomials. Ca$Σ$oS currently provides interfaces to the conic solvers SeDuMi, Mosek, and SCS as well as methods to solve quasiconvex optimization problems (via bisection) and nonconvex optimization problems (via sequential convexification). Numerical examples for benchmark problems including region-of-attraction and reachable set estimation for nonlinear dynamic systems demonstrate significant improvements in computation time compared to existing toolboxes. Ca$Σ$oS is available open-source at https://github.com/ifr-acso/casos.

math.OC↗
arXiv2024

Input-to-State Stability of Newton Methods for Generalized Equations in Nonlinear Optimization

We show that Newton methods for generalized equations are input-to-state stable with respect to disturbances such as due to inexact computations. We then use this result to obtain convergence and robustness of a multistep Newton-type method for multivariate generalized equations. We demonstrate the usefulness of the results with other applications to nonlinear optimization. In particular, we provide a new proof for (robust) local convergence of the augmented Lagrangian method.

math.OC↗
arXiv2023

Probabilistic Region-of-Attraction Estimation with Scenario Optimization and Converse Theorems

The region of attraction characterizes well-behaved and safe operation of a nonlinear system and is hence sought after for verification. In this paper, a framework for probabilistic region of attraction estimation is developed that combines scenario optimization and converse theorems. With this approach, the probability of an unstable condition being included in the estimate is independent of the system's complexity, while convergence in probability to the true region of attraction is proven. Numerical examples demonstrate the effectiveness for optimization-based control applications. Combining systems theory and sampling, the complexity of Monte--Carlo-based verification techniques can be reduced. The results can be extended to arbitrary level sets of which the defining function can be sampled, such as finite-horizon viability. Thus, the proposed approach is applicable and/or adaptable to verification of a wide range of safety-related properties for nonlinear systems including feedback laws based on optimization or learning.

math.OC↗
arXiv2023

Real-time Nonlinear Model Predictive Control using One-step Optimizations and Reachable Sets

Model predictive control allows solving complex control tasks with control and state constraints. However, an optimal control problem must be solved in real-time to predict the future system behavior, which is hardly possible on embedded hardware. To solve this problem, this paper proposes to compute a sequence of one-step optimizations aided by pre-computed inner approximations of reachable sets rather than solving the full-horizon optimal control problem at once. This feature can be used to virtually predict the future system behavior with a low computational footprint. Proofs for recursive feasibility and for the sufficient conditions for asymptotic stability under mild assumptions are given. The presented approach is demonstrated in simulation for functional verification.

eess.SY↗
arXiv2022

Sequential sum-of-squares programming for analysis of nonlinear systems

Numerous interesting properties in nonlinear systems analysis can be written as polynomial optimization problems with nonconvex sum-of-squares problems. To solve those problems efficiently, we propose a sequential approach of local linearizations leading to tractable, convex sum-of-squares problems. Local convergence is proven under the assumption of strong regularity and the new approach is applied to estimate the region of attraction of a polynomial aircraft model.

math.OC↗
arXiv2021

Nonlinear Trajectory-Based Region of Attraction Estimation for Aircraft Dynamics Analysis

Current flight control validation is heavily based on linear analysis and high fidelity, nonlinear simulations. Continuing developments of nonlinear analysis tools for flight control has greatly enhanced the validation process. Many analysis tools are reliant on assuming the analytical flight dynamics but this paper proposes an approach using only simulation data. First, this paper presents improvements to a method for estimating the region of attraction (ROA) of nonlinear systems governed by ordinary differential equations (ODEs) based only on trajectory measurements. Faster and more accurate convergence to the true ROA results. These improvements make the proposed algorithm feasible in higher-dimensional and more complex systems. Next, these tools are used to analyze the four-state longitudinal dynamics of NASA's Generic Transport Model (GTM) aircraft. A piecewise polynomial model of the GTM is used to simulate trajectories and the developed analysis tools are used to estimate the ROA around a trim condition based only on this trajectory data. Finally, the algorithm presented is extended to estimate the ROA of finitely many equilibrium point systems and of general equilibrium set (arbitrary equilibrium points and limit cycles) systems.

eess.SY↗
arXiv2021

Feasibility Governor for Linear Model Predictive Control

This paper introduces the Feasibility Governor (FG): an add-on unit that enlarges the region of attraction of Model Predictive Control by manipulating the reference to ensure that the underlying optimal control problem remains feasible. The FG is developed for linear systems subject to polyhedral state and input constraints. Offline computations using polyhedral projection algorithms are used to construct the feasibility set. Online implementation relies on the solution of a convex quadratic program that guarantees recursive feasibility. The closed-loop system is shown to satisfy constraints, achieve asymptotic stability, and exhibit zero-offset tracking.

math.OC↗
arXiv2020

A Feasibility Governor for Enlarging the Region of Attraction of Linear Model Predictive Controllers

This paper proposes a method for enlarging the region of attraction of Linear Model Predictive Controllers (MPC) when tracking piecewise-constant references in the presence of pointwise-in-time constraints. It consists of an add-on unit, the Feasibility Governor (FG), that manipulates the reference command so as to ensure that the optimal control problem that underlies the MPC feedback law remains feasible. Offline polyhedral projection algorithms based on multi-objective linear programming are employed to compute the set of feasible states and reference commands. Online, the action of the FG is computed by solving a convex quadratic program. The closed-loop system is shown to satisfy constraints, be asymptotically stable, exhibit zero-offset tracking, and display finite-time convergence of the reference.

math.OC↗
arXiv2016

First free-flight flow visualisation of a flapping-wing robot

Flow visualisations are essential to better understand the unsteady aerodynamics of flapping wing flight. The issues inherent to animal experiments, such as poor controllability and unnatural flapping when tethered, can be avoided by using robotic flyers. Such an approach holds a promise for a more systematic and repeatable methodology for flow visualisation, through a better controlled flight. Such experiments require high precision position control, however, and until now this was not possible due to the challenging flight dynamics and payload restrictions of flapping wing Micro Air Vehicles (FWMAV). Here, we present a new FWMAV-specific control approach that, by employing an external motion tracking system, achieved autonomous wind tunnel flight with a maximum root-mean-square position error of 28 mm at low speeds (0.8 - 1.2 m/s) and 75 mm at high speeds (2 - 2.4 m/s). This allowed the first free-flight flow visualisation experiments to be conducted with an FWMAV. Time-resolved stereoscopic Particle Image Velocimetry (PIV) was used to reconstruct the 3D flow patterns of the FWMAV wake. A good qualitative match was found in comparison to a tethered configuration at similar conditions, suggesting that the obtained free-flight measurements are reliable and meaningful.

physics.bio-ph↗