arXiv subjects

Felix Biertümpfel

Publications and source records attributed to Felix Biertümpfel.

11 recordsLinked to original sources

arXiv2026

Control of Decommissioned Satellites and Space Debris Using CubeSats with Ion Electrospray Engines

The emergence of the New Space era has led to a rapidly increasing number of satellites in Low Earth Orbit (LEO). Consequently, more stringent deorbiting requirements have recently been imposed to avoid the Kessler syndrome in LEO. This has resulted in the proposal of new concepts for space debris removal, including attaching CubeSats to space debris as a promising mitigation strategy. The initial phase of this strategy involves stabilizing and controlling the debris' attitude. This paper proposes an attitude control design for decommissioned satellites using attached CubeSats with staged ion electrospray engines (iESE). The compact design of iESE combined with staging provides increased reliability and mission durations. The large uncertainty in the dynamics of the combined system, i.e. satellite and attached CubeSats, poses a significant challenge to the control design. The approach taken here uses the robust control framework, specifically $μ$-synthesis, to tackle this challenge. The feasibility of the approach is demonstrated on a decommissioned satellite with multiple flexile appendages.

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arXiv2026

Backup Control Barrier Function Synthesis using Sum-of-Squares Reachability

Backup control barrier functions (bCBFs) enforce safety for input-constrained nonlinear systems using a pre-certified backup set and controller, but their performance depends strongly on this prescribed pair. This letter develops a constructive method for synthesizing a less conservative backup pair via finite horizon sum-of-squares (SOS) backward reachability. Starting from an initial backup set, we compute an SOS-certified finite horizon backward reachable set and controller that satisfy safety and input constraints while steering trajectories to the original backup set. We then provide conditions under which this certified set becomes a valid backup set for a piecewise backup controller. The resulting backup pair is integrated into the bCBF framework to certify larger safe sets.

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arXiv2026

Robust $\mathcal{H}_\infty$ Observer Design via Finsler's Lemma and IQCs

This paper develops a Finsler-based LMI for robust $\mathcal{H}_\infty$ observer design with integral quadratic constraints (IQCs) and block-structured uncertainty. By introducing a slack variable that relaxes the coupling between the Lyapunov matrix, the observer gain, and the IQC multiplier, the formulation addresses two limitations of the standard block-diagonal approach: the LMI requirement $\mathrm{He}(PA) \prec 0$ (which fails for marginally stable dynamics), and a multiplier--Lyapunov trade-off that causes infeasibility for wide uncertainty ranges. For marginally stable dynamics, artificial damping in the design model balances certified versus actual performance. The framework is demonstrated on quaternion attitude estimation with angular velocity uncertainty and mass-spring-damper state estimation with uncertain physical parameters.

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arXiv2026

Robust Time-Varying Control Barrier Functions with Sector-Bounded Nonlinearities

This paper presents a novel approach for ensuring safe operation of systems subject to input nonlinearities and time-varying safety constraints. We extend the time-varying barrier function framework to address time-varying safety constraints and explicitly account for control-dependent nonlinearities at the plant input. Guaranteed bounds on the input-output behavior of these nonlinearities are provided through pointwise-in-time quadratic constraints. The result is a class of robust time-varying control barrier functions that define a safety filter. This filter ensures robust safety for all admissible nonlinearities while minimally modifying the command generated by a baseline controller. We derive a second-order cone program (SOCP) to compute this safety filter online and provide novel feasibility conditions for ball-constrained inputs. The proposed approach is demonstrated on a spacecraft docking maneuver.

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arXiv2026

Method to Compute Pointing Displacement, Smear, and Jitter Covariances for Optical Payloads

This paper presents a method to assess the pointing and image motion performance of optical payloads in the presence of image displacement (shift), smear, and jitter. The method assumes the motion is a stationary random process over an image exposure interval. Displacement, smear, and jitter covariances are computed from the solution to a Lyapunov differential equation. These covariances parameterize statistical image motion modulation transfer functions (MTFs), and they can be used to verify pointing and image motion MTF requirements. The method in the present paper extends a previous method to include smear, as well as displacement, and hence jitter. The approach in the present paper also leads, as a special case, to a more efficient method to compute the displacement covariance than the previous method. Numerical examples illustrate the proposed method.

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arXiv2025

An Exact, Finite Dimensional Representation for Full-Block, Circle Criterion Multipliers

This paper provides the first finite-dimensional characterization for the complete set of full-block, circle criterion multipliers. We consider the interconnection of a discrete-time, linear time-invariant system in feedback with a non-repeated, sector-bounded nonlinearity. Sufficient conditions for stability and performance can be derived using: (i) dissipation inequalities, and (ii) Quadratic Constraints (QCs) that bound the input/output pairs of the nonlinearity. Larger classes of QCs (or multipliers) reduce the conservatism of the conditions. Full-block, circle criterion multipliers define the complete set of all possible QCs for non-repeated, sector-bounded nonlinearities. These provide the least conservative conditions. However, full-block multipliers are defined by an uncountably infinite number of constraints and hence do not lead to computationally tractable solutions if left in this raw form. This paper provides a new finite-dimensional characterization for the set of full-block, circle criterion multipliers. The key theoretical insight is: the set of all input/output pairs of non-repeated sector-bounded nonlinearities is equal to the set of all incremental pairs for an appropriately constructed piecewise linear function. Our new description for the complete set of multipliers only requires a finite number of matrix copositivity constraints. These conditions have an exact, computationally tractable implementation for problems where the nonlinearity has small input/output dimensions $(\le 4)$. We illustrate the use of our new characterization via a simple example.

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arXiv2025

Tube-Based Model Predictive Control with Random Fourier Features for Nonlinear Systems

This paper presents a computationally efficient approach for robust Model Predictive Control of nonlinear systems by combining Random Fourier Features with tube-based MPC. Tube-based Model Predictive Control provides robust constraint satisfaction under bounded model uncertainties arising from approximation errors and external disturbances. The Random Fourier Features method approximates nonlinear system dynamics by solving a numerically tractable least-squares problem, thereby reducing the approximation error. We develop the integration of RFF-based residual learning with tube MPC and demonstrate its application to an autonomous vehicle path-tracking problem using a nonlinear bicycle model. Compared to the linear baseline, the proposed method reduces the tube size by approximately 50%, leading to less conservative behavior and resulting in around 70% smaller errors in the test scenario. Furthermore, the proposed method achieves real-time performance while maintaining provable robustness guarantees.

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arXiv2025

A Robust Periodic Controller for Spacecraft Attitude Tracking

This paper presents a novel approach for robust periodic attitude control of satellites. Respecting the periodicity of the satellite dynamics in the synthesis allows to achieve constant performance and robustness requirements over the orbit. The proposed design follows a mixed sensitivity control design employing a physically motivated weighting scheme. The controller is calculated using a novel structured linear time-periodic output feedback synthesis with guaranteed optimal L2-performance. The synthesis poses a convex optimization problem and avoids grid-wise evaluations of coupling conditions inherent for classical periodic H-infinity-synthesis. Moreover, the controller has a transparent and easy to implement structure. A solar power plant satellite is used to demonstrate the effectiveness of the proposed method for periodic satellite attitude control.

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arXiv2025

Control Synthesis Along Uncertain Trajectories Using Integral Quadratic Constraints

The paper presents a novel approach to synthesize robust controllers for nonlinear systems along perturbed trajectories. The approach linearizes the system with respect to a reference trajectory. In contrast to existing methods rooted in robust linear time-varying synthesis, the approach accurately includes perturbations that drive the system away from the reference trajectory. Hence, the controller obtained in the linear framework provides a significantly more robust nonlinear performance. The calculation of the controller is derived from robust synthesis approaches rooted in the integral quadratic constraints framework. The feasibility of the approach is demonstrated on a pitch tracker design for a space launcher.

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arXiv2025

Linear Parameter Varying Attitude Control For CubeSats Using Electrospray Thrusters

This paper proposes the design of a single linear parameter-varying (LPV) controller for the attitude control of CubeSats using electro spray thrusters. CubeSat attitude control based on electro spray thrusters faces two main challenges. Firstly, the thruster can only generate a small control torque leading to easily saturating the actuation system. Secondly, CubeSats need to operate multiple different maneuvers from large to small slews to pointing tasks. LPV control is ideally suitable to address these challenges. The proposed design follows a mixed-sensitivity control scheme. The parameter-varying weights depend on the attitude error and are derived from the performance and robustness requirements of individual typical CubeSat maneuvers. The controller is synthesized by minimizing the induced L2-norm of the closed-loop interconnections between the controller and weighted plant. The performance and robustness of the controller is demonstrated on a simulation of the MIT Space Propulsion Lab's Magnetic Levitation CubeSat Testbed.

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arXiv2021

Finite Horizon Worst-Case Analysis of Linear Time-Varying Systems Applied to Launch Vehicle

This paper presents an approach to compute the worst-case gain of the interconnection of a finite time horizon linear time-variant system and a perturbation. The input/output behavior of the uncertainty is described by integral quadratic constraints (IQCs). A condition for the worst-case gain of such an interconnection can be formulated using dissipation theory as a parameterized Riccati differential equation, which depends on the chosen IQC multiplier. A nonlinear optimization problem is formulated to minimize the upper bound of the worst-case gain over a set of admissible IQC multipliers. This problem can be efficiently solved with a custom-tailored logarithm scaled, adaptive differential evolution algorithm. It provides a fast alternative to similar approaches based on solving semidefinite programs. The algorithm is applied to the worst-case aerodynamic load analysis for an expendable launch vehicle (ELV). The worst-case load of the uncertain ELV is calculated under wind turbulence during the atmospheric ascend and compared to results from nonlinear simulation.

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