arXiv subjects

Peter Seiler

Publications and source records attributed to Peter Seiler.

At least 19 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 $\mu$-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

Data-Driven Stability and Performance Analysis of Lurye Systems

This paper develops data-driven conditions for certifying internal stability and induced-$\ell_2$ performance of discrete-time Lurye systems. The Lurye system is an interconnection of a nominal LTI system in feedback with a static, memoryless nonlinearity. The nonlinearity satisfies a known set of quadratic constraints on the inputs and outputs. Existing conditions for Lurye systems require a state-space realization of the nominal LTI dynamics. Our first data-driven result instead formulates the stability and performance conditions using finite input, output, and state trajectories of the nominal LTI block. Our second condition removes the need for measured state trajectories by reconstructing the state sequence, up to a similarity transformation, from input/output data. This state reconstruction is performed using deterministic subspace-identification techniques. Both data-driven conditions are expressed as convex semidefinite programs. These conditions, given sufficiently exciting inputs, recover the corresponding model-based Lurye condition in the noiseless setting. The proposed methods are illustrated via a simple example with a sector-bounded nonlinearity. Both proposed methods obtain the same induced-$\ell_2$ gain bound as the model-based approach while using only trajectory data from the nominal system.

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arXiv2026

Polynomial Constraints for Robustness Analysis of Nonlinear Systems

This paper presents a framework for abstracting uncertain or non-polynomial components of dynamical systems using polynomial constraints. This enables the application of polynomial-based analysis tools, such as sum-of-squares programming, to a broader class of non-polynomial systems. A numerical method for constructing these constraints is proposed. The relationship between polynomial constraints and existing integral quadratic constraints (IQCs) is investigated, providing transformations of IQCs into polynomial constraints. The effectiveness of polynomial constraints in characterizing nonlinearities is validated via numerical examples to compute inner estimates of the region of attraction for two systems.

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arXiv2026

Partial Attention in Deep Reinforcement Learning for Safe Multi-Agent Control

Attention mechanisms excel at learning sequential patterns by discriminating data based on relevance and importance. This provides state-of-the-art performance in advanced generative artificial intelligence models. This paper applies this concept of an attention mechanism for multi-agent safe control. We specifically consider the design of a neural network to control autonomous vehicles in a highway merging scenario. The environment is modeled as a Decentralized Partially Observable Markov Decision Process (Dec-POMDP). Within a QMIX framework, we include partial attention for each autonomous vehicle, thus allowing each ego vehicle to focus on the most relevant neighboring vehicles. Moreover, we propose a comprehensive reward signal that considers the global objectives of the environment (e.g., safety and vehicle flow) and the individual interests of each agent. Simulations are conducted in the Simulation of Urban Mobility (SUMO). The results show better performance compared to other driving algorithms in terms of safety, driving speed, and reward.

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arXiv2026

A Model Predictive Control Approach to Dual-Axis Agrivoltaic Panel Tracking

Agrivoltaic systems--photovoltaic (PV) panels installed above agricultural land--have emerged as a promising dual-use solution to address competing land demands for food and energy production. In this paper, we propose a model predictive control (MPC) approach to dual-axis agrivoltaic panel tracking control that dynamically adjusts panel positions in real time to maximize power production and crop yield given solar irradiance and ambient temperature measurements. We apply convex relaxations and shading factor approximations to reformulate the MPC optimization problem as a convex second-order cone program that determines the PV panel position adjustments away from the sun-tracking trajectory. Through case studies, we demonstrate our approach, exploring the Pareto front between i) an approach that maximizes power production without considering crop needs and ii) crop yield with no agrivoltaics. We also conduct a case study exploring the impact of forecast error on MPC performance. We find that dynamically adjusting agrivoltaic panel position helps us actively manage the trade-offs between power production and crop yield, and that active panel control enables the agrivoltaic system to achieve land equivalent ratio values of up to 1.897.

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arXiv2026

Integral Quadratic Constraints for Repeated ReLU

This paper presents a new dynamic integral quadratic constraint (IQC) for the repeated Rectified Linear Unit (ReLU). These dynamic IQCs can be used to analyze stability and induced $\ell_2$-gain performance of discrete-time, recurrent neural networks (RNNs) with ReLU activation functions. These analysis conditions can be incorporated into learning-based controller synthesis methods, which currently rely on static IQCs. We show that our proposed dynamic IQCs for repeated ReLU form a superset of the dynamic IQCs for repeated, slope-restricted nonlinearities. We also prove that the $\ell_2$-gain bounds are nonincreasing with respect to the horizon used in the dynamic IQC filter. A numerical example using a simple (academic) RNN shows that our proposed IQCs lead to less conservative bounds than existing IQCs.

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arXiv2026

Transformers As Generalizable Optimal Controllers

We study whether optimal state-feedback laws for a family of heterogeneous Multiple-Input, Multiple-Output (MIMO) Linear Time-Invariant (LTI) systems can be captured by a single learned controller. We train one transformer policy on LQR-generated trajectories from systems with different state and input dimensions, using a shared representation with standardization, padding, dimension encoding, and masked loss. The policy maps recent state history to control actions without requiring plant matrices at inference time. Across a broad set of systems, it achieves empirically small sub-optimality relative to Linear Quadratic Regulator (LQR), remains stabilizing under moderate parameter perturbations, and benefits from lightweight fine-tuning on unseen systems. These results support transformer policies as practical approximators of near-optimal feedback laws over structured linear-system families.

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arXiv2026

Parameterization of Seed Functions for Equivalent Representations of Time-Varying Delay Systems

Abel's classic transformation shows that any well-posed system with time-varying delay is equivalent to a parameter-varying system with fixed delay. The existence of such a parameter-varying constant delay representation then simplifies the problems of stability analysis and optimal control. Unfortunately, the method for construction of such transformations has been ad-hoc -- requiring an iterative time-stepping approach to constructing the transformation beginning with a seed function subject to boundary-value constraints. Moreover, a poor choice of seed function often results in a constant delay representation with large time-variations in system parameters -- obviating the benefits of such a representation. In this paper, we show how the set of all feasible seed functions can be parameterized using a basis for $L_2$. This parameterization is then used to search for seed functions for which the corresponding time-transformation results in smaller parameter variation. The parameterization of admissible seed functions is illustrated with numerical examples that contrast how well-chosen and poorly chosen seed functions affect the boundedness of a time transformation.

math.OC↗

arXiv2026

Time-Transformation-Based Analysis of Systems with Periodic Delay via Perturbative Expansion

It is difficult to analyze the stability of systems with time-varying delays. One approach is to construct a time-transformation that converts the system into a form with a constant delay but with a time-varying scalar appearing in the system matrices. The stability of this transformed system can then be analyzed using methods to bound the effect of the time-varying scalar. One issue is that this transformation is non-unique and requires the solution of an Abel equation. A specific time-transformation typically must be computed numerically. We address this issue by computing an explicit, although approximate, time-transformation for systems where the delay has a constant plus small periodic term. We use a perturbative expansion to construct our explicit solutions. We provide a simple numerical example to illustrate the approach. We also demonstrate the use of this time-transformation to analyze stability of the system with this class of periodic delays.

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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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arXiv2026

Regret of $H_\infty$ Preview Controllers

This paper studies preview control in both the $H_\infty$ and regret-optimal settings. The plant is modeled as a discrete-time, linear time-invariant system subject to external disturbances. The performance baseline is the optimal non-causal controller that has full knowledge of the disturbance sequence. We first review the construction of the $H_\infty$ preview controller with $p$-steps of disturbance preview. We then show that the closed-loop $H_\infty$ performance of this preview controller converges as $p\to \infty$ to the performance of the optimal non-causal controller. Furthermore, we prove that the optimal regret of the preview controller converges to zero. These results demonstrate that increasing preview length allows controllers to asymptotically achieve non-causal performance in both the $H_\infty$ and regret frameworks. A numerical example illustrates the theoretical results.

math.OC↗

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

On Boundedness of Quadratic Dynamics with Energy-Preserving Nonlinearity

Boundedness is an important property of many physical systems. This includes incompressible fluid flows, which are often modeled by quadratic dynamics with an energy-preserving nonlinearity. For such systems, Schlegel and Noack proposed a sufficient condition for boundedness utilizing quadratic Lyapunov functions. They also propose a necessary condition for boundedness aiming to provide a more complete characterization of boundedness in this class of models. The sufficient condition is based on Lyapunov theory and is true. Our paper focuses on this necessary condition. We use an independent proof to show that the condition is true for two dimensional systems. However, we provide a three dimensional counterexample to illustrate that the necessary condition fails to hold in higher dimensions. Our results highlight a theoretical gap in boundedness analysis and suggest future directions to address the conservatism.

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arXiv2025

Discrete-Time Stability Analysis of ReLU Feedback Systems via Integral Quadratic Constraints

This paper analyzes internal stability of a discrete-time feedback system with a ReLU nonlinearity. This feedback system is motivated by recurrent neural networks. We first review existing static quadratic constraints (QCs) for slope-restricted nonlinearities. Next, we derive hard integral quadratic constraints (IQCs) for scalar ReLU by using finite impulse filters and structured matrices. These IQCs are combined with a dissipation inequality leading to an LMI condition that certifies internal stability. We show that our new dynamic IQCs for ReLU are a superset of the well-known Zames-Falb IQCs specified for slope-restricted nonlinearities. Numerical results show that the proposed hard IQCs give less conservative stability margins than Zames-Falb multipliers and prior static QC methods, sometimes dramatically so.

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arXiv2025

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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arXiv2025

Robust Regret Control with Uncertainty-Dependent Baseline

This paper proposes a robust regret control framework in which the performance baseline adapts to the realization of system uncertainty. The plant is modeled as a discrete-time, uncertain linear time-invariant system with real-parametric uncertainty. The performance baseline is the optimal non-causal controller constructed with full knowledge of the disturbance and the specific realization of the uncertain plant. We show that a controller achieves robust additive regret relative to this baseline if and only if it satisfies a related, robust $H_\infty$ performance condition on a modified plant. One technical issue is that the modified plant can, in general, have a complicated nonlinear dependence on the uncertainty. We use a linear approximation step so that the robust additive regret condition can be recast as a standard $\mu$-synthesis problem. A numerical example is used to demonstrate the proposed approach.

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arXiv2025

Data-driven nonlinear aerodynamics models with certifiably optimal boundedness properties

Obtaining predictive low-order models is a central challenge in fluid dynamics. Data-driven frameworks have been widely used to obtain low-order models of aerodynamic systems; yet, resulting models tend to yield predictions that grow unbounded with time. Recently introduced stability-promoting methods can facilitate the identification of bounded models, but tend to require extensive brute-force tuning even in the context of simple academic systems. Here, we show how recent theoretical advances in the long-term boundedness of dynamical systems can be integrated into data-driven modeling frameworks to ensure that resulting models will yield bounded predictions of incompressible flows. Specifically, we propose to solve a specific set of convex semi-definite programming problems to (i) certify whether a system admits a globally attracting bounded set for the chosen modeling parameters, and (ii) compute a model with the optimal (tightest) bound on this globally attracting set. We demonstrate the approach via integration within the sparse identification of nonlinear dynamics (SINDy) modeling framework. Application on two low-order benchmark problems establishes the merits of the approach. We then apply our approach to obtain a low-order (6-mode) model of unsteady separation over a NACA-65(1)-412 airfoil at Re = 20, 0000, a flow that has been notoriously difficult to model using data-driven methods. The resulting model is found to accurately predict the dynamics of unsteady separation, with model predictions remaining bounded indefinitely. We anticipate this work will benefit future efforts in modeling strongly nonlinear flows, especially in settings where physically-viable long-term forecasts are paramount.

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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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