arXiv subjects

Peter Seiler

Publications and source records attributed to Peter Seiler.

At least 37 records · Page 2Linked to original sources

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.

eess.SY↗

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.

eess.SY↗

arXiv2025

Toward Engineering AGI: Benchmarking the Engineering Design Capabilities of LLMs

Modern engineering, spanning electrical, mechanical, aerospace, civil, and computer disciplines, stands as a cornerstone of human civilization and the foundation of our society. However, engineering design poses a fundamentally different challenge for large language models (LLMs) compared with traditional textbook-style problem solving or factual question answering. Although existing benchmarks have driven progress in areas such as language understanding, code synthesis, and scientific problem solving, real-world engineering design demands the synthesis of domain knowledge, navigation of complex trade-offs, and management of the tedious processes that consume much of practicing engineers' time. Despite these shared challenges across engineering disciplines, no benchmark currently captures the unique demands of engineering design work. In this work, we introduce EngDesign, an Engineering Design benchmark that evaluates LLMs' abilities to perform practical design tasks across nine engineering domains. Unlike existing benchmarks that focus on factual recall or question answering, EngDesign uniquely emphasizes LLMs' ability to synthesize domain knowledge, reason under constraints, and generate functional, objective-oriented engineering designs. Each task in EngDesign represents a real-world engineering design problem, accompanied by a detailed task description specifying design goals, constraints, and performance requirements. EngDesign pioneers a simulation-based evaluation paradigm that moves beyond textbook knowledge to assess genuine engineering design capabilities and shifts evaluation from static answer checking to dynamic, simulation-driven functional verification, marking a crucial step toward realizing the vision of engineering Artificial General Intelligence (AGI).

cs.CE↗

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 $μ$-synthesis problem. A numerical example is used to demonstrate the proposed approach.

math.OC↗

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.

physics.flu-dyn↗

arXiv2025

Robust Regret Optimal Control

This paper presents a synthesis method for robust, regret optimal control. The plant is modeled in discrete-time by an uncertain linear time-invariant (LTI) system. An optimal non-causal controller is constructed using the nominal plant model and given full knowledge of the disturbance. Robust regret is defined relative to the performance of this optimal non-causal control. It is shown that a controller achieves robust regret if and only if it satisfies a robust $H_\infty$ performance condition. DK-iteration can be used to synthesize a controller that satisfies this condition and hence achieve a given level of robust regret. The approach is demonstrated three examples: (i) a simple single-input, single-output classical design, (ii) a longitudinal control for a simplified model for a Boeing 747 model, and (iii) an active suspension for a quarter car model. All examples compare the robust regret optimal against regret optimal controllers designed without uncertainty.

math.OC↗

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.

eess.SY↗

arXiv2025

Safety Filter for Robust Disturbance Rejection via Online Optimization

Disturbance rejection in high-precision control applications can be significantly improved upon via online convex optimization (OCO). This includes classical techniques such as recursive least squares (RLS) and more recent, regret-based formulations. However, these methods can cause instabilities in the presence of model uncertainty. This paper introduces a safety filter for systems with OCO in the form of adaptive finite impulse response (FIR) filtering to ensure robust disturbance rejection. The safety filter enforces a robust stability constraint on the FIR coefficients while minimally altering the OCO command in the $\infty$-norm cost. Additionally, we show that the induced $\ell_\infty$-norm allows for easy online implementation of the safety filter by directly limiting the OCO command. The constraint can be tuned to trade off robustness and performance. We provide a simple example to demonstrate the safety filter.

eess.SY↗

arXiv2025

Structured Input-Output Modeling and Robust Stability Analysis of Compressible Flows

The recently introduced structured input-output analysis is a powerful method for capturing nonlinear phenomena associated with incompressible flows, and this paper extends that method to the compressible regime. The proposed method relies upon a reformulation of the compressible Navier-Stokes equations, which allows for an exact quadratic formulation of the dynamics of perturbations about a steady base flow. To facilitate the structured input-output analysis, a pseudo-linear model for the quadratic nonlinearity is proposed and the structural information of the nonlinearity is embedded into a structured uncertainty comprising unknown `perturbations'. The structured singular value framework is employed to compute the input-output gain, which provides an estimate of the robust stability margin of the flow perturbations, as well as the forcing and response modes that are consistent with the nonlinearity structure. The analysis is then carried out on a plane, laminar compressible Couette flow over a range of Mach numbers. The structured input-output gains identify an instability mechanism, characterized by a spanwise elongated structure in the streamwise-spanwise wavenumber space at a subsonic Mach number, that takes the form of an oblique structure at sonic and supersonic Mach numbers. In addition, the structured input-output forcing and response modes provide insight into the thermodynamic and momentum characteristics associated with a source of instability. Comparisons with a resolvent/unstructured analysis reveal discrepancies in the distribution of input-output gains over the wavenumber space as well as in the modal behavior of an instability, thus highlighting the strong correlation between the structural information of the nonlinearity and the underlying flow physics.

physics.flu-dyn↗

arXiv2024

ControlAgent: Automating Control System Design via Novel Integration of LLM Agents and Domain Expertise

Control system design is a crucial aspect of modern engineering with far-reaching applications across diverse sectors including aerospace, automotive systems, power grids, and robotics. Despite advances made by Large Language Models (LLMs) in various domains, their application in control system design remains limited due to the complexity and specificity of control theory. To bridge this gap, we introduce ControlAgent, a new paradigm that automates control system design via novel integration of LLM agents and control-oriented domain expertise. ControlAgent encodes expert control knowledge and emulates human iterative design processes by gradually tuning controller parameters to meet user-specified requirements for stability, performance, and robustness. ControlAgent integrates multiple collaborative LLM agents, including a central agent responsible for task distribution and task-specific agents dedicated to detailed controller design for various types of systems and requirements. ControlAgent also employs a Python computation agent that performs complex calculations and controller evaluations based on standard design information provided by task-specified LLM agents. Combined with a history and feedback module, the task-specific LLM agents iteratively refine controller parameters based on real-time feedback from prior designs. Overall, ControlAgent mimics the design processes used by (human) practicing engineers, but removes all the human efforts and can be run in a fully automated way to give end-to-end solutions for control system design with user-specified requirements. To validate ControlAgent's effectiveness, we develop ControlEval, an evaluation dataset that comprises 500 control tasks with various specific design goals. The effectiveness of ControlAgent is demonstrated via extensive comparative evaluations between LLM-based and traditional human-involved toolbox-based baselines.

eess.SY↗

arXiv2024

Stability Margins of Neural Network Controllers

We present a method to train neural network controllers with guaranteed stability margins. The method is applicable to linear time-invariant plants interconnected with uncertainties and nonlinearities that are described by integral quadratic constraints. The type of stability margin we consider is the disk margin. Our training method alternates between a training step to maximize reward and a stability margin-enforcing step. In the stability margin enforcing-step, we solve a semidefinite program to project the controller into the set of controllers for which we can certify the desired disk margin.

eess.SY↗

arXiv2024

A Complete Set of Quadratic Constraints for Repeated ReLU and Generalizations

This paper derives a complete set of quadratic constraints (QCs) for the repeated ReLU. The complete set of QCs is described by a collection of matrix copositivity conditions. We also show that only two functions satisfy all QCs in our complete set: the repeated ReLU and flipped ReLU. Thus our complete set of QCs bounds the repeated ReLU as tight as possible up to the sign invariance inherent in quadratic forms. We derive a similar complete set of incremental QCs for repeated ReLU, which can potentially lead to less conservative Lipschitz bounds for ReLU networks than the standard LipSDP approach. The basic constructions are also used to derive the complete sets of QCs for other piecewise linear activation functions such as leaky ReLU, MaxMin, and HouseHolder. Finally, we illustrate the use of the complete set of QCs to assess stability and performance for recurrent neural networks with ReLU activation functions. We rely on a standard copositivity relaxation to formulate the stability/performance condition as a semidefinite program. Simple examples are provided to illustrate that the complete sets of QCs and incremental QCs can yield less conservative bounds than existing sets.

cs.LG↗

arXiv2024

Analysis of Gradient Descent with Varying Step Sizes using Integral Quadratic Constraints

The framework of Integral Quadratic Constraints (IQCs) is used to perform an analysis of gradient descent with varying step sizes. Two performance metrics are considered: convergence rate and noise amplification. We assume that the step size is produced from a line search and varies in a known interval. Modeling the algorithm as a linear, parameter-varying (LPV) system, we construct a parameterized linear matrix inequality (LMI) condition that certifies algorithm performance, which is solved using a result for polytopic LPV systems. Our results provide convergence rate guarantees when the step size lies within a restricted interval. Moreover, we recover existing rate bounds when this interval reduces to a single point, i.e. a constant step size. Finally, we note that the convergence rate depends only on the condition number of the problem. In contrast, the noise amplification performance depends on the individual values of the strong convexity and smoothness parameters, and varies inversely with them for a fixed condition number.

math.OC↗

arXiv2024

Learning Reduced-Order Linear Parameter-Varying Models of Nonlinear Systems

In this paper, we consider the learning of a Reduced-Order Linear Parameter-Varying Model (ROLPVM) of a nonlinear dynamical system based on data. This is achieved by a two-step procedure. In the first step, we learn a projection to a lower dimensional state-space. In step two, an LPV model is learned on the reduced-order state-space using a novel, efficient parameterization in terms of neural networks. The improved modeling accuracy of the method compared to an existing method is demonstrated by simulation examples.

eess.SY↗

arXiv2024

Stability and Performance Analysis of Discrete-Time ReLU Recurrent Neural Networks

This paper presents sufficient conditions for the stability and $\ell_2$-gain performance of recurrent neural networks (RNNs) with ReLU activation functions. These conditions are derived by combining Lyapunov/dissipativity theory with Quadratic Constraints (QCs) satisfied by repeated ReLUs. We write a general class of QCs for repeated RELUs using known properties for the scalar ReLU. Our stability and performance condition uses these QCs along with a "lifted" representation for the ReLU RNN. We show that the positive homogeneity property satisfied by a scalar ReLU does not expand the class of QCs for the repeated ReLU. We present examples to demonstrate the stability / performance condition and study the effect of the lifting horizon.

eess.SY↗

arXiv2024

Robust Online Convex Optimization for Disturbance Rejection

Online convex optimization (OCO) is a powerful tool for learning sequential data, making it ideal for high precision control applications where the disturbances are arbitrary and unknown in advance. However, the ability of OCO-based controllers to accurately learn the disturbance while maintaining closed-loop stability relies on having an accurate model of the plant. This paper studies the performance of OCO-based controllers for linear time-invariant (LTI) systems subject to disturbance and model uncertainty. The model uncertainty can cause the closed-loop to become unstable. We provide a sufficient condition for robust stability based on the small gain theorem. This condition is easily incorporated as an on-line constraint in the OCO controller. Finally, we verify via numerical simulations that imposing the robust stability condition on the OCO controller ensures closed-loop stability.

eess.SY↗

arXiv2024

Fast Assignment in Asset-Guarding Engagements using Function Approximation

This letter considers assignment problems consisting of n pursuers attempting to intercept n targets. We consider stationary targets as well as targets maneuvering toward an asset. The assignment algorithm relies on an n x n cost matrix where entry (i, j) is the minimum time for pursuer i to intercept target j. Each entry of this matrix requires the solution of a nonlinear optimal control problem. This subproblem is computationally intensive and hence the computational cost of the assignment is dominated by the construction of the cost matrix. We propose to use neural networks for function approximation of the minimum time until intercept. The neural networks are trained offline, thus allowing for real-time online construction of cost matrices. Moreover, the function approximators have sufficient accuracy to obtain reasonable solutions to the assignment problem. In most cases, the approximators achieve assignments with optimal worst case intercept time. The proposed approach is demonstrated on several examples with increasing numbers of pursuers and targets.

eess.SY↗

arXiv2024

Capabilities of Large Language Models in Control Engineering: A Benchmark Study on GPT-4, Claude 3 Opus, and Gemini 1.0 Ultra

In this paper, we explore the capabilities of state-of-the-art large language models (LLMs) such as GPT-4, Claude 3 Opus, and Gemini 1.0 Ultra in solving undergraduate-level control problems. Controls provides an interesting case study for LLM reasoning due to its combination of mathematical theory and engineering design. We introduce ControlBench, a benchmark dataset tailored to reflect the breadth, depth, and complexity of classical control design. We use this dataset to study and evaluate the problem-solving abilities of these LLMs in the context of control engineering. We present evaluations conducted by a panel of human experts, providing insights into the accuracy, reasoning, and explanatory prowess of LLMs in control engineering. Our analysis reveals the strengths and limitations of each LLM in the context of classical control, and our results imply that Claude 3 Opus has become the state-of-the-art LLM for solving undergraduate control problems. Our study serves as an initial step towards the broader goal of employing artificial general intelligence in control engineering.

math.OC↗