Peter Seiler
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View article: An Exact, Finite Dimensional Representation for Full-Block, Circle Criterion Multipliers
An Exact, Finite Dimensional Representation for Full-Block, Circle Criterion Multipliers Open
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-rep…
View article: Discrete-Time Stability Analysis of ReLU Feedback Systems via Integral Quadratic Constraints
Discrete-Time Stability Analysis of ReLU Feedback Systems via Integral Quadratic Constraints Open
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-restr…
View article: Robust Time-Varying Control Barrier Functions with Sector-Bounded Nonlinearities
Robust Time-Varying Control Barrier Functions with Sector-Bounded Nonlinearities Open
This paper presents a novel approach for ensuring safe operation of systems subject to input nonlinearities and time-varying safety constraints. We formulate robust time-varying control barrier functions by combining two ingredients: (i) t…
View article: Safety filter for robust disturbance rejection via online optimization
Safety filter for robust disturbance rejection via online optimization Open
View article: Control Synthesis Along Uncertain Trajectories Using Integral Quadratic Constraints
Control Synthesis Along Uncertain Trajectories Using Integral Quadratic Constraints Open
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 r…
View article: Toward Engineering AGI: Benchmarking the Engineering Design Capabilities of LLMs
Toward Engineering AGI: Benchmarking the Engineering Design Capabilities of LLMs Open
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 c…
View article: L2-Gain Stability Analysis via LMIs for Polytopic Systems with Sector-Bounded Memoryless Nonlinearities
L2-Gain Stability Analysis via LMIs for Polytopic Systems with Sector-Bounded Memoryless Nonlinearities Open
View article: Stochastic LQR Design With Disturbance Preview
Stochastic LQR Design With Disturbance Preview Open
This paper considers the discrete-time, stochastic LQR problem with $p$ steps of disturbance preview information where $p$ is finite. We first derive the solution for this problem on a finite horizon with linear, time-varying dynamics and …
View article: Safety Filter for Robust Disturbance Rejection via Online Optimization
Safety Filter for Robust Disturbance Rejection via Online Optimization Open
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 fo…
View article: ControlAgent: Automating Control System Design via Novel Integration of LLM Agents and Domain Expertise
ControlAgent: Automating Control System Design via Novel Integration of LLM Agents and Domain Expertise Open
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)…
View article: Stability Margins of Neural Network Controllers
Stability Margins of Neural Network Controllers Open
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 quadrat…
View article: Structured Input-Output Modeling and Robust Stability Analysis of Compressible Flows
Structured Input-Output Modeling and Robust Stability Analysis of Compressible Flows Open
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…
View article: A Complete Set of Quadratic Constraints for Repeated ReLU and Generalizations
A Complete Set of Quadratic Constraints for Repeated ReLU and Generalizations Open
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 com…
View article: Robust Online Convex Optimization for Disturbance Rejection
Robust Online Convex Optimization for Disturbance Rejection Open
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 contro…
View article: Stability and Performance Analysis of Discrete-Time ReLU Recurrent Neural Networks
Stability and Performance Analysis of Discrete-Time ReLU Recurrent Neural Networks Open
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 Quad…
View article: Synthesizing Neural Network Controllers with Closed-Loop Dissipativity Guarantees
Synthesizing Neural Network Controllers with Closed-Loop Dissipativity Guarantees Open
In this paper, a method is presented to synthesize neural network controllers such that the feedback system of plant and controller is dissipative, certifying performance requirements such as L2 gain bounds. The class of plants considered …
View article: Capabilities of Large Language Models in Control Engineering: A Benchmark Study on GPT-4, Claude 3 Opus, and Gemini 1.0 Ultra
Capabilities of Large Language Models in Control Engineering: A Benchmark Study on GPT-4, Claude 3 Opus, and Gemini 1.0 Ultra Open
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…
View article: Model-Free $μ$-Synthesis: A Nonsmooth Optimization Perspective
Model-Free $μ$-Synthesis: A Nonsmooth Optimization Perspective Open
In this paper, we revisit model-free policy search on an important robust control benchmark, namely $μ$-synthesis. In the general output-feedback setting, there do not exist convex formulations for this problem, and hence global optimality…
View article: Robust regret optimal control
Robust regret optimal control Open
Summary 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 …
View article: A Convex Optimization Approach to Compute Trapping Regions for Lossless Quadratic Systems
A Convex Optimization Approach to Compute Trapping Regions for Lossless Quadratic Systems Open
Quadratic systems with lossless quadratic terms arise in many applications, including models of atmosphere and incompressible fluid flows. Such systems have a trapping region if all trajectories eventually converge to and stay within a bou…
View article: Learning Reduced-Order Linear Parameter-Varying Models of Nonlinear Systems
Learning Reduced-Order Linear Parameter-Varying Models of Nonlinear Systems Open
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…
View article: Frequency-domain Gaussian Process Models for $H_\infty$ Uncertainties
Frequency-domain Gaussian Process Models for $H_\infty$ Uncertainties Open
Complex-valued Gaussian processes are commonly used in Bayesian frequency-domain system identification as prior models for regression. If each realization of such a process were an $H_\infty$ function with probability one, then the same mo…
View article: Learning Reduced-Order Linear Parameter-Varying Models of Nonlinear Systems
Learning Reduced-Order Linear Parameter-Varying Models of Nonlinear Systems Open
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…
View article: Integral Quadratic Constraints with Infinite-Dimensional Channels
Integral Quadratic Constraints with Infinite-Dimensional Channels Open
Modern control theory provides us with a spectrum of methods for studying the interconnection of dynamic systems using input-output properties of the interconnected subsystems. Perhaps the most advanced framework for such input-output anal…
View article: Robust Regret Optimal Control
Robust Regret Optimal Control Open
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 mo…
View article: On the convexity of static output feedback control synthesis for systems with lossless nonlinearities
On the convexity of static output feedback control synthesis for systems with lossless nonlinearities Open
Computing a stabilizing static output-feedback (SOF) controller is an NP-hard problem, in general. Yet, these controllers have amassed popularity in recent years because of their practical use in feedback control applications, such as flui…
View article: Exact Solution for the Rank-One Structured Singular Value with Repeated Complex Full-Block Uncertainty
Exact Solution for the Rank-One Structured Singular Value with Repeated Complex Full-Block Uncertainty Open
In this note, we present an exact solution for the structured singular value (SSV) of rank-one complex matrices with repeated complex full-block uncertainty. A key step in the proof is the use of Von Neumman's trace inequality. Previous wo…
View article: Integral Quadratic Constraints with Infinite-Dimensional Channels
Integral Quadratic Constraints with Infinite-Dimensional Channels Open
Modern control theory provides us with a spectrum of methods for studying the interconnection of dynamic systems using input-output properties of the interconnected subsystems. Perhaps the most advanced framework for such input-output anal…
View article: Trajectory-based Robustness Analysis for Nonlinear Systems
Trajectory-based Robustness Analysis for Nonlinear Systems Open
This paper considers the robustness of an uncertain nonlinear system along a finite-horizon trajectory. The uncertain system is modeled as a connection of a nonlinear system and a perturbation. The analysis relies on three ingredients. Fir…
View article: On the necessity and sufficiency of discrete-time O’Shea–Zames–Falb multipliers
On the necessity and sufficiency of discrete-time O’Shea–Zames–Falb multipliers Open