Publications (78)
Robustness against Adversarial Attacks in Neural Networks using Incremental Dissipativity
Bernardo Aquino, Arash Rahnama, Peter Seiler +2
Adversarial examples can easily degrade the classification performance in neural networks. Empirical methods for promoting robustness to such examples have been proposed, but often…
An Efficient Algorithm to Compute Norms for Finite Horizon, Linear Time-Varying Systems
Jyot Buch, Murat Arcak, Peter Seiler
We present an efficient algorithm to compute the induced norms of finite-horizon Linear Time-Varying (LTV) systems. The formulation includes both induced and termin…
Construction of Periodic Counterexamples to the Discrete-Time Kalman Conjecture
Peter Seiler, Joaquin Carrasco
This paper considers the Lurye system of a discrete-time, linear time-invariant plant in negative feedback with a nonlinearity. Both monotone and slope-restricted nonlinearities ar…
Backward Reachability using Integral Quadratic Constraints for Uncertain Nonlinear Systems
He Yin, Peter Seiler, Murat Arcak
A method is proposed to compute robust inner-approximations to the backward reachable set for uncertain nonlinear systems. It also produces a robust control law that drives traject…
Exact Solution for the Rank-One Structured Singular Value with Repeated Complex Full-Block Uncertainty
Talha Mushtaq, Peter Seiler, Maziar S. Hemati
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 proo…
Nonlinear Stability Analysis of Transitional Flows using Quadratic Constraints
Aniketh Kalur, Peter Seiler, Maziar S. Hemati
The dynamics of transitional flows are governed by an interplay between the non-normal linear dynamics and quadratic nonlinearity in the incompressible Navier-Stokes equations. In…
Frequency Domain Gaussian Process Models for Uncertainties
Alex Devonport, Peter Seiler, Murat Arcak
Complex-valued Gaussian processes are used in Bayesian frequency-domain system identification as prior models for regression. If each realization of such a process were an $H_\inft…
Trajectory-based Robustness Analysis for Nonlinear Systems
Peter Seiler, Raghu Venkataraman
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…
Robust Regret Control with Uncertainty-Dependent Baseline
Jietian Liu, Peter Seiler
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, un…
A Unified Analysis of Stochastic Optimization Methods Using Jump System Theory and Quadratic Constraints
Bin Hu, Peter Seiler, Anders Rantzer
We develop a simple routine unifying the analysis of several important recently-developed stochastic optimization methods including SAGA, Finito, and stochastic dual coordinate asc…
Optimal assignment of collaborating agents in multi-body asset-guarding games
Emmanuel Sin, Murat Arcak, Andrew Packard +2
We study a multi-body asset-guarding game in missile defense where teams of interceptor missiles collaborate to defend a non-manuevering asset against a group of threat missiles. W…
Nondegeneracy and Inexactness of Semidefinite Relaxations of Optimal Power Flow
Raphael Louca, Peter Seiler, Eilyan Bitar
The Optimal Power Flow (OPF) problem can be reformulated as a nonconvex Quadratically Constrained Quadratic Program (QCQP). There is a growing body of work on the use of semidefini…
Time-Transformation-Based Analysis of Systems with Periodic Delay via Perturbative Expansion
Jungbae Chun, Sengiyumva Kisole, Matthew M. Peet +1
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 constan…
Data-driven nonlinear aerodynamics models with certifiably optimal boundedness properties
A. Leonid Heide, Shih-Chi Liao, Sergio Castiblanco-Ballesteros +3
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,…
Learning Reduced-Order Linear Parameter-Varying Models of Nonlinear Systems
Patrick J. W. Koelewijn, Rajiv Sing, Peter Seiler +1
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 pro…
Method to Compute Pointing Displacement, Smear, and Jitter Covariances for Optical Payloads
Peter Seiler, Mark E. Pittelkau, Felix Biertümpfel
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 as…
SOSOPT: A Toolbox for Polynomial Optimization
Peter Seiler
SOSOPT is a Matlab toolbox for formulating and solving Sum-of-Squares (SOS) polynomial optimizations. This document briefly describes the use and functionality of this toolbox. Sec…
Polynomial Constraints for Robustness Analysis of Nonlinear Systems
Neelay Junnarkar, Peter Seiler, Murat Arcak
This paper presents a framework for abstracting uncertain or non-polynomial components of dynamical systems using polynomial constraints. This enables the application of polynomial…
Iterative Best Response for Multi-Body Asset-Guarding Games
Emmanuel Sin, Murat Arcak, Douglas Philbrick +1
We present a numerical approach to finding optimal trajectories for players in a multi-body, asset-guarding game with nonlinear dynamics and non-convex constraints. Using the Itera…
Conic-sector-based analysis and control synthesis for linear parameter varying systems
S Sivaranjani, James Richard Forbes, Peter Seiler +1
We present a conic sector theorem for linear parameter varying (LPV) systems in which the traditional definition of conicity is violated for certain values of the parameter. We sho…
Quadratic Constraints for Local Stability Analysis of Quadratic Systems
Shih-Chi Liao, Maziar S. Hemati, Peter Seiler
This paper proposes new quadratic constraints (QCs) to bound a quadratic polynomial. Such QCs can be used in dissipation ineqaulities to analyze the stability and performance of no…
Regret of Preview Controllers
Jietian Liu, Peter Seiler
This paper studies preview control in both the and regret-optimal settings. The plant is modeled as a discrete-time, linear time-invariant system subject to external dis…
Synthesis of Stabilizing Recurrent Equilibrium Network Controllers
Neelay Junnarkar, He Yin, Fangda Gu +2
We propose a parameterization of a nonlinear dynamic controller based on the recurrent equilibrium network, a generalization of the recurrent neural network. We derive constraints…
Model-Free -Synthesis: A Nonsmooth Optimization Perspective
Darioush Keivan, Xingang Guo, Peter Seiler +2
In this paper, we revisit model-free policy search on an important robust control benchmark, namely -synthesis. In the general output-feedback setting, there do not exist conve…
Tractable Reinforcement Learning of Signal Temporal Logic Objectives
Harish Venkataraman, Derya Aksaray, Peter Seiler
Signal temporal logic (STL) is an expressive language to specify time-bound real-world robotic tasks and safety specifications. Recently, there has been an interest in learning opt…
Transformers As Generalizable Optimal Controllers
Turki Bin Mohaya, Maitham F. AL-Sunni, John M. Dolan +1
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 le…
Model-Free Synthesis via Adversarial Reinforcement Learning
Darioush Keivan, Aaron Havens, Peter Seiler +2
Motivated by the recent empirical success of policy-based reinforcement learning (RL), there has been a research trend studying the performance of policy-based RL methods on standa…
Efficient Data Structures for Exploiting Sparsity and Structure in Representation of Polynomial Optimization Problems: Implementation in SOSTOOLS
Declan Jagt, Sachin Shivakumar, Peter Seiler +1
We present a new data structure for representation of polynomial variables in the parsing of sum-of-squares (SOS) programs. In SOS programs, the variables are polynomial i…
On the Necessity and Sufficiency of Discrete-Time O'Shea-Zames-Falb Multipliers
Lanlan Su, Peter Seiler, Joaquin Carrasco +1
This paper considers the robust stability of a discrete-time Lurye system consisting of the feedback interconnection between a linear system and a bounded and monotone nonlinearity…
Parameterization of Seed Functions for Equivalent Representations of Time-Varying Delay Systems
Sengiyumva Kisole, Jungbae Chun, Peter Seiler +1
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 paramet…
Revisiting PGD Attacks for Stability Analysis of Large-Scale Nonlinear Systems and Perception-Based Control
Aaron Havens, Darioush Keivan, Peter Seiler +2
Many existing region-of-attraction (ROA) analysis tools find difficulty in addressing feedback systems with large-scale neural network (NN) policies and/or high-dimensional sensing…
Toward Engineering AGI: Benchmarking the Engineering Design Capabilities of LLMs
Xingang Guo, Yaxin Li, Xiangyi Kong +62
Modern engineering, spanning electrical, mechanical, aerospace, civil, and computer disciplines, stands as a cornerstone of human civilization and the foundation of our society. Ho…
Frequency-domain Gaussian Process Models for Uncertainties
Alex Devonport, Peter Seiler, Murat Arcak
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…
A PIE Representation of Scalar Quadratic PDEs and Global Stability Analysis Using SDP
Declan Jagt, Peter Seiler, Matthew Peet
It has recently been shown that the evolution of a linear Partial Differential Equation (PDE) can be more conveniently represented in terms of the evolution of a higher spatial der…
Reachability Analysis Using Dissipation Inequalities For Uncertain Nonlinear Systems
He Yin, Andrew Packard, Murat Arcak +1
We propose a method to outer bound forward reachable sets on finite horizons for uncertain nonlinear systems with polynomial dynamics. This method makes use of time-dependent polyn…
A Complete Set of Quadratic Constraints for Repeated ReLU and Generalizations
Sahel Vahedi Noori, Bin Hu, Geir Dullerud +1
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 a…
Single Molecule Studies Under Constant Force Using Model Based Robust Control Design
Shreyas Bhaban, Saurav Talukdar, Mingang Li +3
Optical tweezers have enabled important insights into intracellular transport through the investigation of motor proteins, with their ability to manipulate particles at the microsc…
Discrete-Time Stability Analysis of ReLU Feedback Systems via Integral Quadratic Constraints
Sahel Vahedi Noori, Bin Hu, Geir Dullerud +1
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…
Imitation Learning with Stability and Safety Guarantees
He Yin, Peter Seiler, Ming Jin +1
A method is presented to learn neural network (NN) controllers with stability and safety guarantees through imitation learning (IL). Convex stability and safety conditions are deri…
Stochastic LQR Design With Disturbance Preview
Jietian Liu, Laurent Lessard, Peter Seiler
This paper considers the discrete-time, stochastic LQR problem with steps of disturbance preview information where is finite. We first derive the solution for this problem…
Integral Quadratic Constraints with Infinite-Dimensional Channels
Aleksandr Talitckii, Peter Seiler, Matthew M. Peet
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. Per…
Analysis of Biased Stochastic Gradient Descent Using Sequential Semidefinite Programs
Bin Hu, Peter Seiler, Laurent Lessard
We present a convergence rate analysis for biased stochastic gradient descent (SGD), where individual gradient updates are corrupted by computation errors. We develop stochastic qu…
Analysis of Gradient Descent with Varying Step Sizes using Integral Quadratic Constraints
Ram Padmanabhan, Peter Seiler
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: convergen…
Capabilities of Large Language Models in Control Engineering: A Benchmark Study on GPT-4, Claude 3 Opus, and Gemini 1.0 Ultra
Darioush Kevian, Usman Syed, Xingang Guo +5
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 contro…
Robust Online Convex Optimization for Disturbance Rejection
Joyce Lai, Peter Seiler
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 u…
Simplification Methods for Sum-of-Squares Programs
Peter Seiler, Qian Zheng, Gary Balas
A sum-of-squares is a polynomial that can be expressed as a sum of squares of other polynomials. Determining if a sum-of-squares decomposition exists for a given polynomial is equi…
Noncausal FIR Zames-Falb Multiplier Search for Exponential Convergence Rate
Jingfan Zhang, Peter Seiler, Joaquin Carrasco
In the existing literature, there are two approaches to estimate tighter bounds of the exponential convergence rate of stable Lure systems. On one hand, the classical integral quad…
Structured Singular Value of a Repeated Complex Full-Block Uncertainty
Talha Mushtaq, Diganta Bhattacharjee, Peter Seiler +1
The structured singular value (SSV), or mu, is used to assess the robust stability and performance of an uncertain linear time-invariant system. Existing algorithms compute upper a…
Partial Attention in Deep Reinforcement Learning for Safe Multi-Agent Control
Turki Bin Mohaya, Peter Seiler
Attention mechanisms excel at learning sequential patterns by discriminating data based on relevance and importance. This provides state-of-the-art performance in advanced generati…
Estimating Regions of Attraction for Transitional Flows using Quadratic Constraints
Aniketh Kalur, Talha Mushtaq, Peter Seiler +1
This letter describes a method for estimating regions of attraction and bounds on permissible perturbation amplitudes in nonlinear fluids systems. The proposed approach exploits qu…
Integral Quadratic Constraints for Repeated ReLU
Sahel Vahedi Noori, Bin Hu, Geir Dullerud +1
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…
Finite Horizon Robust Synthesis Using Integral Quadratic Constraints
Jyot Buch, Peter Seiler
We present a robust synthesis algorithm for uncertain linear time-varying (LTV) systems on finite horizons. The uncertain system is described as an interconnection of a known LTV s…
Recurrent Neural Network Controllers Synthesis with Stability Guarantees for Partially Observed Systems
Fangda Gu, He Yin, Laurent El Ghaoui +3
Neural network controllers have become popular in control tasks thanks to their flexibility and expressivity. Stability is a crucial property for safety-critical dynamical systems,…
Direct Synthesis of Iterative Algorithms With Bounds on Achievable Worst-Case Convergence Rate
Laurent Lessard, Peter Seiler
Iterative first-order methods such as gradient descent and its variants are widely used for solving optimization and machine learning problems. There has been recent interest in an…
An Introduction to Disk Margins
Peter Seiler, Andrew Packard, Pascal Gahinet
This paper provides a tutorial introduction to disk margins. These are robust stability measures that account for simultaneous gain and phase perturbations in a feedback system. Th…
Fast Assignment in Asset-Guarding Engagements using Function Approximation
Neelay Junnarkar, Emmanuel Sin, Peter Seiler +2
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.…
Stability and Performance Analysis of Discrete-Time ReLU Recurrent Neural Networks
Sahel Vahedi Noori, Bin Hu, Geir Dullerud +1
This paper presents sufficient conditions for the stability and -gain performance of recurrent neural networks (RNNs) with ReLU activation functions. These conditions are d…
An Exact, Finite Dimensional Representation for Full-Block, Circle Criterion Multipliers
Felix Biertümpfel, Bin Hu, Geir Dullerud +1
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-ti…
Robust Regret Optimal Control
Jietian Liu, Peter Seiler
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-…
Data-Driven Stability and Performance Analysis of Lurye Systems
Sahel Vahedi Noori, Peter Seiler
The paper proposes data‑driven convex conditions, based on input‑output trajectories, to certify internal stability and induced‑ℓ₂ performance of discrete‑time Lurye systems withou…
Stability Analysis using Quadratic Constraints for Systems with Neural Network Controllers
He Yin, Peter Seiler, Murat Arcak
A method is presented to analyze the stability of feedback systems with neural network controllers. Two stability theorems are given to prove asymptotic stability and to compute an…
Control Synthesis Along Uncertain Trajectories Using Integral Quadratic Constraints
Felix Biertümpfel, Peter Seiler, Harald Pfifer
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 refere…
On the convexity of static output feedback control synthesis for systems with lossless nonlinearities
Talha Mushtaq, Peter Seiler, Maziar S. Hemati
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 p…
Backward Reachability for Polynomial Systems on A Finite Horizon
He Yin, Murat Arcak, Andrew Packard +1
A method is presented to obtain an inner-approximation of the backward reachable set (BRS) of a given target tube, along with an admissible controller that maintains trajectories i…
ControlAgent: Automating Control System Design via Novel Integration of LLM Agents and Domain Expertise
Xingang Guo, Darioush Keivan, Usman Syed +5
Control system design is a crucial aspect of modern engineering with far-reaching applications across diverse sectors including aerospace, automotive systems, power grids, and robo…
Stability Margins of Neural Network Controllers
Neelay Junnarkar, Murat Arcak, Peter Seiler
We present a method to train neural network controllers with guaranteed stability margins. The method is applicable to linear time-invariant plants interconnected with uncertaintie…
Robust Control Barrier Functions with Sector-Bounded Uncertainties
Jyot Buch, Shih-Chi Liao, Peter Seiler
This paper focuses on safety critical control with sector-bounded uncertainties at the plant input. The uncertainties can represent nonlinear and/or time-varying components. We pro…
Safety Filter for Robust Disturbance Rejection via Online Optimization
Joyce Lai, Peter Seiler
Disturbance rejection in high-precision control applications can be significantly improved upon via online convex optimization (OCO). This includes classical techniques such as rec…
On Boundedness of Quadratic Dynamics with Energy-Preserving Nonlinearity
Shih-Chi Liao, Maziar S. Hemati, Peter Seiler
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 non…
Synthesizing Neural Network Controllers with Closed-Loop Dissipativity Guarantees
Neelay Junnarkar, Murat Arcak, Peter Seiler
This paper presents a method to synthesize neural network controllers to maximize reward subject to the hard constraint that the feedback system of plant and controller be dissipat…
Finite Horizon Robustness Analysis of LTV Systems Using Integral Quadratic Constraints
Peter Seiler, Robert Moore, Chris Meissen +2
The goal of this paper is to assess the robustness of an uncertain linear time-varying (LTV) system on a finite time horizon. The uncertain system is modeled as a connection of a k…
Structured Input-Output Modeling and Robust Stability Analysis of Compressible Flows
Diganta Bhattacharjee, Talha Mushtaq, Peter Seiler +1
The recently introduced structured input-output analysis is a powerful method for capturing nonlinear phenomena associated with incompressible flows, and this paper extends that me…
Finite Step Performance of First-order Methods Using Interpolation Conditions Without Function Evaluations
Bruce Lee, Peter Seiler
We present a procedure to numerically compute finite step worst case performance guarantees on a given algorithm for the unconstrained optimization of strongly convex functions wit…
Conditions for the equivalence between IQC and graph separation stability results
Joaquin Carrasco, Peter Seiler
This paper provides a link between time-domain and frequency-domain stability results in the literature. Specifically, we focus on the comparison between stability results for a fe…
Robust Time-Varying Control Barrier Functions with Sector-Bounded Nonlinearities
Felix Biertümpfel, Jungbae Chun, Peter Seiler
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…
An Overview of Integral Quadratic Constraints for Delayed Nonlinear and Parameter-Varying Systems
Harald Pfifer, Peter Seiler
A general framework is presented for analyzing the stability and performance of nonlinear and linear parameter varying (LPV) time delayed systems. First, the input/output behavior…
A Model Predictive Control Approach to Dual-Axis Agrivoltaic Panel Tracking
Anna Stuhlmacher, Panupong Srisuthankul, Johanna L. Mathieu +1
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…
Control Barrier Functions With Unmodeled Dynamics Using Integral Quadratic Constraints
Peter Seiler, Mrdjan Jankovic, Erik Hellstrom
This paper presents a control design method that achieves safety for systems with unmodeled dynamics at the plant input. The proposed method combines control barrier functions (CBF…