Jared F. Miller

selected publications

Theses

1. PhD

   Safety Quantification for Nonlinear and Time-Delay Systems using Occupation Measures

   Miller, Jared

   2023

   Abs Bib HTML PDF Poster Slides

   This research extends an occupation measure framework to analyze and quantify the safety of dynamical systems. A motivating application of trajectory analysis is in peak estimation, which finds the extreme values of a state function along trajectories. Examples of peak estimation include finding the maximum height of a wave, voltage on a power line, speed of a vehicle, and infected population in an epidemic. Peak estimation can be applied towards safety quantification, such as by measuring the safety of a trajectory by its distance of closest approach to an unsafe set. A finite-dimensional but nonconvex peak estimation problem can be converted into an infinite-dimensional linear program (LP) in measures, which is in turn bounded by a convergent sequence of semidefinite programs. The LP is posed in terms of an initial, a terminal, and an occupational measure, where the occupation measure contains all possible information about the dynamical systems’ trajectories. This research applies measure-based methods towards safety quantification (e.g. distance estimation, control effort needed to crash), hybrid systems, bounded-uncertain systems (including for data-driven analysis), stochastic systems, and time-delay systems. The modularity of this measure-based framework allows for multiple problem variations to be applied simultaneously (e.g., distance estimation under time-delays), and for optimization models to be synthesized using MATLAB. Solving these optimization problems results in certifiable guarantees on system performance and behavior.

   @phdthesis{miller2023thesis,
     title = {Safety Quantification for Nonlinear and Time-Delay Systems using Occupation Measures},
     author = {Miller, Jared},
     year = {2023},
     school = {Northeastern University},
     bibtex_show = {true},
     selected = {true},
     abbr = {PhD},
     pdf = {Thesis_Final.pdf},
     url = {https://repository.library.northeastern.edu/files/neu:4f196v79r},
     html = {https://repository.library.northeastern.edu/files/neu:4f196v79r},
     slides = {Thesis_Presentation_Merged.pdf},
     poster = {Safety_Poster__PhD_Expo.pdf},
     tag = {peakddc}
   }

Journal Articles

1. TAC

   Robust Data-Driven Control of Discrete-Time Linear Systems with Errors in Variables

   Miller, Jared, Dai, Tianyu, and Sznaier, Mario

   IEEE Transactions on Automatic Control 2024

   Abs arXiv Bib HTML Code Slides

   This work presents a Sum-of-Squares (SOS) based framework to perform data-driven stabilization and robust control tasks on discrete-time linear systems where the full-state observations are corrupted by L-infinity bounded input, measurement, and process noise (error in variable setting). Certificates of full-state-feedback robust performance, superstabilization or quadratic stabilization of all plants in a consistency set are provided by solving a feasibility program formed by polynomial nonnegativity constraints. Under mild compactness and data-collection assumptions, SOS tightenings in rising degree will converge to recover the true worst-case optimal L-infinity (extended) superstabilizing controllers. With some conservatism, quadratically stabilizing controllers with certified H2 performance bounds can also be found. The performance of this SOS method is improved through the application of a theorem of alternatives while retaining tightness, in which the unknown noise variables are eliminated from the consistency set description. This SOS feasibility method is extended to provide worst-case-optimal robust controllers under H2 control costs.

   @article{miller2024eiv,
     author = {Miller, Jared and Dai, Tianyu and Sznaier, Mario},
     journal = {IEEE Transactions on Automatic Control},
     title = {{Robust Data-Driven Control of Discrete-Time Linear Systems with Errors in Variables}},
     year = {2024},
     volume = {70},
     number = {2},
     pages = {947-962},
     abbr = {TAC},
     bibtex_show = {true},
     code = {https://github.com/jarmill/error_in_variables},
     keywords = {Noise;Symmetric matrices;Polynomials;Noise measurement;Linear matrix inequalities;Process control;Linear systems;Data-Driven Control;Robust Control;Optimization;Linear Matrix Inequality;Sum of Squares},
     url = {https://ieeexplore.ieee.org/document/10643715},
     href = {https://ieeexplore.ieee.org/document/10643715},
     html = {https://ieeexplore.ieee.org/document/10643715},
     selected = {true},
     tag = {ddc},
     slides = {EIV_Presentation__Austin.pdf},
     arxiv = {2210.13430},
     doi = {10.1109/TAC.2024.3447809}
   }

2. LCSS

   Data-Driven Gain Scheduling Control of Linear Parameter-Varying Systems using Quadratic Matrix Inequalities

   Miller, Jared, and Sznaier, Mario

   IEEE Control Systems Letters 2022

   Abs arXiv Bib HTML PDF Code

   This paper synthesizes a gain-scheduled controller to stabilize all possible Linear Parameter-Varying (LPV) plants that are consistent with measured input/state data records. Inspired by prior work in data informativity and LTI stabilization, a set of Quadratic Matrix Inequalities is developed to represent the noise set, the class of consistent LPV plants, and the class of stabilizable plants. The bilinearity between unknown plants and ‘for all’ parameters is avoided by vertex enumeration of the parameter set. Effectiveness and computational tractability of this method is demonstrated on example systems.

   @article{miller2022lpvqmi,
     title = {{Data-Driven Gain Scheduling Control of Linear Parameter-Varying Systems using Quadratic Matrix Inequalities}},
     author = {Miller, Jared and Sznaier, Mario},
     year = {2022},
     abbr = {LCSS},
     pdf = {LPVQMI_LCSS.pdf},
     eprint = {2209.06251},
     archiveprefix = {arXiv},
     primaryclass = {math.OC},
     tag = {ddc},
     bibtex_show = {true},
     journal = {IEEE Control Systems Letters},
     doi = {10.1109/LCSYS.2022.3227182},
     url = {https://ieeexplore.ieee.org/abstract/document/9971732},
     html = {https://ieeexplore.ieee.org/abstract/document/9971732},
     code = {https://github.com/Jarmill/lpv_qmi},
     arxiv = {2209.06251},
     selected = {true}
   }

Preprints

1. Structure, Analysis, and Synthesis of First-Order Algorithms

   Miller, Jared, Scherer, Carsten, Jakob, Fabian, and Iannelli, Andrea

   Preprint 2026

   Abs arXiv Bib PDF Code Slides

   Optimization algorithms can be interpreted through the lens of dynamical systems as the interconnection of linear systems and a set of subgradient nonlinearities. This dynamical systems formulation allows for the analysis and synthesis of optimization algorithms by solving robust control problems. In this work, we use the celebrated internal model principle in control theory to structurally factorize convergent composite optimization algorithms into suitable network-dependent internal models and core subcontrollers. As the key benefit, we reveal that this permits us to synthesize optimization algorithms even if information is transmitted over networks featuring dynamical phenomena such as time delays, channel memory, or crosstalk. Design of these algorithms is achieved under bisection in the exponential convergence rate either through a nonconvex local search or by alternation of convex semidefinite programs. We demonstrate factorization of existing optimization algorithms and the automated synthesis of new optimization algorithms in the networked setting.

   @preprint{miller2026structureanalysissynthesisfirstorder,
     title = {Structure, Analysis, and Synthesis of First-Order Algorithms},
     author = {Miller, Jared and Scherer, Carsten and Jakob, Fabian and Iannelli, Andrea},
     year = {2026},
     arxiv = {2603.24795},
     selected = {true},
     pdf = {structure_optimization.pdf},
     slides = {structure_algorithms_slides_KTH.pdf},
     archiveprefix = {arXiv},
     primaryclass = {math.OC},
     code = {https://github.com/Jarmill/constrained_opt},
     url = {https://arxiv.org/abs/2603.24795},
     bibtex_show = {true}
   }

2. Bounding the Minimal Current Harmonic Distortion in Optimal Modulation of Single-Phase Power Converters

   Miller, Jared, Karamanakos, Petros, and Geyer, Tobias

   Preprint 2025

   Abs arXiv Bib Code Poster Slides

   Optimal pulse patterns (OPPs) are a modulation technique in which a switching signal is computed offline through an optimization process that accounts for selected performance criteria, such as current harmonic distortion. The optimization determines both the switching angles (i.e., switching times) and the pattern structure (i.e., the sequence of voltage levels). This optimization task is a challenging mixed-integer nonconvex problem, involving integer-valued voltage levels and trigono metric nonlinearities in both the objective and the constraints. We address this challenge by reinterpreting OPP design as a periodic mode-selecting optimal control problem of a hybrid system, where selecting angles and levels corresponds to choosing jump times in a transition graph. This time-domain formulation enables the direct use of convex-relaxation techniques from optimal control, producing a hierarchy of semidefinite programs that lower-bound the minimal achievable harmonic distortion and scale subquadratically with the number of converter levels and switching angles. Numerical results demonstrate the effectiveness of the proposed approachs.

   @preprint{miller2025boundingminimalcurrentharmonic,
     title = {{Bounding the Minimal Current Harmonic Distortion in Optimal Modulation of Single-Phase Power Converters}},
     author = {Miller, Jared and Karamanakos, Petros and Geyer, Tobias},
     year = {2025},
     arxiv = {2512.08201},
     archiveprefix = {arXiv},
     bibtex_show = {true},
     selected = {true},
     slides = {opp_fau_erlangen.pdf},
     tag = {pe},
     primaryclass = {eess.SY},
     url = {https://arxiv.org/abs/2512.08201},
     code = {https://github.com/jarmill/opp_pop},
     poster = {OPP_Poster__CLOCK.pdf}
   }