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 = {},
     number = {},
     pages = {1-15},
     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. TAC

   Bounding the Distance to Unsafe Sets with Convex Optimization

   Miller, Jared, and Sznaier, Mario

   IEEE Transactions on Automatic Control 2023

   Abs arXiv Bib PDF Code Slides

   This work proposes an algorithm to bound the minimum distance between points on trajectories of a dynamical system and points on an unsafe set. Prior work on certifying safety of trajectories includes barrier and density methods, which do not provide a margin of proximity to the unsafe set in terms of distance. The distance estimation problem is relaxed to a Monge-Kantorovich type optimal transport problem based on existing occupation-measure methods of peak estimation. Specialized programs may be developed for polyhedral norm distances (e.g. L1 and Linfinity) and for scenarios where a shape is traveling along trajectories (e.g. rigid body motion). The distance estimation problem will be correlatively sparse when the distance objective is separable.

   @article{miller2023distance,
     title = {{Bounding the Distance to Unsafe Sets with Convex Optimization}},
     author = {Miller, Jared and Sznaier, Mario},
     year = {2023},
     eprint = {2110.14047},
     archiveprefix = {arXiv},
     primaryclass = {math.OC},
     tag = {peak},
     note = {arXiv: 2110.14047},
     url = {https://ieeexplore.ieee.org/document/10149398},
     pdf = {distance_arxiv.pdf},
     pages = {1-15},
     journal = {IEEE Transactions on Automatic Control},
     abbr = {TAC},
     doi = {10.1109/TAC.2023.3285862},
     code = {https://github.com/Jarmill/distance},
     bibtex_show = {true},
     slides = {Distance_CDC_Presentation.pdf},
     arxiv = {2110.14047},
     selected = {true}
   }

3. 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}
   }

Conference Articles

1. CDC

   Peak Estimation for Uncertain and Switched Systems

   Miller, Jared, Henrion, Didier, Sznaier, Mario, and Korda, Milan

   In 60th IEEE Conference on Decision and Control (CDC) 2021

   Abs Bib HTML PDF Code Slides

   Peak estimation bounds extreme values of a function of state along trajectories of a dynamical system. This paper focuses on extending peak estimation to continuous and discrete settings with time-independent and time-dependent uncertainty. Techniques from optimal control are used to incorporate uncertainty into an existing occupation measure-based peak estimation framework, which includes special consideration for handling switching uncertainties. The resulting infinite-dimensional linear programs can be solved approximately with Linear Matrix Inequalities arising from the moment-SOS hierarchy.

   @inproceedings{miller2021uncertain,
     author = {Miller, Jared and Henrion, Didier and Sznaier, Mario and Korda, Milan},
     booktitle = {60th IEEE Conference on Decision and Control (CDC)},
     title = {{Peak Estimation for Uncertain and Switched Systems}},
     year = {2021},
     volume = {},
     number = {},
     tag = {peak},
     pages = {3222-3228},
     doi = {10.1109/CDC45484.2021.9683778},
     slides = {CDC_uncertain.pdf},
     abbr = {CDC},
     url = {https://ieeexplore.ieee.org/document/9683778},
     html = {https://ieeexplore.ieee.org/document/9683778},
     pdf = {peak_uncertain_arxiv.pdf},
     code = {https://github.com/jarmill/peak/},
     selected = {true},
     bibtex_show = {true}
   }

Preprints

1. Analysis and Control of Input-Affine Dynamical Systems using Infinite-Dimensional Robust Counterparts

   Miller, Jared, and Sznaier, Mario

   Preprint 2023

   Abs Bib HTML Code Slides

   Input-affine dynamical systems often arise in control and modeling scenarios, such as the data-driven case when state-derivative observations are recorded under bounded noise. Common tasks in system analysis and control include optimal control, peak estimation, reachable set estimation, and maximum control invariant set estimation. Existing work poses these types of problems as infinite-dimensional linear programs in auxiliary functions with sum-of-squares tightenings. The bottleneck in most of these programs is the Lie derivative nonnegativity constraint posed over the time-state-control set. Decomposition techniques to improve tractability by eliminating the control variables include vertex decompositions (switching), or facial decompositions in the case where the polytopic set is a scaled box. This work extends the box-facial decomposition technique to allow for a robust-counterpart decomposition of semidefinite representable sets (e.g. polytopes, ellipsoids, and projections of spectahedra). These robust counterparts are proven to be equivalent to the original Lie constraint under mild compactness and regularity constraints. Efficacy is demonstrated under peak/distance/reachable set data-driven analysis problems and Region of Attraction maximizing control.

   @preprint{miller2023robustcounterpart,
     title = {Analysis and Control of Input-Affine Dynamical Systems using Infinite-Dimensional Robust Counterparts},
     author = {Miller, Jared and Sznaier, Mario},
     year = {2023},
     eprint = {2112.14838},
     url = {https://arxiv.org/abs/2112.14838},
     html = {https://arxiv.org/abs/2112.14838},
     archiveprefix = {arXiv},
     primaryclass = {math.OC},
     tag = {peakddc},
     bibtex_show = {true},
     slides = {MTNS_Robust_Counterpart.pdf},
     code = {https://github.com/Jarmill/data_driven_occ},
     selected = {true}
   }