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

   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}
   }

2. LCSS

   Robust Data-Driven Safe Control using Density Functions

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

   IEEE Control Systems Letters 2023

   Abs arXiv Bib HTML Code

   This paper presents a tractable framework for data-driven synthesis of robustly safe control laws. Given noisy experimental data and some priors about the structure of the system, the goal is to synthesize a state feedback law such that the trajectories of the closed loop system are guaranteed to avoid an unsafe set even in the presence of unknown but bounded disturbances (process noise). The main result of the paper shows that for polynomial dynamics, this problem can be reduced to a tractable convex optimization by combining elements from polynomial optimization and the theorem of alternatives. This optimization provides both a rational control law and a density function safety certificate. These results are illustrated with numerical examples.

   @article{zheng2023robustsafety,
     title = {{Robust Data-Driven Safe Control using Density Functions}},
     author = {Zheng, Jian and Dai, Tianyu and Miller, Jared and Sznaier, Mario},
     year = {2023},
     journal = {IEEE Control Systems Letters},
     eprint = {2303.09004},
     arxiv = {2303.09004},
     archiveprefix = {arXiv},
     primaryclass = {math.OC},
     url = {https://ieeexplore.ieee.org/document/10158326},
     html = {https://ieeexplore.ieee.org/document/10158326},
     tag = {ddc},
     doi = {10.1109/LCSYS.2023.3287801},
     volume = {7},
     number = {},
     pages = {2611-2616},
     abbr = {LCSS},
     selected = {true},
     bibtex_show = {true},
     code = {https://github.com/J-mzz/ddc-safety}
   }

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}
   }

4. AUT

   Decomposed structured subsets for semidefinite and sum-of-squares optimization

   Miller, Jared, Zheng, Yang, Sznaier, Mario, and Papachristodoulou, Antonis

   Automatica 2022

   Abs arXiv HTML PDF Code Poster

   Semidefinite programs (SDPs) are standard convex problems that are frequently found in control and optimization applications. Interior-point methods can solve SDPs in polynomial time up to arbitrary accuracy, but scale poorly as the size of matrix variables and the number of constraints increases. To improve scalability, SDPs can be approximated with lower and upper bounds through the use of structured subsets (e.g., diagonally-dominant and scaled-diagonally dominant matrices). Meanwhile, any underlying sparsity or symmetry structure may be leveraged to form an equivalent SDP with smaller positive semidefinite constraints. In this paper, we present a notion of decomposed structured subsets to approximate an SDP with structured subsets after an equivalent conversion. The lower/upper bounds found by approximation after conversion become tighter than the bounds obtained by approximating the original SDP directly. We apply decomposed structured subsets to semidefinite and sum-of-squares optimization problems with examples of H∞ norm estimation and constrained polynomial optimization. An existing basis pursuit method is adapted into this framework to iteratively refine bounds.

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 = {SIAM_data_driven.pdf},
     code = {https://github.com/Jarmill/data_driven_occ},
     selected = {true}
   }

2. Data-Driven Stabilizing and Robust Control of Discrete-Time Linear Systems with Error in Variables

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

   Preprint 2022

   Abs arXiv Bib PDF 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 measurement noise (error in variable setting). Certificates of state-feedback superstability or quadratic stability 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 superstabilizing controller, with slight conservatism introduced for quadratic stabilizability. 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. The consistency set description may be broadened to include cases where the data and process are affected by a combination of L-infinity bounded measurement, process, and input noise. Further generalizations include varying noise sets, non-uniform sampling, and switched systems stabilization.

   @preprint{miller2022eiv,
     title = {Data-Driven Stabilizing and Robust Control of Discrete-Time Linear Systems with Error in Variables},
     author = {Miller, Jared and Dai, Tianyu and Sznaier, Mario},
     year = {2022},
     eprint = {2210.13430},
     arxiv = {2210.13430},
     archiveprefix = {arXiv},
     tag = {ddc},
     primaryclass = {math.OC},
     note = {arXiv: 2210.13430},
     bibtex_show = {true},
     code = {https://github.com/jarmill/error_in_variables},
     pdf = {Noise_in_Variable__Journal_Arxiv.pdf},
     selected = {true},
     slides = {EIV_Presentation__Austin.pdf}
   }