skip to main content
US FlagAn official website of the United States government
dot gov icon
Official websites use .gov
A .gov website belongs to an official government organization in the United States.
https lock icon
Secure .gov websites use HTTPS
A lock ( lock ) or https:// means you've safely connected to the .gov website. Share sensitive information only on official, secure websites.


Title: Task Decomposition for MPC: A Computationally Efficient Approach for Linear Time-Varying Systems
A Task Decomposition method for iterative learning Model Predictive Control (TDMPC) for linear time-varying systems is presented. We consider the availability of state- input trajectories which solve an original task T1, and design a feasible MPC policy for a new task, T2, using stored data from T1. Our approach applies to tasks T2 which are composed of subtasks contained in T1. In this paper we formally define the task decomposition problem, and provide a feasibility proof for the resulting policy. The proposed algorithm reduces the computational burden for linear time-varying systems with piecewise convex constraints. Simulation results demonstrate the improved efficiency of the proposed method on a robotic path-planning task.  more » « less
Award ID(s):
1931853
PAR ID:
10176527
Author(s) / Creator(s):
;
Date Published:
Journal Name:
IFACPapersOnLine
ISSN:
2405-8963
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
More Like this
  1. Abstract PurposeTo compare T1 and T2 measurements across commercial and prototype 0.55T MRI systems in both phantom and healthy participants using the same vendor‐neutral pulse sequences, reconstruction, and analysis methods. MethodsStandard spin echo measurements and abbreviated protocol measurements of T1, B1, and T2 were made on two prototype 0.55 T systems and two commercial 0.55T systems using an ISMRM/NIST system phantom. Additionally, five healthy participants were imaged at each system using the abbreviated protocol for T1, B1, and T2 measurement. The phantom measurements were compared to NMR‐based reference measurements to determine accuracy, and both phantom and in vivo measurements were compared to assess reproducibility and differences between the prototype and commercial systems. ResultsVendor‐neutral sequences were implemented across all four systems, and the code for pulse sequences and reconstruction is freely available. For participants, there was no difference in the mean T1 and T2 relaxation times between the prototype and commercial systems. In the phantom, there were no significant differences between the prototype and commercial systems for T1 and T2 measurements using the abbreviated protocol. ConclusionQuantitative T1 and T2 measurements at 0.55T in phantom and healthy participants are not statistically different across the prototype and commercial systems. 
    more » « less
  2. This paper builds model-theoretic tools to detect changes in complexity among the simple theories. We develop a generalization of dividing, called shearing, which depends on a so-called context c. This leads to defining c-superstability, a syntactical notion, which includes supersimplicity as a special case. The main result is a separation theorem showing that for any countable context and any two theories T1, T2, such that T1 is c-superstable and T2 is c-unsuperstable, and for arbitrarily large mu, it is possible to build models of any theory interpreting both T1 and T2 whose restriction to tau(T1) is mu-saturated and whose restriction to tau(T2) is not aleph1-saturated. (This suggests “c-superstable” is really a dividing line.) The proof uses generalized Ehrenfeucht-Mostowski models, and along the way, we clarify the use of these techniques to realize certain types while omitting others. In some sense, shearing allows us to study the interaction of complexity coming from the usual notion of dividing in simple theories and the more combinatorial complexity detected by the general definition. This work is inspired by our recent progress on Keisler’s order, but does not use ultrafilters, rather aiming to build up the internal model theory of these classes. https://doi.org/10.1090/tran/8513 
    more » « less
  3. null (Ed.)
    In the conventional robust T -colluding private information retrieval (PIR) system, the user needs to retrieve one of the possible messages while keeping the identity of the requested message private from any T colluding servers. Motivated by the possible heterogeneous privacy requirements for different messages, we consider the ( N,T1:K1,T2:K2 ) two-level PIR system, where K1 messages need to be retrieved privately against T1 colluding servers, and all the messages need to be retrieved privately against T2 colluding servers where T2≤T1 . We obtain a lower bound to the capacity by proposing a novel coding scheme, namely the non-uniform successive cancellation scheme. A capacity upper bound is also derived. The gap between the upper bound and the lower bound is analyzed, and shown to vanish when T1=T2 . 
    more » « less
  4. Interstitial patterning of nuclear spins is a nascent design principle for controlling electron spin superposition lifetimes in open-shell complexes and solid-state defects. Herein we report the first test of the impact of the patterning principle on ligand-based nuclear spin dynamics. We test how substitutional patterning of 1H and 79/81Br nuclear spins on ligands modulates proton nuclear spin dynamics in the ligand shell of metal complexes. To do so, we studied the 1H nuclear magnetic resonance relaxation times (T1 and T2) of a series of eight polybrominated catechol ligands and six complexes formed by coordination of the ligands to a Ti(IV) ion. These studies reveal that 1H T1 values can be enhanced in the individual ligands by a factor of 4 (from 10.8(3) to 43(5) s) as a function of substitution pattern, reaching the maximum value for 3,4,6-tribromocatechol. The T2 for 1H is also enhanced by a factor of 4, varying by ∼14 s across the series. When complexed, the impact of the patterning design strategy on nuclear spin dynamics is amplified and 1H T1 and T2 values vary by over an order of magnitude. Importantly, the general trends observed in the ligands also match those when complexed. Hence, these results demonstrate a new design principle to control 1H spin dynamics in metal complexes through pattern-based design strategies in the ligand shell. 
    more » « less
  5. Abstract Little research has examined the associations between perceived inclusivity within informal science learning sites, youth program belonging and perceptions of program career preparation. This study explored relations between these factors at three timepoints (T1 = start of program, T2 = 3 months and T3 = 12 months after start). Participants were a diverse sample of 209 adolescents participating in STEM youth programs within informal science learning sites situated in the United States and United Kingdom (70% females: M age  = 15.27, SD age  = 1.60), with 53.1% British and 64.1% non-White. Path analysis revealed that only perceptions of inclusivity for own social identity group (i.e., gender, ethnicity) at T1 were associated with T2 STEM youth program belonging. There was a significant indirect effect of T1 perceptions of inclusivity for one’s own social identity groups on T3 perceptions of program career preparation via T2 program belonging. This study highlights that, over time, perceptions of inclusivity around youth’s own social identity groups (i.e., gender and ethnicity/culture) are related to a sense of youth program belonging, which in turn is later associated with perceptions of program career preparation. 
    more » « less