skip to main content

Attention:

The NSF Public Access Repository (NSF-PAR) system and access will be unavailable from 11:00 PM ET on Thursday, May 23 until 2:00 AM ET on Friday, May 24 due to maintenance. We apologize for the inconvenience.


Title: Clustering-based Mode Reduction for Markov Jump Systems
While Markov jump systems (MJSs) are more appropriate than LTI systems in terms of modeling abruptly changing dynamics, MJSs (and other switched systems) may suffer from the model complexity brought by the potentially sheer number of switching modes. Much of the existing work on reducing switched systems focuses on the state space where techniques such as discretization and dimension reduction are performed, yet reducing mode complexity receives few attention. In this work, inspired by clustering techniques from unsupervised learning, we propose a reduction method for MJS such that a mode-reduced MJS can be constructed with guaranteed approximation performance. Furthermore, we show how this reduced MJS can be used in designing controllers for the original MJS to reduce the computation cost while maintaining guaranteed suboptimality.  more » « less
Award ID(s):
1845076
NSF-PAR ID:
10408031
Author(s) / Creator(s):
; ;
Date Published:
Journal Name:
Learning for Decision and Control
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
More Like this
  1. While Markov jump systems (MJSs) are more appropriate than LTI systems in terms of modeling abruptly changing dynamics, MJSs (and other switched systems) may suffer from the model complexity brought by the potentially sheer number of switching modes. Much of the existing work on reducing switched systems focuses on the state space where techniques such as discretization and dimension reduction are performed, yet reducing mode complexity receives few attention. In this work, inspired by clustering techniques from unsupervised learning, we propose a reduction method for MJS such that a mode-reduced MJS can be constructed with guaranteed approximation performance. Furthermore, we show how this reduced MJS can be used in designing controllers for the original MJS to reduce the computation cost while maintaining guaranteed suboptimality. Keywords: Markov Jump Systems, System Reduction, Clustering 
    more » « less
  2. While Markov jump systems (MJSs) are more appropriate than LTI systems in terms of modeling abruptly changing dynamics, MJSs (and other switched systems) may suffer from the model complexity brought by the potentially sheer number of switching modes. Much of the existing work on reducing switched systems focuses on the state space where techniques such as discretization and dimension reduction are performed, yet reducing mode complexity receives few attention. In this work, inspired by clustering techniques from unsupervised learning, we propose a reduction method for MJS such that a mode-reduced MJS can be constructed with guaranteed approximation performance. Furthermore, we show how this reduced MJS can be used in designing controllers for the original MJS to reduce the computation cost while maintaining guaranteed suboptimality. 
    more » « less
  3. Learning how to effectively control unknown dynamical systems from data is crucial for intelligent autonomous systems. This task becomes a significant challenge when the underlying dynamics are changing with time. Motivated by this challenge, this paper considers the problem of controlling an unknown Markov jump linear system (MJS) to optimize a quadratic objective in a data-driven way. By taking a model-based perspective, we consider identification-based adaptive control for MJS. We first provide a system identification algorithm for MJS to learn the dynamics in each mode as well as the Markov transition matrix, underlying the evolution of the mode switches, from a single trajectory of the system states, inputs, and modes. Through mixing-time arguments, sample complexity of this algorithm is shown to be O(1/T−−√). We then propose an adaptive control scheme that performs system identification together with certainty equivalent control to adapt the controllers in an episodic fashion. Combining our sample complexity results with recent perturbation results for certainty equivalent control, we prove that when the episode lengths are appropriately chosen, the proposed adaptive control scheme achieves O(T−−√) regret. Our proof strategy introduces innovations to handle Markovian jumps and a weaker notion of stability common in MJSs. Our analysis provides insights into system theoretic quantities that affect learning accuracy and control performance. Numerical simulations are presented to further reinforce these insights. 
    more » « less
  4. Metal-mediated cross-coupling reactions offer organic chemists a wide array of stereo- and chemically-selective reactions with broad applications in fine chemical and pharmaceutical synthesis.1 Current batch-based synthesis methods are beginning to be replaced with flow chemistry strategies to take advantage of the improved consistency and process control methods offered by continuous flow systems.2,3 Most cross-coupling chemistries still encounter several issues in flow using homogeneous catalysis, including expensive catalyst recovery and air sensitivity due to the chemical nature of the catalyst ligands.1 To mitigate some of these issues, a ligand-free heterogeneous catalysis reaction was developed using palladium (Pd) loaded into a polymeric network of a silicone elastomer, poly(hydromethylsiloxane) (PHMS), that is not air sensitive and can be used with mild reaction solvents (ethanol and water).4 In this work we present a novel method of producing soft catalytic microparticles using a multiphase flow-focusing microreactor and demonstrate their application for continuous Suzuki-Miyaura cross-coupling reactions. The catalytic microparticles are produced in a coaxial glass capillary-based 3D flow-focusing microreactor. The microreactor consists of two precursors, a cross-linking catalyst in toluene and a mixture of the PHMS polymer and a divinyl cross-linker. The dispersed phase containing the polymer, cross-linker, and cross-linking catalyst is continuously mixed and then formed into microdroplets by the continuous phase of water and surfactant (sodium dodecyl sulfate) introduced in a counter-flow configuration. Elastomeric microdroplets with a diameter ranging between 50 to 300 micron are produced at 25 to 250 Hz with a size polydispersity less than 3% in single stream production. The physicochemical properties of the elastomeric microparticles such as particle swelling/softness can be tuned using the ratio of cross-linker to polymer as well as the ratio of polymer mixture to solvent during the particle formation. Swelling in toluene can be tuned up to 400% of the initial particle volume by reducing the concentration of cross-linker in the mixture and increasing the ratio of polymer to solvent during production.5 After the particles are produced and collected, they are transferred into toluene containing palladium acetate, allowing the particles to incorporate the palladium into the polymer network and then reduce the palladium to Pd0 with the Si-H functionality present on the PHMS backbones. After the reduction, the Pd-loaded particles can be washed and dried for storage or switched into an ethanol/water solution for loading into a micro-packed bed reactor (µ-PBR) for continuous organic synthesis. The in-situ reduction of Pd within the PHMS microparticles was confirmed using energy dispersive X-ray spectroscopy (EDS), X-ray photoelectron spectroscopy (XPS) and focused ion beam-SEM, and TEM techniques. In the next step, we used the developed µ-PBR to conduct continuous organic synthesis of 4-phenyltoluene by Suzuki-Miyaura cross-coupling of 4-iodotoluene and phenylboronic acid using potassium carbonate as the base. Catalyst leaching was determined to only occur at sub ppm concentrations even at high solvent flow rates after 24 h of continuous run using inductively coupled plasma mass spectrometry (ICP-MS). The developed µ-PBR using the elastomeric microparticles is an important initial step towards the development of highly-efficient and green continuous manufacturing technologies in the pharma industry. In addition, the developed elastomeric microparticle synthesis technique can be utilized for the development of a library of other chemically cross-linkable polymer/cross-linker pairs for applications in organic synthesis, targeted drug delivery, cell encapsulation, or biomedical imaging. References 1. Ruiz-Castillo P, Buchwald SL. Applications of Palladium-Catalyzed C-N Cross-Coupling Reactions. Chem Rev. 2016;116(19):12564-12649. 2. Adamo A, Beingessner RL, Behnam M, et al. On-demand continuous-flow production of pharmaceuticals in a compact, reconfigurable system. Science. 2016;352(6281):61 LP-67. 3. Jensen KF. Flow Chemistry — Microreaction Technology Comes of Age. 2017;63(3). 4. Stibingerova I, Voltrova S, Kocova S, Lindale M, Srogl J. Modular Approach to Heterogenous Catalysis. Manipulation of Cross-Coupling Catalyst Activity. Org Lett. 2016;18(2):312-315. 5. Bennett JA, Kristof AJ, Vasudevan V, Genzer J, Srogl J, Abolhasani M. Microfluidic synthesis of elastomeric microparticles: A case study in catalysis of palladium-mediated cross-coupling. AIChE J. 2018;0(0):1-10. 
    more » « less
  5. This paper proposes a data-driven framework to address the worst-case estimation problem for switched discrete-time linear systems based solely on the measured data (input & output) and an ℓ ∞ bound over the noise. We start with the problem of designing a worst-case optimal estimator for a single system and show that this problem can be recast as a rank minimization problem and efficiently solved using standard relaxations of rank. Then we extend these results to the switched case. Our main result shows that, when the mode variable is known, the problem can be solved proceeding in a similar manner. To address the case where the mode variable is unmeasurable, we impose the hybrid decoupling constraint(HDC) in order to reformulate the original problem as a polynomial optimization which can be reduced to a tractable convex optimization using moments-based techniques. 
    more » « less