The main area of our research is in control systems and mechatronics, with particular focus on

(i) stability analysis and control synthesis of dynamical systems with delays

(ii) interplay between stability, delays, and graphs

(iii) control-systems-aided human-machine systems

(iv) engineering education research

 

Our research program is supported by external funds (total of about $780K), which we gratefully acknowledge:

(1) National Science Foundation ECCS program on "Interplay between Network Topology and Stability of Control Systems with Delays"

(2) National Science Foundation CBET program on "EAGER: Mechatronics Based Braille Writing Device for the Blind"

(3) CIMIT: Center for Integration of Medicine and Innovative Technologyon "Building Handheld Devices To Accommodate Essential Tremor" with Prof. Andrew Gouldstone and Neurologist Dr. Ludy Shih.

(4) DARPA Young Faculty Award on "Model-Free Algorithms to Assist and Control Human-Task Missions against Dynamic Environments"

(5) National Science Foundation ECCS program on "GRDS (Graduate Student Diversity Supplement) Interplay between Network Topology and Stability of Control Systems with Delays"

(6) The MathWorks award on "A New Hands-on Mechatronics Course in Emerging Engineering Fields" with Prof. Nader Jalili


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Project 1
Stability analysis and Control synthesis of Dynamical Systems with Delays

Support: National Science Foundation

Thesis work: Dr. Ismail Ilker Delice (graduated in May 2011),
Payam M. Nia (PhD student)

In this research program, the primary focus is on understanding the stability mechanisms of linear time-invariant (LTI) systems with “multiple delays”. Such problems stem from real-world systems encompassing engineering, physics, biology, operations research, and economics, where delays arise from sensors, actuations, decision-making, mass transfer, information transmission.

More specifically, our main goal is to develop novel paradigms for analyzing the stability of systems with “multiple” delays, and for designing controllers for these systems, so that their stability can be guaranteed and their functionality can be assured using controllers, despite the detrimental effects of delays. In the past five years, our research team developed unique capabilities that can address several problems that were unresolved to date.

Our contributions can be summarized as follows:

  • “Stability maps/charts” display regions of delays where a given system is either stable or unstable; see our studies in inventory control problems of supply chains (SUPPLY CHAINS), and car following dynamics with human reaction delays (TRAFFIC FLOW). Extraction of the stability map of a given LTI system with more than two delays is extremely difficult, if not impossible. To address this difficulty, we developed novel frequency-domain approaches with three unique aspects:

    • we constructed a mathematical approach that can be used to take cross sections of the stability maps. This way, it becomes possible to visualize the stability maps of systems with arbitrarily large number of delays.

    • we are able to obtain the stability maps based on non-conservative approaches consistent with necessary and sufficient conditions of stability.

    • we have the ability to time-efficiently extract these maps.

  • Based on algebraic geometry, polynomial theory, discriminant of multi-variate polynomials, and elimination techniques, we developed an analytical and non-conservative framework that can be used to test the “delay-independent stability” (DIS) property of LTI systems with “multiple” delays. To the best of our knowledge, the approach is novel for multiple-delay problems, and it simplifies the DIS test dramatically, requiring only the inspection of the roots of several single-variable polynomials. Besides the mathematical challenges in creating such a DIS test, it opens ways for system design, where delays are uncertain and the system should remain stable, regardless of the amount of delays.

  • We further developed our DIS test and established rules by which we can synthesize controllers so that multi-input multi-output LTI systems with “multiple delays” can be rendered delay-independent stable (DIS). These rules permit controllers to be structured, and the synthesis approach to be an algebraic one. The novelty is due to our ability to simplify the synthesis problem with the tools of Sturm sequences and Descartes rule of signs. These results pave the way for not only making the control systems DIS, but also combining them with semi-definite programming, trajectory tracking, state observer design, and disturbance rejection. Further opportunities are in designing DIS-based Model Predictive Control (MPC) schemes for controlling nonlinear systems with multiple delays.

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Project 2
Interplay between Stability, Delays, and Graphs

Support: National Science Foundation

Thesis work: Wei Qiao (PhD student), Andranik Valedi (BS/MS student)

In this program, the goal is to find generalizing/specific graph-design rules by which we can design interconnections of nodes/agents/dynamics that are ultimately more tolerant to detrimental effects of inter-agent communication delays, and/or that can function stably even if the delays are large, and/or that can function even if some catastrophic events happen, such as abrupt changes in graph structure. This is obviously not a simple problem to resolve, since the solution requires strong understanding of the relations among the graph properties, finite eigenvalues of the corresponding Laplacians, and asymptotic stability analysis, which is infinite-dimensional in the presence of delays.

In this research, various mathematical models can be studied. Initially, we started investigating a LTI consensus dynamics model with heterogeneous agents and identical communication delays among all the agents, and introduced two new concepts: one is the “responsible eigenvalue” (discovered in the spring of 2010) and the other one is the design of “delay-tolerant graphs” (recently developed July 2011). More specifically, our contributions are as follows:

  • “Delay margin” is known as the largest delay that the system can tolerate before the system becomes unstable. We proved that, among the finite number of Laplacian eigenvalues, there exists one and only one called the “Responsible Eigenvalue” (one real or a complex conjugate pair) that directly determines the delay margin. This result yields computationally efficient means of exploring consensus system in large scales using the explicit connections between the delay margin and the Responsible Eigenvalue.

  • We revealed that, under some conditions, we can tailor two small graphs and create a larger graph that can have a desired delay margin. Following a bottom-up approach, this preliminary result paves the way to designing large-scale delay-tolerant networks of dynamical systems.

  • For a stable system, the “rightmost eigenvalue” is the eigenvalue that is the closest to the imaginary axis of the complex plane. Farther this eigenvalue is to the imaginary axis, faster the system response vanishes. In the presence of delays, computation of this eigenvalue is possible only numerically. We could however analytically study the behavior of the rightmost eigenvalue, and reveal conditions on the Laplacian eigenvalues such that system response decays much faster. This line of research resonates with the recent studies on ultra-fast consensus of multi-agents. What is unique in our studies is that we explicitly show how the Laplacian eigenvalues should be designed such that consensus can be made faster despite inter-agent communication delays.


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Project 3
Control-Systems-Aided Human-Machine Systems

Support: National Science Foundation, DARPA, CIMIT

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Theme 1: Developing a Low-Cost Mechatronics-based Braille-writing Device

Thesis work: Melda Ulusoy (PhD student), Matt Ouelette (BS/MS student)

Collaborators: National Braille Press & National Federation of Blind

This research program started three years ago, after having realized that a low-cost and effective device that can write Braille letters on paper does not exist, leaving the blind people with either too expensive options (in the order of $5,000) or too underdeveloped options which are cumbersome to use (e.g., slate and stylus). Currently, we are developing a new electro-mechanical prototype that we believe will supersede the existing technical capabilities while offering reasonable manufacturing cost.

The novelty of the prototype (invention disclosure filed in February 2011) we are developing is due to its ability to write any Braille letter using only one actuator, unlike existing approaches, which use a total of six independent actuators per Braille letter, one for each Braille dot. This not only makes our device lighter, but it also gives hopes for a small portable device that can be energized by rechargeable batteries. We already characterized the forces needed to emboss a Braille letter on paper, and based on this, we now know that we can create a low-cost electro-mechanical system that is able to emboss the Braille letters with a single actuator. So far, we built several prototypes, and converged to a functional mechanical design, on which we are implementing the aforementioned electro-mechanical actuation system.

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Theme 2: Model-Free Algorithms to Assist and Control Human-Task Missions against Dynamic Environments

Thesis work: Open position

Under our DARPA YFA grant, we will explore non-model based techniques to develop controllers with which we can render a human-task mission stable, in ways to assist the humans such that the overall mission success is improved. The controllers are envisioned to reduce human cognitive load while still guaranteeing mission success.

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Theme 3: Interfacing hand tremor and handheld devices through control

Thesis work: Open position

This research theme is focused on developing novel control paradigms, based on dynamical modeling and vibration systems, with which undesirable effects of hand tremor can be diminished when a hand interacts with objects for precision tasks such as drinking from a cup and eating with a utensil.

 

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Project 4
Engineering Education Research

Support: The MathWorks

I and Prof. Nader Jalili were awarded an engineering-education and curriculum-development grant from the MathWorks. With this grant, we will develop a mechatronics-based hands-on course for undergraduate students based on projects from emerging engineering fields, such as energy systems, biomedical devices, and sustainability. Another novelty of the project is to bring low-cost mechatronics solutions to classroom in order to use logistics effectively while maximizing impacts on learning. To this end, we are currently developing several open ended project modules, which will be picked up by groups of students that will work on these projects throughout the semester. The course will be similar to a capstone project but at a smaller scale. The student groups will present progress, prepare reports, and have budgets to spend to achieve their project goals, while the PIs will provide expertise and technical support during the semester. Student presentations will also enrich knowledge, and make all students become aware of several technical problems and their solution methods. The curriculum will initially be piloted as part of the existing System Analysis and Control course in the fall 2011 and spring 2012, and its effectiveness will be assessed before moving the curriculum to a new course tentatively in the fall of 2012. Further plans include transferring the gained experience to Roxbury Community College via collaborations.

 

Our most recent results are documented at Northeastern University’s Institutional Repository IRis

Publication list >>