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RESEARCH INTERESTS

My research interests lie on the intersection of systems and control theory, systems biology, and computer science. Engineers and natural scientists are facing the problem of dealing with ever more complex systems. The advance of technology has spurred the emergence of more complex engineering systems. It has also made available a large quantity of experimental data that requires systems understanding of natural systems. This is particularly true in the field of molecular biology, with the availability of genome scale genetic expression profiling technology. This development poses a research challenge. The design and synthesis of complex engineering and biological systems requires rigorous analysis to ensure that they will function as intended. Analyzing complex systems require extensive computational resources, if it is possible at all. The challenge thus lies in devising correct methodologies, with which the complexity can be reduced.

The approach to biology that highlights the use of quantitative models and reasoning based on systems and control theory leads to the field of systems biology. There are many problems in systems biology that are essentially engineering problems, and require engineering mindset to solve.

Several areas that I have been working on are listed below (click to go to the subject).

I gratefully acknowledge the institutions below for supporting and sponsoring my research:

NSFThe National Science Foundation
AROThe Army Research Office
RPIRensselaer Polytechnic Institute



Networks in molecular biology
Experimental data from cellular and molecular biology suggest that entities in cellular systems influence one another and can be thought of as forming a vast and complex network. With the advent of experimental and measurement technology, obtaining a large quantity of data, such as genome scale expression profiles of microorganisms is possible. The availability of these data gives rise to new challenges in identifying the vast, complex, yet structured network that generates the data. In systems biology, this is often called reverse engineering of the network. Network structures in systems biology appear in many levels, for example, genetic regulatory network, protein-protein interaction,  and metabolic networks. My research interest in this topic is in utilization of optimization techniques in identification and analysis of such networks.
Network    
                                                                         
Image source: Decourty et al, PNAS 2008
 


This material is based upon work supported by the National Science Foundation under Grant No. 1137906. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.

References:

1. G. Richard, C. Belta, A.A. Julius, and S. Amar, Controlling the outcome of the Toll-Like Receptor Signaling Pathway, PLoS ONE, vol. 7(2), e:31341, 2012.

2. N.G. Cooper, C. Belta, A.A. Julius, Genetic regulatory network identification using multivariate monotone functions, in the Proc. IEEE Conf. Decision and Control, pp. 2208 - 2213, Orlando, USA, 2011.

2. M.M. Zavlanos, A.A. Julius, S.P. Boyd and G.J. Pappas, Inferring stable genetic networks from steady-state data, Automatica, vol. 47(6), pp. 1113-1122, Special Issue on Systems Biology, 2011.

3. A.A. Julius, M.M. Zavlanos, S.P. Boyd, G.J. Pappas, Genetic network identification using convex programming, IET Systems Biology, vol. 5(3), pp. 155-166, 2009.

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Microbiorobotics

MicrobiorobotThe idea of using microorganisms as actuators for microscale structures is very appealing and a recent breakthrough in engineering, particularly because they are very easy and cheap to produce. I am collaborating with Dr. MinJun Kim at Drexel University, an expert experimentalist in microbiorobotics. We have been using both prokaryotic (bacteria) cells and eukaryotic cells as microactuators.

Our bacteria based system uses Serratia marcescens to provide propulsion to microfabricated structures (see picture on the left). My research interest is in building a mathematical model of the random behavior of the bacteria under chemotactic environment and the microstructures in a low Reynold number environment that enables understanding and control of the colony-scale behavior. So far, our model has been able to reproduce and provide a clear explanation for the puzzling experimental results, where a colony-scale synchrony seems to arise from completely random individual behavior.
Our eukaryotic based system uses Tetrahymena pyriformis, a ciliated protozoa swimmer. T. pyriformis can be artificially magnetized by introducing a magnetic dipole into the cell. We can then use external magnetic field to steer the motion of the cell. Unlike the bacteria based system, the motion of T. pyriformis can be controlled as individual cell. My research interest is in building a mathematical model for the dynamics of the T. pyriformis swimmers, and designing effective motion control algorithm for them.

In the movie below, a
T. pyriformis swimmer is being controlled to trace the letters "R D", which are the initials of Rensselaer and Drexel.



This material is based upon work supported by the National Science Foundation under Grant No. 100284, and the Army Research Office under Grant No. W911F-11-1-0490. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.

References:

1.  M.J. Kim, A.A. Julius, E.A. Steager (eds), Microbiorobotics, Elsevier, 2012.

2. D.H. Kim, P.S. Kim, A.A. Julius, M.J. Kim, Three-dimensional control of Tetrahymena pyriformis using artificial magnetotaxis, Applied Physics Letters, Vol. 100, 053702, 2012.

3. Y. Ou, D.H. Kim, P.S. Kim, M.J. Kim, A.A. Julius, Motion control of Tetrahymena pyriformis cells with artificial magnetotaxis: Model Predictive Control (MPC) approach, in the Proc. IEEE Intl. Conf. Robotics and Automation, pp. 2492 - 2497, St. Paul, USA, 2012.

4. D.H. Kim, P.S. Kim, A.A. Julius, M.J. Kim, Three-dimensional control of engineered motile cellular microrobots, in the Proc. IEEE Intl. Conf. Robotics and Automation, pp. 721 - 726, St. Paul, USA, 2012.

5. M.S. Sakar, E.B. Steager, D.H. Kim, A.A. Julius, M.J. Kim, V. Kumar, G.J. Pappas, Modeling, control and experimental characterization of microbiorobots, International Journal of Robotics Research, Vol. 30(6), pp. 647-658, 2011.

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Human Powered Controller Synthesis
Hybrid system is a mathematical framework that has been widely used to model engineering and natural systems, whose dynamics have both continuous and discrete aspects. Its applications range from fly-by-wire modern airplanes to cellular biology. A controller for a hybrid system observes the execution of the system and issues input signals and/or trigger events in the hybrid system so as to meet the system’s goal and safety requirements. For complex hybrid systems, existing methods for controller synthesis require exceedingly large computational resources.

My research interest lies in constructing controllers for hybrid systems. The specialty of our approach lies in the use of  human-generated inputs, while ensuring that the obtained controller is correct. The human-generated inputs can be obtained through various ways. We are primarily looking at inputs that can be obtained through human-played simulations of the system to be controlled. Naturally, our approach is compatible with crowdsourcing, where the simulation is played by a massive number of human players. The amount of computing resource that can be harvested through crowdsourcing is very high. Earlier crowdsourcing applications such as reCAPTCHA, FoldIt, and Wikipedia have recorded billions of hours of effort by their human contributors. Beyond solving the controller synthesis problem, the outcomes of this project can lead to new ways to tap into this resource for solving new problems.

In the movie below, Peter Bailie (a former member of my lab), demonstrates a computer game that he created. The game works with Microsoft Kinect interface, and it simulates the classical inverted pendulum control problem.



This material is based upon work supported by the National Science Foundation under Grant No. 1218109. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.

References:

1.  A.A. Julius, A.K. Winn, Safety controller synthesis using human generated trajectories: nonlinear dynamics with feedback linearization and differential flatness, in the Proc. American Control Conference, Montreal, Canada, 2012.

2. A.A. Julius, S. Afshari, Using computer games for hybrid systems controller synthesis, in the Proc. IEEE Conf. Decision and Control, pp. 5887-5892, Atlanta, USA, 2010.

3. A.A. Julius, Trajectory-based controller design for hybrid systems with ane continuous dynamics, in the Proc. 6th IEEE Conf. Automation Science and Engineering, pp. 1007 - 1012, Toronto, Canada, 2010.

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Abstraction of Complex Hybrid Systems and Its Applications

As engineering systems gain more functionality and complexity, there is a need for sound discipline in their design, development and deployment. In particular, ensuring the safety and correctness of these large and complex systems is becoming increasingly hard. One way to deal with the increasing complexity is by performing consistent abstraction on the system, to get a simpler model. Consistent abstraction means that the simpler model either conserves the original system's properties of interest, or is an approximation of the original system with a quantifiable deviation.

Allowing the abstraction to be an approximation of the original system turns out to be particularly beneficial, as it allows for stronger abstraction. Using the pioneering work
Girard and Pappas, I extended the results to the stochastic domain, where I consider hybrid systems with probabilistic dynamics and stochastic noise/disturbance (see references).

Another application of approximate abstraction is in the robust testing of hybrid systems, where we design automatic test generation for hybrid systems that can cover the system in finitely many tests, while at the same time provide a robustness guarantee on the tested property. 

 

References:

1. A. Girard and G.J. Pappas, Approximation metrics for discrete and continuous systems, IEEE Trans. Automatic Control,  52(5):782-798, May 2007.

2. A.A. Julius, G. Fainekos, M. Anand, I. Lee, and G.J. Pappas, Robust test generation and coverage for hybrid systems, in Hybrid Systems: Computation and Control, vol. 4416 of LNCS, Springer Verlag, 2007, pp. 329 - 342.

3. A. D'Innocenzo, A.A. Julius, G.J. Pappas, M.D. Di Benedetto, S. Di Gennaro, Verification of temporal properties on hybrid automata by simulation relations, in the Proc. IEEE Conf. Decision and Control, pp. 4039 - 4044, New Orleans, USA, 2007.

4. A. D'Innocenzo, A.A. Julius, M.D. Di Benedetto, G.J. Pappas, Approximate timed abstractions of hybrid automata, in the Proc. IEEE Conf. Decision and Control, pp. 4045-4050, New Orleans, USA, 2007.

3. A.A. Julius, Approximate abstraction of stochastic hybrid automata, in Hybrid Systems: Computation and Control, vol. 3927 of LNCS, Springer Verlag, 2006, pp. 318 - 332.

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Theoretical research on the interface between systems theory, computer science and systems biology

 

Breakthroughs in science and engineering often require a significant progress in the underlying theory. As I work in the interface between systems theory, computer science and systems biology, I am also interested in theoretical research, particularly that promotes cross fertilization of ideas across the
disciplines. Here are a couple of examples. The idea of bisimulation, which is traditionally a computer science concept, is applied to more general classes of systems in systems theory (see references). Bisimulation is an important concept of system abstraction. On the other hand, the theory of stability from systems theory, is applied to the approximate equivalence of transition systems (see references).

My doctoral thesis is about behavioral systems theory, which is a general mathematical systems theory that can potentially bridge some theoretical differences between discrete, continuous and hybrid systems. Along this direction, I have worked on the solution of some LTI control problems of designing a controller that has a particular input/output structure.

 

References:

1. A.A. Julius, J.C. Willems, M.N. Belur, and H.L. Trentelman, The canonical controllers and regular interconnection, Systems and Control Letters, 54 (2005), pp. 787 - 797.

2. A.A. Julius, J.W. Polderman, A.J. van der Schaft, Parametrization of the regular equivalences of the canonical controller, IEEE Trans. Automatic Control, vol.53(4), pp. 1032 - 1036, 2008.

3. P. Tabuada, A.D. Ames, A.A. Julius, G.J. Pappas, Approximate reduction of dynamical systems, in Systems and Control Letters, vol.57(7), pp. 538-545, July 2008.

4. A.A. Julius, On interconnection and equivalence of continuous and discrete systems: a behavioral perspective, PhD thesis, University of Twente, The Netherlands, February 2005.

 

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