(8y) Modeling and Control of Hybrid and Nonsmooth Process Systems

Broadly, my interests lie in the modeling, simulation, and control of hybrid and nonsmooth systems. Hybrid systems display a mixture of continuous and discrete dynamics, where the continuous portion is often modeled using differential equations. Nonsmooth systems refers here to dynamic systems whose participating functions exhibit non-differentiability, which can be problematic in conventional simulation and optimization methods. Possible sources of such behavior include thermodynamic phase changes, flow regime transitions, and valve activation, among others. Hybrid and nonsmooth modeling frameworks have become widely applied tools in a variety of real-world problems. Examples are found in pharmaceutical manufacturing, biological systems with changes in population behavior, secure communications via supervisory switching control, and multistream heat exchanger design. My pursuits and contributions are found in this area of research, with an emphasis on sensitivity, stability, and optimization techniques for use in controller and parametric design.

Research Experiences: I am currently a postdoctoral fellow working on dynamic optimization of campaign continuous manufacturing processes, under the supervision of Professor Paul I. Barton (successful proposal: NSERC Postdoctoral Fellowship). This collaborative work is a part of the Novartis-MIT Center for Continuous Manufacturing initiative to revolutionize drug manufacturing. I have developed new theory to characterize sensitivities of nonsmooth dynamic systems (e.g., [1, 2]), mirroring the classical results on the topic. These findings lay the theoretical groundwork upon which efficient numerical methods can be designed for large-scale problems, where standard methods can fail. This work thus extends nonsmooth equation-solving and optimization methods to problems with nonsmooth differential-algebraic equations embedded.

I obtained my Ph.D. in Applied Mathematics at the University of Waterloo, under the supervision of Professor Xinzhi Liu (successful proposal: NSERC Alexander Graham Bell Canada Scholarship). My Ph.D. studies related to the analysis of complex physical phenomena exhibiting time-delays, which are an inherent feature in a wide range of biological and physical problems. By uncovering underlying mechanisms, I made contributions here in the stabilization, synchronization, and robust control of nonlinear hybrid systems with time-delays (e.g., [3, 4]). I designed switching control strategies to achieve desired performance outcomes where classical methods are either unavailable or inadequate. I connected the theoretical findings to biological systems through the introduction and analysis of hybrid modeling approaches to disease transmission (e.g., [5, 6, 7]).

Future Directions: My goal as faculty would be to combine my training and research experiences in applied mathematics and engineering to uniquely approach high-impact problems in chemical and biological process control. Using my expertise in theoretical and computational mathematics, and by collaborating with experimentalists, I plan to design, develop, implement, and optimize state-of-the-art process control methods. Short-term projects include efforts in characterizing the behavior of high-index differential-algebraic equations and new approaches to nonlinear model predictive control. Long-term projects suitable for Ph.D. students are comprised of problems in stochastic modeling of biological systems, fundamental extensions in the setting of optimal control theory, and the development of global optimization theory and methods for hybrid process systems. Industrial applications in mind include ones in continuous manufacturing processes, power and energy systems, and biological population models.

Teaching Interests: Optimization; Computational methods; Advanced dynamic systems; Process control.

I was the full-time lecturer for two undergraduate engineering courses (approximate class size of 100 each) at the University of Waterloo. I have also acted as a teaching assistant in mathematics and engineering courses (11 undergraduate, 3 graduate level) on topics ranging from computational mathematics to applied functional analysis. My teaching philosophies are instructed by these opportunities, along with the completion of the Kaufman Teaching Certificate Program at MIT. For example, my course design is dictated as follows:

• My lecture and assessment design for first and second-year courses (e.g., differential equations, numerical methods) will aim to solidify the studentsâ?? foundations going forward in their field of study.
• Upper-year and graduate-level courses (e.g., control theory, optimization) will be designed so that students understand the material in a way that an expert in the field would expect.
• In specialized graduate-level courses (e.g., modeling and simulation of hybrid systems, nonsmooth analysis, topics in mathematical biology), research-oriented goals will be included whenever possible.

Selected Publications (11 accepted peer-reviewed journal articles as lead author):

 

[1] P.G. Stechlinski and P.I. Barton, In Press. â??Generalized Derivatives of Nonsmooth Differential-Algebraic Equations.â? Journal of Optimization Theory and Applications, DOI: 10.1007/s10957-016-0988-9.

[2] P.G. Stechlinski and P.I. Barton, Accepted Invited Session Paper. â??Generalized Derivatives of Optimal Control Problems with Nonsmooth Differential-Algebraic Equations Embedded.â? 55^th IEEE Conference on Decision and Control 2016.

[3] X.Z. Liu and P.G. Stechlinski, 2016. â??Hybrid stabilization and synchronization of nonlinear systems with unbounded delays.â? Applied Mathematical Modelling, 280, 140-161.

[4] X.Z. Liu and P.G. Stechlinski, 2014. â??Hybrid control of impulsive systems with distributed delays.â? Nonlinear Analysis: Hybrid Systems, 11, 57-70.

[5] X.Z. Liu and P.G. Stechlinski, 2015. â??Application of control strategies to a seasonal model of Chikungunya disease.â? Applied Mathematical Modelling, 39, 3194-3220.

[6] X.Z. Liu and P.G. Stechlinski, 2014. â??SIS models with switching and pulse control.â? Journal of Applied Mathematics and Computation, 232, 727-742.

[7] X.Z. Liu and P.G. Stechlinski, 2013. â??Transmission dynamics of a switched multi-city model with transport-related infections.â? Nonlinear Analysis: Real World Applications, 14, 264-279.