The above considerations provide a strong motivation for the development of methods and strategies for the design of advanced process control systems that (1) account for the complex and multiscale process dynamics, including issues such as optimality and constraints, and (2) ensure an efficient and timely response to disturbances rejection, prevent disturbances from propagating or developing into total failures, and reduce the risk of safety hazards. I was able to develop and implement practical solutions to problems including optimal regulation of spatial profiles in transport-reaction processes subject to constraints, in collaboration with Prof. Christofides (UCLA), and in collaboration with prof. Kazantsis (WPI) to address the design of nonlinear ``energy'' based control, and monitoring of nonlinear processes for the purpose of fault detection in chemical process operations. My current research efforts lie within mathematical and computational explorations of cardiac models and systems that describe dynamic features of single cell to large scale myocardium dynamics. In particular, finite-element and finite-difference algorithms of cardiac action potential propagation is considered in order to obtain more precise insight in the cardiac systems dynamics and physiological characteristics of the tissue. Control of arrhythmic beat-to-beat oscillations, named alternans, which are observed in experiments and established theoretically, is under investigation. This research is focused on developing of pacing protocols that would build on current advances in recording abilities of sensor devices and subsequently annihilate life threatening arrhythmias.
[1] Constrained Optimal Control of Distributed Parameter Systems: Research work in the area of distributed parameter system has led to the development of efficient model predictive algorithms that were able to account for the infinite-dimensionality of the distributed parameter system modeled by parabolic partial differential equations, and provide optimal stabilization of linear [4,1] and nonlinear systems [7,3] subject to spatially distributed input and state constraints. Along the same line the challenging and industrially appealing problem of boundary controlled system [2] modeled by parabolic PDEs has been resolved in the optimal control setting under the presence of actuator and state constraints. Complemented to the transport-reaction processes that are modeled by parabolic PDEs, optimal control of the distributed parameter system modeled by hyperbolic PDE system subject to input and state constraints has been addressed in [7]. The constructed model predictive control synthesis was applied through computer simulation to the constrained stabilization of the temperature profile of a diffusion-reaction process at an unstable steady-state in the case of spatially distributed control [4,7,3,1] and in the case of boundary controlled problem [2].
[2] Nonlinear Control of Complex Systems: Another contribution of my research is in the field of complex systems control. The control issue related to distributed parameter systems is primarily an issue of suppression of complex dynamic behavior and stabilization of unstable steady state. While the above efforts have led to the development of a number of systematic approaches for distributed controller design, an underlying theme of available approaches is the use of a finite (typically small) number of control actuators and measurement sensors, distributed along the spatial extent of the process, to achieve stabilization of the process at a (possibly open-loop unstable) spatially non-uniform profile. Significant recent advances in actuation and sensing technology enable the use of large numbers of actuators and sensors to control spatially distributed processes. Examples include the manufacturing of arrays of micro-actuators/sensors for flow control and the development of computer-controlled focused laser beams for temperature control of catalytic surfaces. Motivated by the possibility of using such finely spatially distributed actuation/sensing, in this part of my research work, the extension of the traditional control formulation for spatially-distributed processes to an ``infinite sensing'' - ``infinite actuation'' formulation has been developed in order to suppress the dynamics of an arbitrary PDE and to induce a spatiotemporal profile of another "targeted" PDE that admits different spatiotemporal dynamics [5,8].
[3] Nonlinear controller synthesis : Research work in this area (in collaboration with Prof. Kazantzis) has focused on the development [9,6] of practically implementable framework for model-based control of nonlinear processes that is based on the methodological principles of Lyapunov design. In particular, it relies on a short-horizon model-based prediction and optimization of the rate of ``energy dissipation'' of the system in the synthesis of the controller that integrates the following desirable properties: 1) optimality with respect to meaningful performance objectives that guarantee the use of reasonable control action to achieve desired control objectives such as stability, 2) an explicit characterization of the region of guaranteed closed-loop stability from which the system can be stabilized. In this sense, two important notions such as optimality and characterization of the closed-loop stability are provided in the formulation of the control law which is appealing to the control practitioner whose a priori desire is to determine the size of the region of guaranteed closed loop stability and how strong or mild control action can be imposed on the system. Another important aspect of my research work within the area of nonlinear systems considers the design of nonlinear observes [10] that are inevitably present in the current chemical engineering practice as a complementary integral part of the controller design. Namely, a large number of process variable can not be directly measured either due to inherent characteristics of the process (e.g. concentration of the reactant) or due to inaccessibility of the measuring devices to the variable of interest (e.g., velocity measurement in the plug-flow reactor). In order to obtain accurate and reliable knowledge of the desired process variable for the purpose of reliable monitoring, nonlinear observer design has been extended for the purpose of fault detection such that detrimental and highly unpredictable nonlinear phenomena which make integral part of any real process are captured with high degree of accuracy and may crucially impinge on the stringent product specification requirements and safety protocols.
[1] Dubljevic, S. and P. D. Christofides, “Predictive Output Feedback Control of Parabolic PDEs,” Proceedings of American Control Conference, submitted, Minneapolis, Minnesota, 2006.
[2] Dubljevic, S. and P. D. Christofides, “Boundary Predictive Control of Parabolic PDEs,” Proceedings of American Control Conference, submitted, Minneapolis, Minnesota, 2006.
[3] Dubljevic, S., P. Mhaskar, N. H. El-Farra and P. D. Christofides, “Predictive Control of Diffusion-Reaction Processes,” Proceedings of American Control Conference, 4551 - 4556, Portland, Oregon, 2005.
[4] Dubljevic, S., P. Mhaskar, N. H. El-Farra and P. D. Christofides, “Predictive control of parabolic PDEs with state and control constraints,” Proceedings of American Control Conference, 254 - 260 vol.1, Boston, Massachusetts, 2004.
[5] Dubljevic, S., P. D. Christofides and I. G. Kevrekidis, “Distributed Nonlinear Control of Diffusion-Reaction Processes,” Proceedings of American Control Conference, 1341 - 1348, Denver, Colorado, 2003.
[6] Kazantzis N. and S. Dubljevic, “Nonlinear Discrete-Time State Feedback Regulators with Assignable Closed-Loop Dynamics,” Proceedings of American Control Conference, 3177 - 3182, vol.4, Arlington, Virginia, 2001.
[7] Dubljevic, S., P. Mhaskar, N. H. El-Farra and P. D. Christofides, “Predictive Control of Transport-Reaction Processes,” Comp. & Chem. Eng., in press, 2005.
[8] Dubljevic, S. and P. D. Christofides and I. G. Kevrekidis, “Distributed nonlinear control of diffusion-reaction processes,” Inter. Jour. Robus. Nonl. Cont., 14(2): 133 - 156, 2004.
[9] Dubljevic, S. and N. Kazantzis “A new Lyapunov design approach for nonlinear systems based on Zubov's method,” Automatica, 38, 1999 - 2007, 2002.
[10] Dubljevic S., S. Rajaraman and M. S. Mannan, “Nonlinear observer based sensor fault detection,” AIChE Annual Meeting, paper 385af, Reno, Nevada, 2001.