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Verica Gajic
- Assistant Professor
- Ext: 5439
My expertise are in Dynamics and Control of complex systems
Education
- PhD, Rutgers University, USA, 2001
PhD, Rutgers University, USA, 2001
Teaching Area
- Dynamics, Systems, Vibration, and Control. In addition, I have been teaching Thermo-Fluids and Mechanics classes
Dynamics, Systems, Vibration, and Control. In addition, I have been teaching Thermo-Fluids and Mechanics classes
Research
- Dynamics, Systems, and Control theory and applications to Bio systems, Fuel cells, Infinite dimensional Sytems. IoT
Dynamics, Systems, and Control theory and applications to Bio systems, Fuel cells, Infinite dimensional Sytems. IoT
Publications
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JournalVerica Radisavljevic-Gajic, Design of reduced-order observer based steady state optimal linear-quadratic feedback controllers, Journal of the Franklin Institute, Jul 2024, doi: 10.1016/j.jfranklin.2024.107015
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Journal[2] V. Radisavljevic-Gajic, D. Karagiannis, and Z. Gajic, Linear, Nonlinear, and Distributed-Parameter Observers Used for (Renewable) Energy Processes and Systems—An Overview, Energies, Jun 2024, doi: 10.3390/en17112700
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JournalDimitri Karagiannis, Verica Radisavljevic-Gajic, Control of Resonant Disturbances on an Euler–Bernoulli Beam Using a Robust Partial Differential Equation Boundary Control Technique, ASME Letters in Dynamic Systems and Control, Jan 2024, doi: https://doi.org/10.1115/1.4064600
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JournalV. Radisavljevic-Gajic, D. Karagiannis, and Z. Gajic, The Modeling and Control of (Renewable) Energy Systems by Partial Differential Equations—An Overview, Energies, Dec 2023, doi: 10.3390/en16248042
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Journal[5] V. Radisavljevic-Gajic, Control of Autonomous Vehicles Via Multistage Linear Feedback Design, Transactions of ASME Journal of Dynamic Systems, Measurement, and Control, Feb 2023, doi: https://doi.org/10.1115/1.4056781
Verica Radisavljevic-Gajic, Design of reduced-order observer based steady state optimal linear-quadratic feedback controllers, Journal of the Franklin Institute, Jul 2024, doi: 10.1016/j.jfranklin.2024.107015
n this paper we formulate and solve a problem encountered in engineering applications when a linear-quadratic (LQ) optimal feedback controller uses state estimates obtained via a reduced-order observer. Due to the use of state estimates instead of the actual state variables, the optimal quadratic performance is degraded in a pretty complex manner. In the paper, we show how to find the exact formula for the optimal performance degradation (optimal performance loss) in linear time invariant systems for the steady state case (infinite horizon optimization problem). The optimal performance loss is obtained in terms of solution of a reduced-order algebraic Lyapunov equation whose dimension is equal to the dimension of the reduced-order observer. The quantities that impact the performance criterion loss are identified. Practical examples (an inverted pendulum on a cart and an aircraft) show that the optimal performance loss can be very significant in some applications, and even very high in the presented linear-quadratic optimal control of an inverted pendulum problem. We have shown, using the derived formula, how the optimal performance loss can be considerably reduced by properly choosing the reduced-order observer initial conditions via the least square method.
About the journal
[2] V. Radisavljevic-Gajic, D. Karagiannis, and Z. Gajic, Linear, Nonlinear, and Distributed-Parameter Observers Used for (Renewable) Energy Processes and Systems—An Overview, Energies, Jun 2024, doi: 10.3390/en17112700
Full- and reduced-order observers have been used in many engineering applications, particularly for energy systems. Applications of observers to energy systems are twofold: (1) the use of observed variables of dynamic systems for the purpose of feedback control and (2) the use of observers in their own right to observe (estimate) state variables of particular energy processes and systems. In addition to the classical Luenberger-type observers, we will review some papers on functional, fractional, and disturbance observers, as well as sliding-mode observers used for energy systems. Observers have been applied to energy systems in both continuous and discrete time domains and in both deterministic and stochastic problem formulations to observe (estimate) state variables over either finite or infinite time (steady-state) intervals. This overview paper will provide a detailed overview of observers used for linear and linearized mathematical models of energy systems and review the most important and most recent papers on the use of observers for nonlinear lumped (concentrated)-parameter systems. The emphasis will be on applications of observers to renewable energy systems, such as fuel cells, batteries, solar cells, and wind turbines. In addition, we will present recent research results on the use of observers for distributed-parameter systems and comment on their actual and potential applications in energy processes and systems. Due to the large number of papers that have been published on this topic, we will concentrate our attention mostly on papers published in high-quality journals in recent years, mostly in the past decade.
About the journal
Dimitri Karagiannis, Verica Radisavljevic-Gajic, Control of Resonant Disturbances on an Euler–Bernoulli Beam Using a Robust Partial Differential Equation Boundary Control Technique, ASME Letters in Dynamic Systems and Control, Jan 2024, doi: https://doi.org/10.1115/1.4064600
This article discusses and analyzes the capabilities and limitations of a series of related controllers for Euler–Bernoulli beam vibration, and the powerful capabilities of a robust second-order sliding mode backstepping control method are exhibited. Motivated by the open-loop unstable response to harmonic excitations at resonant frequencies, specific attention is given to disturbances at system resonant frequencies. It is shown that the second-order sliding mode backstepping controller provides arbitrary exponential stability of the beam position where other similar controllers cannot. Furthermore, it is shown that other controllers exhibit large (relative to the disturbance) steady-state harmonic vibrations, or otherwise do not return the system to the origin. This article is an extension of the Dynamic Systems and Control Division Vibrations Technical Committee “Best Vibrations Paper Award”-winning conference paper (Karagiannis and Radisavlejevic-Gajic, 2017, “Robust Boundary Control for an Euler Bernoulli Beam Subject to Unknown Harmonic Disturbances With a Focus on Resonance”). The previous work is significantly extended to include an exponentially stabilizing, second-order sliding mode controller and discusses several boundary conditions.
About the journal
V. Radisavljevic-Gajic, D. Karagiannis, and Z. Gajic, The Modeling and Control of (Renewable) Energy Systems by Partial Differential Equations—An Overview, Energies, Dec 2023, doi: 10.3390/en16248042
Mathematical models of energy systems have been mostly represented by either linear or nonlinear ordinary differential equations. This is consistent with lumped-parameter dynamic system modeling, where dynamics of system state variables can be fully described only in the time domain. However, when dynamic processes of energy systems display both temporal and spatial evolutions (as is the case of distributed-parameter systems), the use of partial differential equations is necessary. Distributed-parameter systems, being described by partial differential equations, are mathematically (and computationally) much more difficult for modeling, analysis, simulation, and control. Despite these difficulties in recent years, quite a significant number of papers that use partial differential equations to model and control energy processes and systems have appeared in journal and conference publications and in some books. As a matter of fact, distributed-parameter systems are a modern trend in the areas of control systems engineering and some energy systems. In this overview, we will limit our attention mostly to renewable energy systems, particularly to partial differential equation modeling, simulation, analysis, and control papers published on fuel cells, wind turbines, solar energy, batteries, and wave energy. In addition, we will indicate the state of some papers published on tidal energy systems that can be modelled, analyzed, simulated, and controlled using either lumped or distributed-parameter models. This paper will first of all provide a review of several important research topics and results obtained for several classes of renewable energy systems using partial differential equations. Due to a substantial number of papers published on these topics in the past decade, the time has come for an overview paper that will help researchers in these areas to develop a systematic approach to modeling, analysis, simulation, and control of energy processes and systems whose time–space evolutions are described by partial differential equations. The presented overview was written after the authors surveyed more than five hundred publications available in well-known databases such as IEEE, ASME, Wiley, Google, Scopus, and Web of Science. To the authors’ best knowledge, no such overview on PDEs for energy systems is available in the scientific and engineering literature. Throughout the paper, the authors emphasize novelties, originalities, and new ideas, and identify open problems for future research. To achieve this goal, the authors reviewed more than five hundred journal articles and conference papers. © 2023 by the authors.
About the journal
[5] V. Radisavljevic-Gajic, Control of Autonomous Vehicles Via Multistage Linear Feedback Design, Transactions of ASME Journal of Dynamic Systems, Measurement, and Control, Feb 2023, doi: https://doi.org/10.1115/1.4056781
In this paper, we show how autonomous vehicles performing a certain task can be controlled from one command center in order to achieve certain goals. The command center provides individual feedback gains to each vehicle in the form of one compounded feedback gain that in fact carries feedback gain information for each individual vehicle. Vehicles may be of different nature: satellites, cars, tanks, drowns, robots, unmanned aircraft, underwater vehicles, and ships. It is assumed that their dynamic is weakly coupled, namely, dynamics of each individual vehicle is weakly coupled to dynamics of all other vehicles and that they have the same control input. The weak coupling among the vehicles is represented either by physical interactions among vehicles or coordinating or communication signals. The results obtained are applicable to vehicles having different mathematical linear/linearized state space models. In the case when no interaction/ coordination/communication among vehicles is present, and all feedback signals come from the command center (central controller) controller, the vehicle mathematical models can be identical. An important feature of the presented results is that different local feedback controllers can be facilitated for different vehicles using a unique global feedback controller signal designed by the command center. In this paper, we will consider cases of two and three vehicles, but the presented multistage feedback design methodology can be potentially extended to N vehicles. The presentation is done in continuous time. Similar derivations hold in the discrete-time domain.
About the journal
Memberships, Awards and Honors
- ASME, IEEE, WE