RESEARCH
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Currently I work on the problem of air flow controller design for a ventilator system, which is a hybrid nonlinear dynamical system with time delays.
Prior to that, I have explored problems in linear control theory, optimization and structured control. I have also worked on the alternating direction method of multipliers for convex optimization (U2) and sensorless control design (C3). I have also worked on the suboptimal control (U1), suboptimal consensus protocol design for multi-agent systems (J2), optimal control in Krotov framework for linear (J1), nonlinear (C4), and multi-agent systems (C11).
One of the contribution of my PhD work is captured in the following image.
Unpublished Work** in progress
Below is the list of my publications.
Journal Publications
Below is the list of my publications.
Journal Publications
J3. Kumar, Avinash and Tushar Jain. "Characterization of Upper Bound on Cost for Linear Quadratic Problems with a Norm-bounded Gain Matrix, Optimal Control, Applications and Methods (2025): 1-11.
J2. Kumar, Avinash, and Tushar Jain. "Suboptimal consensus protocol design for a class of multiagent systems." Journal of the Franklin Institute 360.18 (2023): 14553-14566.
J2. Kumar, Avinash, and Tushar Jain. "Suboptimal consensus protocol design for a class of multiagent systems." Journal of the Franklin Institute 360.18 (2023): 14553-14566.
J1. Kumar, Avinash, and Tushar Jain. "Some insights on synthesizing optimal linear quadratic controllers using Krotov sufficient conditions." IEEE Control Systems Letters 4.2 (2020): 486-491.
In Conference Proceedings
C12 Kumar, Avinash Choosing Augmentation Parameters in OSQP- A New Approach based on Conjugate Directions (accepted )( International Conference on System Theory, Control and Computing)
C11 Kumar, Avinash, and Tushar Jain. "An alternative method for optimal consensus protocol design for scalar single-integrators using Krotov conditions." IFAC-PapersOnLine 53.2 (2020): 2982-2987.
C10 Kumar, Avinash, and Tushar Jain. "Sub-optimal Consensus Protocol Design for Double Integrator Agents using Krotov Conditions." IFAC-PapersOnLine 53.1 (2020): 483-487.
C9 Kumar, Avinash, and Tushar Jain. "Sub-optimal Control Design for Second Order Non-linear Systems using Krotov Sufficient Conditions." IFAC-PapersOnLine 53.1 (2020): 272-276.
C8 Kumar, Avinash, and Tushar Jain. "Optimal consensus protocol design for scalar single integrators using krotov conditions." IFAC-PapersOnLine 53.1 (2020): 471-476.
C7 Kumar, Avinash, and Tushar Jain. "Optimal and Sub-optimal Control Design for Second Order Nonlinear Affine Systems using Krotov Sufficient Conditions." 2019 4th Conference on Control and Fault Tolerant Systems (SysTol). IEEE, 2019.
C6 Kumar, Avinash, and Tushar Jain. "Suboptimal Control of Linear Systems with Bounded Disturbances using Krotov sufficient Conditions." 2019 IEEE Conference on Control Technology and Applications (CCTA). IEEE, 2019.
C5 Kumar, Avinash, and Tushar Jain. "Computation of non-iterative optimal linear quadratic controllers using Krotov's sufficient conditions." 2019 American Control Conference (ACC). IEEE, 2019.
C4 Kumar, Avinash, and Tushar Jain. "Analytical infinite-time optimal and sub-optimal controllers for scalar nonlinear systems using Krotov sufficient conditions." 2019 18th European Control Conference (ECC). IEEE, 2019.
C3 Kumar, Avinash, and Subashish Datta. "Elimination of Expensive Sensors in Static State Feedback Control with Specified Transient Behaviour." 2019 Fifth Indian Control Conference (ICC). IEEE, 2019.
C2 Kumar, Avinash, and Tushar Jain. "Computation of linear quadratic regulator using Krotov sufficient conditions." 2019 Fifth Indian Control Conference (ICC). IEEE, 2019.
C1 Kumar, Avinash, and B. B. Sharma. "Non-linear system identification using a real coded genetic algorithm."
The manuscripts which I find very interesting in general in the control theory are listed below.
1. Khlebnikov, Mikhail Vladimirovich, Boris Teodorovich Polyak, and Vsevolod Mikhailovich Kuntsevich. "Optimization of linear systems subject to bounded exogenous disturbances: The invariant ellipsoid technique." Automation and Remote Control 72 (2011): 2227-2275.
The manuscripts which I find very interesting in general in the control theory are listed below.
1. Khlebnikov, Mikhail Vladimirovich, Boris Teodorovich Polyak, and Vsevolod Mikhailovich Kuntsevich. "Optimization of linear systems subject to bounded exogenous disturbances: The invariant ellipsoid technique." Automation and Remote Control 72 (2011): 2227-2275.
2. Gurman, Vladimir I., et al. "On certain approaches to optimization of control processes. I." Automation and Remote Control 77 (2016): 1370-1385.
3. Gurman, Vladimir I., et al. "On certain approaches to optimization of control processes. II." Automation and Remote Control 77 (2016): 1544-1556.
4. Khlebnikov, M. V. "Linear Matrix Inequalities in Control Problems." Differential Equations 56 (2020): 1496-1501.
5. Ren, Wei, Randal W. Beard, and Ella M. Atkins. "Information consensus in multivehicle cooperative control." IEEE Control systems magazine 27.2 (2007): 71-82.
6. Willems, Jan. "Least squares stationary optimal control and the algebraic Riccati equation." IEEE Transactions on automatic control 16.6 (1971): 621-634.
7. Polyak, Boris T., and Pavel S. Shcherbakov. "Hard problems in linear control theory: Possible approaches to solution." Automation and Remote Control 66.5 (2005): 681-718.
8. Degenerate Problems of Optimal Control. I. V. I. Gurman∗ and Ni Ming Kang, Automation and Remote Control, 2011, Vol. 72, No. 3, pp. 497–511.
9. Linear Matrix Inequalities in Control Systems with Unx`certainty by B. T. Polyak, M. V. Khlebnikov, and P. S. Shcherbakov
Teaching Interests
Teaching Interests
I have engaged in partially/fully teaching the following courses.
1. Linear Dynamical Systems
2. Network Theory
3. Signals and Systems
4. Digital Signal Processing
5. Data Science (Probability Theory)
6. Digital Logic Design
7. Microprocessor and Embedded Systems
8. Computer System Organization
I use interactive quizzes to ensure active engagement of the students during the class. The samples of quizzes designed by me are here.
Furthermore, I would be happy to teach the following courses which belong to post-graduate level.
1. Nonlinear Dynamics
2. Convex Optimization
3. Multi-agent Systems
4. Linear Algebra
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