# Abhijit Das

Welcome to my page!

## About Me

**Brief Professional Background**

I grew up in a small town in Kharagpur, India, and then I attended IIT Kharagpur, where I received Masters degree in electrical engineering in 2006. I later joined Automation and Robotics Research Institute, University of Texas at Arlington to earn my PhD also in electrical engineering in 2010. Since then I have worked at Caterpillar, Danfoss, and Halliburton. I received several awards including Technical & Service Excellence Award 2017, Danfoss, Certificate of appreciation 2016, Danfoss

Dean Dissertation Fellowship award 2010, UT Arlington STEM Doctoral Fellowship (2007-2010), Automation and Robotics Research Institute. I authored several articles, book chapters, and books. I am a life member of the Systems Society of India, a member of IEEE. My profile has also appeared in Marquis Who’s Who in America.

**Few Fun Facts **

**Model-Based Design of Off-highway Machines**

MBD uses physics-based models of the systems to be controlled (called “plant models”) to provide a basis for the controller design. This process was soon extended to allow the prototype controllers to be tested with the virtual plant model on real-time simulators before integrating them into the real vehicle systems. This allowed One to validate that the system will work within specification or, if it does not, adjust the design to bring it into spec.

Building an MBD platform for a complex machine like excavators is consists of several steps. For example, a vehicle propel (transmission) simulation model of a machine like an excavator consists a medium-fidelity engine model, a very high fidelity pump and motor model, a very high fidelity electronic pump, motor, and engine controller model as well as a medium-fidelity machine driveline, body, and tire model. Danfoss is widely known for its hydraulic components and their electronic controls. So, machine system simulations are mainly focused on building high fidelity models for the pump, motors, and controls. In another example, the work function model of a machine like an excavator is consists of a medium-fidelity engine model, a very high fidelity valve model, and very high fidelity boom, stick and bucket model. A high fidelity model of any hydraulic or electronic control component is generally very complex and requires extensive knowledge and background on that particular product. Using Matlab as a simulation environment, a very high fidelity model of every component described above may provide accurate performance estimate but with a possible sacrifice of simulation speed. Therefore the compromise between fidelity of the model and overall system performance accuracy is always been a challenging choice for engineers. After successfully overcome the hurdle of building the system model, now it is ready to use it as a tool to test and validate the new control algorithms even when the target machine prototype is not available. As the number of electronic controllers increases, using the MBD platform to build the first working prototype is becoming an obvious choice. Also, while testing the tool with a built prototype machine will generate enough feedback to minimize the errors committed in the previous step. Note that the benchmark for the desired outcome and its accuracy with respect to specification is different for different machines and is generally determined by applying rigorous analysis and optimization techniques. It is becoming increasingly important to model and simulate the whole vehicle at a system level very early in the design process. This is the main objective as well as one of the primary applications of MBD. MBD uses physics-based models of the systems to be controlled (also known as “plant models”) to provide a basis for the controller design. This process was soon extended to allow the prototype controllers to be tested with the virtual plant model on real-time simulators before integrating them into the real vehicle systems. This allowed the engineers to validate that the system will work within specification or, if it does not, adjust the design to bring it into spec. Therefore, by the time the controller is integrated into the first vehicle prototype, most of the major risks to the success of the project are significantly mitigated, while prototyping time and costs are dramatically reduced. When the prototype vehicle is built based on initial specification determined by engineers, in the next phase accuracy of response from the MBD platform is thoroughly checked with the prototype response. If not close enough; one has to start tuning the MBD parameters to make that happen. For a complex machine like excavators, it might take a few weeks to months to tune the model completely. Now one can use this tuned MBD platform for that excavator to test future control algorithms. The energy management system plays an obvious part in modern pieces of machinery. This sub-system is connected to almost every other component, which consumes energy directly, or indirectly through internal combustion (IC) engines. Several optimization algorithms can be designed to elevate machine performance while minimizing fuel consumption. MBD once again is the best choice to verify these algorithms before it gets implemented finally on prototype machines. Co-simulation is one another example where MBD plays an important role. Often complex hydraulics and mechanical components are built-in based on different software approaches. Therefore integrating all different models into a single one is necessary. Generally, MATLAB is the preferred tool for control engineers like Abhijit; therefore models designed by software other than MATLAB are imported into MATLAB as S-function to complete the MBD platform. In a different approach, where some component cannot be described as a mathematical model, is required to be integrated as the hardware itself. This type of MBD platform is also known as hardware-in-loop (HIL) simulation and widely popular in Danfoss and in other companies. In this approach, the engineer can directly observe the behavior of the hardware component based on certain control inputs. In summary, MBD, the process adopted throughout industries worldwide including Danfoss is the key in order to understand how the multitude of subsystems interact with each other over the entire range of duties even when a prototype doesn’t exist or engineer does not have customer specification in hand. This needs to be done very early in the design stage so that as the design evolves, the functional behavior can be validated throughout the process, thus ensuring it continues to fulfill the design goals of the product. From the primary design stage to the final fuel-efficient complete prototype machine, model-based development (and simulation) creates the backbone where current and future ideas are created, nurtured and finally delivered.

Coordination and consensus of distributed groups of agents are inspired by naturally occurring phenomena such as flocking in birds, swarming in insects, circadian rhythms in nature, synchronization and phase transitions in physical and chemical systems, and the laws of thermodynamics. Research work has been done in the control systems communities by which by now are well known. Consensus has been studied for systems on communication graphs with fixed or varying topologies and communication delays. The average consensus problem has garnered much interest. Synchronization to time-varying trajectories has been studied based on physical or natural systems. The synchronization of nonlinear passive dynamical systems has also been studied. Consensus using nonlinear protocols has been considered too. The convergence of consensus to a virtual leader or header node, the dynamic consensus for tracking of time-varying signals, and recently, the pinning control have been introduced and studied for synchronization control of coupled complex dynamical systems. Pinning control is a powerful technique that allows controlled synchronization of interconnected dynamical systems by adding a control or leader node that is connected (pinned) into a small percentage of nodes in the network. These pinned or controlled nodes view the control node simply as another neighbor and consider the control node’s state value in computing their local protocols. The analysis shows that all nodes converge to the state of the control node, which may be time-varying. Analysis has been done using Lyapunov techniques by assuming either a Jacobian linearization of the nonlinear node dynamics or a Lipschitz condition. A related idea is a soft control where a shill node moves through the network and is perceived by existing nodes simply as another neighbor for purposes of computation of their own averaging protocols. Proper placement and motion of the shill agent result in consensus to the state of the shill. The idea of pinning control for undirected graph topology using V-stability has been studied by researchers. Consensus and collective motion of distributed agents have been analyzed using the theory of graphs and/or Markov processes. Recent publications allow analysis using traditional control theory notions including matrix analysis, Lyapunov theory, etc., upon the introduction of certain key definitions including irreducibility, M-matrices, Frobenius form, special Lyapunov forms, etc. Such techniques allow one to bring in the machinery of matrix analysis. Instrumental in this analysis are the techniques employed in many well-known pieces of literature. Distributed multi-agent systems with unknown nonlinear dynamics and disturbances were studied in where distributed adaptive controllers were designed to achieve robust consensus. That treatment assumed undirected graphs and solved the consensus problem, that is, the nodes reach a steady-state consensus that depends on the initial conditions. Expressions for the consensus value were not given. The study of control protocols on digraphs is significantly more involved than their study on undirected graphs, where the graph Laplacian can be taken as a Lyapunov function. Pinning control for directed graph topologies was studied with simpler node dynamics. In addition, the dynamics of all nodes were assumed to be the same. Consensus using output feedback and a dynamic compensator is another interesting topic, where it is shown how to design compensator gains to guarantee synchronization on arbitrary strongly connected graphs using a design method based on Finsler’s Lemma. In distributed observers were designed at each node to estimate the state of the control or leader node. State feedback protocols were used between neighbors. A dynamic compensator is designed for consensus, when the leader node’s state is not measured, using a distributed feedback law and a distributed observer for the leader’s unknown state. Riccati equation-based analysis was used. Multi-agent coordination was ensured by designing dynamic output feedback compensators using the output regulation approach. In a method for synchronization was given that used an observer and a dynamic compensator at each node. Here are a few examples of naturally occurring coordinate movements of birds and fish.

The main purposes of a Heating, Ventilation, and Air-Conditioning (HVAC) system are to help maintain good indoor air quality through adequate ventilation with filtration and provide thermal comfort. A quality HVAC system has to be properly sized to provide correct airflow and meet room-by-room calculated heating and cooling loads. It is also required to be installed so that the static air pressure drop across the handler is within manufacturer and design specifications to have the capacity to meet the calculated loads. A good HVAC system should have balanced air flows between supply and return systems to maintain neutral pressure in the home. For a large building, it is not always easy to control thermal comfort for every person inside the building. The airflow through the vent is to be properly controlled at every moment to satisfy the criterion of temperature consensus inside the building. It requires proper coordination among airflow, temperature sensor position, and its accuracy, vent positions, etc. A wide range of studies can be found in the literature regarding indoor air distributions, some of which demonstrate a numerical method to control air distribution inside an office building. It is shown that the efficiency of the HVAC system decreases along with the increase in the number of occupants in the building. The characteristics of air to be distributed inside the building for quality thermal consensus among the occupants are also studied.

The HVAC with a digital control system using computer program demonstrate the use of decentralized control for thermal consensus in the HVAC system. Consensus has been studied for systems on communication graphs with fixed or varying topologies and communication delays, which proposed basic synchronizing protocols for various communication topologies. Early work on consensus studied leaderless consensus or the cooperative regulator problem, where the consensus value reached depends on the initial conditions of the node states. On the other hand, the cooperative tracker problem seeks consensus or synchronization to the state of a control or leader node. The convergence of consensus to a virtual leader or header node is also studied. Dynamic consensus and pinning control has been discussed in earlier sections. Pinning control allows controlled synchronization of interconnected dynamical systems by adding a control or leader node that is connected (pinned) into a small percentage of nodes in the network. Analysis has been done using Lyapunov and other techniques by assuming either a Jacobian linearization of the nonlinear node dynamics, or a Lipschitz condition, or contraction analysis. The agents are homogeneous in that they all have the same nonlinear dynamics. In this research, we discussed the pinning control for HVAC systems. The aim of this particular research is to synchronize the room temperatures at every point with the desired set of temperature values irrespective of the number of occupants. The modeling of the HVAC system as a decentralized control unit is little different than that of standard multiagent systems discussed in the previous sections. Considering each outlet vents as a node point, an undirected graph topology can be defined around the building. As not, all the vents use for control purposes and the neighborhood of a control node can be different than that of undirected modeling graph, a directed control graph topology is defined over the modeling graph. The dynamics of the HVAC system is derived from the poison heat equations and from the flow dynamics in the pipe network installed in the building. The actual control variables are vent positions and airflow rate through the outlet vents. The control variables appear as bilinear fashion in the dynamics. A suitable synchronization control protocol is proposed based on the pinning control formulation. A Lyapunov method is shown to prove the overall system stability under the proposed control protocol.

A quadcopter, also called a quadrotor helicopter, quadrocopter, quadrotor, is a multicopter that is lifted and propelled by four rotors. Quadcopters are classified as rotorcraft, as opposed to fixed-wing aircraft, because their lift is generated by a set of revolving narrow-chord airfoils. Unlike most helicopters, quadcopters generally use symmetrically pitched blades; these can be adjusted as a group, a property known as 'collective', but not individually based upon the blade's position in the rotor disc, which is called 'cyclic'. Control of vehicle motion is achieved by altering the pitch and/or rotation rate of one or more rotor discs, thereby changing its torque load and thrust/lift characteristics (see wiki more general information).

Nowadays unmanned rotorcraft are designed to operate with greater agility, rapid maneuvering, and are capable of work in degraded environments such as wind gusts, etc. The control of this rotorcraft is a subject of research especially in applications such as rescue, surveillance, inspection, mapping, etc. For these applications the ability of the rotorcraft to maneuver sharply and hover precisely is important. Rotorcraft control as in these applications often requires holding a particular trimmed state, generally hover, as well as making changes of velocity and acceleration in the desired way. Similar to aircraft control, rotorcraft control too involves controlling the pitch, yaw, and roll motion. But the main difference is that due to the unique body structure of rotorcraft (as well as the rotor dynamics and other rotating elements) the pitch, yaw, and roll dynamics are strongly coupled. Therefore, it is difficult to design a decoupled control law of sound structure that stabilizes the faster and slower dynamics simultaneously. On the contrary, for a fixed-wing aircraft it is relatively easy to design decoupled standard control laws with intuitively comprehensible structure and guaranteed performance. There are many different approaches available for rotorcraft control such as etc. Popular methods include input-output linearization and backstepping.

The 6-DOF airframe dynamics of a typical quadrotor involves the typical translational and rotational dynamical equations as in. The dynamics of a quadrotor are essentially a simplified form of helicopter dynamics that exhibits the basic problems including underactuation, strong coupling, multi-input/multi-output, and unknown nonlinearities. The quadrotor is classified as a rotorcraft where the lift is derived from the four rotors. Most often they are classified as helicopters as its movements are characterized by the resultant force and moments of the four rotors. Therefore the control algorithms designed for a quadrotor could be applied to a helicopter with relatively straightforward modifications. Most of the previous and existing research works deal with either input-output linearization for decoupling pitch yaw roll or backstepping to confront the underactuation problem. The problem of coupling in the yaw- pitch-roll of a helicopter, as well as the problem of the coupled dynamics-kinematic underactuated system, can be solved by backstepping. Dynamic inversion is effective in the control of both linear and nonlinear systems and involves an inner inversion loop (similar to feedback linearization) which results in tracking if the residual or internal dynamics are stable. Typical usage requires the selection of the output control variables so that the internal dynamics are guaranteed to be stable. This implies that tracking control cannot always be guaranteed for the original outputs of interest.

The application of dynamic inversion on UAV’s and other flying vehicles such as missiles, fighter aircraft, etc are proposed in several research works such as, etc. It is also shown that the inclusion of a dynamic neural network for estimating the dynamic inversion errors can improve the controller stability and tracking performance. It can be shown that a reconfigurable control law can be designed for fighter aircraft using the neural net and dynamic inversion. Sometimes the inverse transformations required in dynamic inversion or feedback linearization are computed by the neural networks to reduce the inversion error by online learning.

The estimation of aerodynamic coefficients for aerospace vehicles remains in the region of interest for researchers in past decades. My previous research shows how to estimate aerodynamic coefficients (lateral and longitudinal) for complex aerospace vehicles.

In this research work, we apply dynamic inversion to tackle the coupling in quadrotor dynamics which is in fact an underactuated system. Dynamic inversion is applied to the inner loop, which yields internal dynamics that are not necessarily stable. Instead of redesigning the output control variables to guarantee the stability of the internal dynamics, we use a robust control approach to stabilize the internal dynamics. This yields a two-loop structured tracking controller with a dynamic inversion inner loop and an internal dynamics stabilization outer loop. But it is interesting to notice that unlike normal two-loop structure, we designed an inner loop that controls and stabilizes altitude and attitude of the quadrotor and an outer loop that controls and stabilizes the position (x,y) of the quadrotor. This yields a new structure of the autopilot in contrast to the conventional loop linear or nonlinear autopilot.

Most work in quadrotor control that uses backstepping design such as or other control formulations like exact linearization are based on state-variable formulations. These results in the control laws that often require the evaluation of Lie derivatives. Some research works perform backstepping on Euler-Lagrange dynamics, but backstepping is performed on a bilinear product involving thrust input, which we avoid. In this research we apply backstepping to the coupled Lagrangian form (not the state-variable form) of the dynamics; this yields a structured controller with an attitude control inner loop and a position control outer loop. It is not straightforward to apply backstepping to the Lagrangian dynamics since the positioning subsystem is bilinear in the control. This is confronted herein using an inverse kinematics solution. To combat unknown nonlinearities we use neural networks to estimate the nonlinear terms and aerodynamic forces and moments. Although the neural network used in this research is the first-order one, it estimates the higher-order unknown state polynomials efficiently. Moreover, the neural net used is a dynamic one as it uses the state-dependent tuning rule. So structurally the neural net is not a higher-order neural net (HONN), but functionally it appears as a dynamic HONN or more precisely one can say it is a higher-order like a neural net (HOLNN). The resulting controller has an appealing structure. Simulation results are shown to validate the control law discussed in this research.

One of the basic requirements for designing an autopilot is fast response time, because of the short amount of time involved in the end game. Secondly, the minimum error is an obvious requirement if the missile has to achieve a hit to kill miss. Finally, the robustness of model uncertainties and decoupling between longitudinal and lateral motion is also important in order for the missile to achieve its objective in the physical environment.

The highly nonlinear nature of the missile dynamics due to the severe kinematic and inertial coupling of the missile airframe as well as the aerodynamics has been a great challenge to the autopilot design that is required to have a satisfactory performance for all flight conditions in probable engagements.

Classically, missile autopilots are designed using linear control approaches. The traditional approach is to first linearize the missile short period dynamics for each axis about an operating condition, and then to apply linear control theory to synthesize a feedback controller. This process is repeated at multiple operating conditions and the controllers are then scheduled with respect to the flight conditions. The assumptions hold insignificant at a high angle of attack because of lack of knowledge of the complex missile model i.e. aerodynamic parameter uncertainties and coupling. Severe coupling due to high unwanted roll disturbances generates especially at a high angle of attack is the most common concern in homing head missiles in the view of :

May cause track loss of the missile homing head as the seeker is having limited Gimbal freedom from physical considerations.

High side force disturbance may lead to control of the saturation of the actuation servo system.

Lateral corrections will be slower as the guidance demand is restricted to keep the angle of attack below the specified value to avoid coupling and uncertainty. This may cause high miss distance, particularly for minimum range engagement scenarios.

A natural idea for handling the nonlinear dynamics is to design the autopilot on the basis of the more accurate nonlinear model, thus leading to nonlinear autopilots. One such strategy is a well-known feedback linearization approach that uses the feedback and uses coordinate transformations to linearize the nonlinear system. Then it addresses the design issues on the linearized system thus obtained.

The fundamental problem due to the coupling of three axes and the method of decoupling is mainly brought out here in two steps. The first one is to design a robust feedback linearization controller. It linearizes the fast dynamics of missile (i.e. body rate loop of missile autopilot) and decouples the axes using the input-output feedback linearization technique. It also caters to high model uncertainty particularly at a high angle of attack and low dynamic pressure condition.

The second step to design a linear controller after feedback linearization that gives the desired tracking performances. The outer loop is designed by a linear controller to control the slow dynamic i.e. lateral accelerations of the missile.

At last, the performances of the design in terms of stability, robustness, the minor coupling between the longitudinal motion and lateral motion, and guaranteed tracking are shown in a full-scaled 6-DOF simulation. The performances are also compared with the performances of a conventional linear controller as already designed by the parent organization. The potentials of the nonlinear controller are brought out through a lot of comparative simulations.

**If you need help with one of the publication copies below, just fill up the contact form with details and I will get back to you as soon as possible. Thanks for visiting!**

**Books**

A. Das and S. Mukhopadhyay. Nonlinear Autopilot Design for Aerospace Vehicles: Nonlinear Design of 3-Axes Autopilot for Short RangeSkid-To-Turn Homing Missiles. VDM Verlag, 2010.

F.L. Lewis, H. Zhang, K. Hengster-Movric and A. Das. Cooperative control of multi-agent systems: optimal and adaptive design approaches. Spring-Verlag, 2014.

**Patents**

Load dependent electronic valve actuator regulation and pressure compensation, patent # US10183852B2

Variable load sense spring setting for axial piston open circuit pump, patent # US9879667B2

**Book Chapters**

A. Das and F. Lewis. "Distributed Adaptive Control for MultiAgent Systems with Pseudo Higher Order Neural Net". In: Artficial Higher Order Neural Networks for Modeling and Simulation. Ed. by Ming Zhang.1st ed. IGI Global, 2012.

A. Das, F. Lewis, and K. Subbarao. "Sliding Mode Approach to Control Quadrotor Using Dynamic Inversion". In: Challenges and Paradigms in Applied Robust Control. Ed. by Andrzej Bartoszewicz. 1st ed. InTech, 2011.

A. Das, F. Lewis, and K. Subbarao. "Quadrotor Control by Dynamic Inversion with Zero Dynamics Stabilization". In: Computational Intelligence, Control and Computer Vision in Robotics and Automation. Ed. by Bidyadhar Subudhi. 1st ed. New Delhi: Narosa, 2009.

A. Das and F. Lewis. "Back-Stepping Control of Quadrotor: A Dynamically Tuned Higher Order Like Neural Network Approach". In: Artificial Higher Order Neural Networks for Computer Science and Engineering:Trends for Emerging Applications. Ed. by Ming Zhang. 1st ed. IGI Global, 2010.

A. Das and F. Lewis. "Distributed Adaptive Control for Networked Multi-Robot Systems". In: Artificial Higher Order Neural Networks for Modeling and Simulation. Ed. by Toshiyuki Yasuda. 1st ed. In-Tech, 2012.

**Journal Papers**

A. Das and F. Lewis. "Distributed Adaptive Control for Synchronization of Second Order Systems with unknown Nonlinearities". In: International Journal of Robust and Nonlinear Control 21.3 (2010), pp. 1493-1610.

H. Zhang, A. Das, and F. Lewis. "Optimal Design for Synchronization of Cooperative Systems: State Feedback, Observer, and Output Feedback". In: IEEE Transaction of Automatic Control 56.8 (2011), pp. 1948-1952.

A. Das and F. Lewis. "Distributed Adaptive Control for Synchronization of Unknown Nonlinear Networked Systems". In: Automatica 46.12 (2010), Automatica.

A. Das, F. Lewis, and S. Subbarao. "Backstepping Approach for Controlling a Quadrotor using Neural Network". In: Journal of Intelligent and Robotics Systems 56.1 (2009). Special Issue, p. 127.

A. Das, S. Subbarao, and F. Lewis. "Dynamic Inversion with Zero-Dynamics Stabilization for Quadrotor Control". In: IET Control Theory & Applications 3.3 (2009), pp. 303-314.

**Conference Proceedings**

A. Das and E. Bretey. Control and Stability analysis of a practical load-sense systems. Accepted for publication in the Proc. International Fluid Power Exposition (IFPE). Las Vegas, Nevada, March 2014.

F. Lewis and A. Das. "Distributed observer, duality, and optimal regulator design for multi-agent systems". In: Proceedings on Decision and Control (CDC). Atlanta, GA.

A. Das and F. Lewis. "Synchronization of unknown nonlinear networked systems via cooperative adaptive control". In: Proceedings of the 8th IEEE International Conference on Control & Automation. Xiamen,China, 2011.

Chaoyong Li, Zhihua Qu, Abhijit Das, and Frank L. Lewis. "Cooperative Control with Improvable Network Connectivity". In: Proceedings of American Control Conference. San Antonio, Texas, 2010

A. Das, S. Subbarao, and F. Lewis. "Dynamic Inversion of Quadrotor with Zero-Dynamic Stabilization". In: Proceedings of IEEE Multiconference on Systems and Control. Baltimore, MD, 2008.

A. Das and F. Lewi sand S. Subbarao. "Dynamic Neural Network based Robust Backstepping Control approach for Quadrotors". In: Proceedings of AIAA Guidance, Navigation and Control Conference and Exhibit,Honolulu, Hawaii, 2008.

R. Das, A. Das, S. Mukhopadhyay, and R. N. Bhattacherjee. "Nonlinear Design of 3-axis Autopilot for a Tactical Aerospace Vehicle". In: Proceedings of Advances in Control and Optimization of Dynamical Systems (ACCODS). Bangalore, India, 2007.

A. Das, R. Das, S. Mukhopadhyay, and A. Patra. "Robust Three Axes Autopilot for a Tactical Aerospace Vehicle". In: Proceedings of IEEE region 10 International conference (TENCON). Hong Kong, 2006.

A. Das, R. Das, S. Mukhopadhyay, and A. Patra. "Robust Autopilot for a Short Range Surface-to-Surface Skid-to-Turn Homing Missile". In: Proceedings of IEEE International Conference on Industrial Technology. Mumbai, India, 2006.

A. Das, R. Das, S. Mukhopadhyay, and A. Patra. "Robust Nonlinear Design of Three Axes Missile Autopilot via Feedback Linearization". In: Proceedings of National Systems Conference. Goa,India, 2006.

A. Das, R. Das, S. Mukhopadhyay, and A. Patra. "Sliding Mode controller along with Feedback linearization for a Nonlinear Missile Model". In: Proceedings of the 1st International Symposium on Systems and Control in Aerospace and Astronautics (ISSCAA), Harbin, China, 2006.

A. Das, R. Das, S. Mukhopadhyay, and A. Patra. "A Practical Approach to Estimate States of an Aerospace Vehicle". In: Proceedings of National Systems Conference. Goa, India, 2006.

A. Das, T. Garai, R. Das, S. Mukhopadhyay, and A. Patra. "Autopilot Design via Feedback Linearization for a Nonlinear Skid-To-Turn Missile". In: National Conference for Control and Dynamical Systems. Mumbai, India, 2005.

A. Das, R. Das, S. Mukhopadhyay, and A. Patra. "Nonlinear Autopilot and Observer design for a Surface-To-Surface, Skid-To-Turn Missile". In: Proceedings of the Second India Annual Conference (IEEE INDICON). Chennai, India, 2005.

A. Das, T. Garai, S. Mukhopadhyay, and A. Patra. "Feedback linearization for a nonlinear skid-to-turn missile model". In: Proceedings of the First India Annual Conference (IEEE INDICON). Kharagpur, India, 2004.