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Welcome to the Intelligent Systems Research Laboratory at Texas A&M University. We focus on developing advanced algorithms and analytical methods to design next-generation autonomous systems operating in uncertain dynamic environments. We achieve these goals using theoretical tools from stochastic dynamical systems, robust control, nonlinear estimation, and convex optimization. Our recent work is summarized below.

Certification of Autonomous Flight with Theory & Data Driven Machine Learning

We expect Urban Air Mobility to rely more on autonomy than any other transportation sector, and consequently, it is critical to quantify their safe flight envelope accurately. Computational tools for critical analyses of the system, such as determining region-of-attraction, establishing local performance bounds, and identifying the largest uncertainty set for which robust performance is guaranteed, are necessary to establish trust in this increased autonomy. This research focuses on developing new formulations and algorithms for determining the region of attraction of uncertain nonlinear system dynamics with various gust models, establishing bounds on exogenous signal attenuations and quantifying the largest uncertainty set for which the control and estimation algorithms perform satisfactorily. These formulations incorporate simulation data (black box) and physics-derived vehicle dynamics, resulting in constrained PDEs in high dimensional space, which are solved using recent developments in scientific machine learning.

Selected Papers

  1. V. Tadiparthi, R. Bhattacharya, Estimating Invariant Sets using Physics-Informed Neural Networks, AIAA SCITECH Forum, 2022.
  2. V. Tadiparthi, R. Bhattacharya, Data-driven Verification using Efficient Active Learning, AIAA SCITECH Forum, 2022.
  3. A. Halder, K. Lee, and R. Bhattacharya, Optimal Transport Approach for Probabilistic Robustness Analysis of F-16 Controllers, AIAA Journal of Guidance, Control, and Dynamics, 2015.
  4. A. Halder, K. Lee, R. Bhattacharya, Probabilistic Robustness Analysis of F- 16 Controller Performance: An Optimal Transport Approach, ACC, 2013.

Sparse Architectures for Control and Estimation

We are interested in determining sparse architectures for control and estimation for large-scale dynamical systems in this work. For large-scale systems it is nontrivial to determine location and precision of sensors and actuators to achieve the desired closed-loop system performance. We also consider the tradeoff between utility and privacy in these problems. These problems are considered in the Kalman filtering framework including ensemble and unscented variants, and \(\mathcal{H}_2\) and \(\mathcal{H}_\infty\) framework. Applications include tracking of aerospace vehicles, structural health-monitoring of wind-turbine blades, and battery thermal management.

Selected Papers

  1. V. Deshpande, R. Bhattacharya, Guaranteed Robust Performance of \(\mathcal{H}_{\infty}\) Filters With Sparse and Low Precision Sensing, IEEE Transactions on Automatic Control, 2023.
  2. V. Deshpande, R. Bhattacharya, K. Subbarao, Sensor Placement with Optimal Precision for Temperature Estimation of Battery Systems, IEEE Control Systems Letters, 2021.
  3. V. Deshpande, R. Bhattacharya, Sparse Sensing Architectures with Optimal Precision for Tracking Multi-Agent Systems in Sensing-Denied Environments, American Control Conference, 2021.
  4. V. Deshpande, R. Bhattacharya, Sparse Sensing and Optimal Precision: Robust \(\mathcal{H}_\infty\) Optimal Observer Design with Model Uncertainty, American Control Conference, 2021.
  5. N. Das, R. Bhattacharya, Privacy and Utility Aware Data Sharing for Space Situational Awareness from Ensemble and Unscented Kalman Filtering Perspective, IEEE Transactions in Aerospace and Electronic Systems, 2020.
  6. V. Deshpande, R. Bhattacharya, Sparse Sensing and Optimal Precision: An Integrated Framework for \(\mathcal{H}_2/\mathcal{H}_\infty\) Optimal Observer Design with Bounded Errors, IEEE Control System Letters, 2020.
  7. N. Das, R. Bhattacharya, Utility and Privacy in Object Tracking from Video Stream using Kalman Filter, Fusion, 2020.
  8. N. Das, R. Bhattacharya, Optimal Sensing Precision in Ensemble and Unscented Kalman Filtering, IFAC World Congress, 2020.

Space Domain Awareness

Space domain awareness is concerned with tracking space objects and classifying them with respect to specific characteristics. In this research, we are developing novel algorithms for uncertainty propagation and state estimation. Challenges include non-Gaussian uncertainty supported on cylindrical coordinate systems \(\mathbb{R}^5\times\mathbb{S}\), sparse sensing, and unknown sensor characteristics. These algorithms are used for conjunction analysis, which predicts upcoming object encounters to notify satellite operators and avoid high-risk encounters.

Selected Papers

  1. N. Das, R. Bhattacharya, Optimal Transport Based Filtering with Nonlinear State Equality Constraints, IFAC World Congress, 2020.
  2. N. Das, V. Deshpande, R. Bhattacharya, Optimal Transport based Tracking of Space Objects using Range Data from a Single Ranging Station, AIAA JGCD, 2019.
  3. N. Das, R. Bhattacharya, Sparse Sensing Architecture for Kalman Filtering with Guaranteed Error Bound, 1st IAA Conference on Space Situational Awareness (ICSSA), Orlando, FL, USA, 2017.
  4. N. Das, R. P. Ghosh, N. Guha, R. Bhattacharya, B. K. Mallick, Optimal Transport Based Tracking of Space Objects in Cylindrical Manifolds, The Journal of Astronautical Sciences, 2019.

Systems Theory for Numerical Algorithms

Future exascale machines are expected to have \(10^5-10^6\) processors, providing a deep hierarchy of systems and resources. However, many challenges exist, which must be overcome before exascale systems can be utilized as a useful tool to further understanding critical scientific inquires. Among the main obstacles to scaling code to exascale levels is the communication necessary in tightly coupled problems, such as in uncertainty propagation, turbulence flow simulations at high Reynolds numbers, and large-scale convex optimization. The synchronization across processors can cause 50-80% processor idle time. Our research focuses on applying systems theory to asynchronous numerical algorithms that do not wait for data to be synchronized. Communication between processors is modeled as a stochastic channel, and the behavior of the numerical algorithm is analyzed in a stochastic jump dynamical system framework. In addition, we present a new systems theory for finite-difference schemes that guarantee a given spectral error, a given approximation order, and numerical stability for a given linear PDE. The formulation treats the coefficients in a finite-difference formulation as control gains and the finite-difference scheme is synthesized as a controller for a linear dynamical system.

Selected Papers

  1. V. Deshpande, R. Bhattacharya, D. Donzis A Unified Framework to Generate Optimized Compact Finite Difference Schemes, Journal of Computational Physics, 2021.
  2. K. Kumari, R. Bhattacharya, D. Donzis, A Unified Approach for Deriving Optimal Finite Differences, Journal of Computational Physics, 2019.
  3. K. Lee, R. Bhattacharya, J. Dass, V. Sakuru, and R. Mahapatra, A Relaxed Synchronization Approach for Solving Parallel Quadratic Programming Problems with Guaranteed Convergence, IPDPS, Chicago,2016.
  4. K. Lee and R. Bhattacharya, On the Relaxed Synchronization for Massively Parallel Numerical Algorithms, American Control Conference, 2016.
  5. K. Lee, R. Bhattacharya, and V. Gupta, A Switched Dynamical System Framework for Analysis of Massively Parallel Asynchronous Numerical Algorithms, ACC, 2015.

Uncertainty Management in Cyber Physical Systems

Cyber-physical systems have strong coupling between physics, communication, and computation. In our research, we develop algorithms for quantifying uncertainty in system behavior due to uncertainties in the physics (unmodeled dynamics, process and sensor noise), communication (irregular channels, packet loss, etc.), computation (jitter in real-time tasks, CPU transients, etc.). The system-level behavior is modeled as a stochastic jump system, and new uncertainty propagation algorithms for such jump systems are developed. New stochastic scheduling algorithms have been developed that switch between computational tasks to ensure system-level robustness.

Selected Papers

  1. K. Lee, R. Bhattacharya, Optimal Controller Switching for Resource-constrained Dynamical Systems, International Journal of Control, Automation, and Systems, 2018.
  2. K. Lee, R. Bhattacharya, Stability Analysis of Large-Scale Distributed Networked Control Systems with Random Communication Delays: A Switched System Approach, System & Control Letters, 2015.
  3. K. Lee, A. Halder, R. Bhattacharya, Probabilistic Robustness Analysis of Stochastic Jump Linear Systems, ACC, 2014.
  4. P. Dutta, A. Halder, R. Bhattacharya, Uncertainty Quantification for Stochastic Nonlinear Systems using Perron-Frobenius Operator and Karhunen-Loeve Expansion, IEEE Multi-Conference on Systems and Control, Dubrovnik, Oct 2012.
  5. R. Bhattacharya, G. J. Balas, Control in Computationally Constrained Environments, IEEE Control Systems Technology, Volume 17, Issue 3, 2009.
  6. R. Bhattacharya, G. J. Balas, Anytime Control Algorithm: Model Reduction Approach, Journal of Guidance, Control, and Dynamics, 2004, Vol. 27, No.5, pp. 767-776, 2004.

Robust Flight Control Design

Our lab has expertise in designing custom aerial platforms for various needs. Our research integrates aerodynamics, structural design, and flight control design in a single unified framework. The objective is to develop next-generation tools for rapid custom design of high confidence unmanned air vehicles for various industries, including defense, oil & gas, and precision agriculture. The vision is to codesign much of the system engineering aspect by integrating state-of-the-art in computational fluid dynamics, structural mechanics, robust control theory, CAD software, and 3D printing. The application focus is currently on aerospace systems but can be extended to general autonomous systems.

Selected Papers

  1. S. C. Hsu, R. Bhattacharya, Design of Stochastic Collocation Based Linear Parameter Varying Quadratic Regulator, American Control Conference, 2017.
  2. A. Halder, K. Lee, and R. Bhattacharya, Optimal Transport Approach for Probabilistic Robustness Analysis of F-16 Controllers, AIAA Journal of Guidance, Control, and Dynamics, 2015.
  3. R. Bhattacharya, S. Mijanovic, E. Scholte, A. Ferrari, M. Huzmezan, M. Lelic, M. Atalla, Rigorous Design of Real-Time Embedded Control Systems, IEEE Advanced Process Control Applications for Industry, Vancouver, May, 2006.
  4. R. Bhattacharya, G. J. Balas, Implementation of Online Control Customization within the Open Control Platform, Software-Enabled Control: Information Technologies for Dynamical Systems, A John Wiley/IEEE Press Publication, 2003.
  5. R. Bhattacharya, G. J. Balas, M. Alpay Kaya, A. Packard, Nonlinear Receding Horizon Control of an F-16 Aircraft, Journal of Guidance, Control, and Dynamics, Vol. 25, No. 5, pp. 924-931, 2002.

Uncertainty Quantification in Hypersonic Flight

Hypersonic flight leading to entry descent landing of a large spacecraft on the surface of Mars has been identified as a research area by NASA. The requirement is to land within a few kilometers of the robotic test sites. One of the significant concerns of high mass entry is the mismatch between entry conditions and deceleration capabilities provided by supersonic parachute technologies. In such applications, there are uncertainties present in initial conditions and other system parameters. Estimating these systems’ parameters is a challenging problem because of the nonlinearities in the system and the lack of frequent measurements. The evolution of uncertainty (as shown in the figure) is non-Gaussian. In our work, we develop new algorithms for UQ, state-estimation, and guidance algorithms. The controlled descent ensures robustness with respect to system uncertainties and guarantees landing at the desired site with high accuracy.

Selected Papers

  1. A. Halder, R. Bhattacharya, Dispersion Analysis in Hypersonic Flight During Planetary Entry Using Stochastic Liouville Equation, AIAA Journal of Guidance, Control, and Dynamics,2011, 0731-5090 vol.34 no.2 (459-474).
  2. P. Dutta & R. Bhattacharya, Nonlinear Estimation of Hypersonic State Trajectories in Bayesian Framework with Polynomial Chaos, Journal of Guidance, Control, and Dynamics, vol.33 no.6 (1765-1778), 2011.
  3. P. Dutta & R. Bhattacharya, Hypersonic State Estimation Using Frobenius-Perron Operator, AIAA Journal of Guidance, Control, and Dynamics, Volume 34, Number 2, 2011.
  4. J. Fisher, R. Bhattacharya, Linear Quadratic Regulation of Systems with Stochastic Parameter Uncertainties, Automatica, 2009.