Research
We develop the theory of estimation and control for uncertain dynamical systems, and test it on aerospace systems through funded projects.
Methods
Uncertainty Quantification
Propagating and characterizing uncertainty in nonlinear dynamics with polynomial chaos and Perron–Frobenius operators.
We study the evolution of probability densities under nonlinear dynamics. Polynomial chaos expansions represent parametric uncertainty in a finite basis and admit a Galerkin projection of the dynamics; the Perron–Frobenius operator and the stochastic Liouville equation propagate the density itself. These representations underlie our work on stochastic LQR design, dispersion analysis in hypersonic flight, and the probabilistic robustness of control laws.
Estimation & Data Assimilation
Information fusion on manifolds for nonlinear and non-Gaussian systems to improve state estimation and prediction.
Our estimators treat the state as a probability distribution conditioned on the measurements. The work spans Kalman, ensemble, and unscented filters; nonlinear filters built on the Perron–Frobenius operator and polynomial chaos; optimal-transport filters on manifolds; and and filters whose error bounds hold under model uncertainty. Applications include attitude estimation for small UAVs and the tracking of space objects from sparse measurements.
Robust Control
/, LPV, and LFT methods for control and filtering with guaranteed performance under model uncertainty.
We design controllers and estimators whose performance is certified for every admissible model. Uncertainty is represented in linear fractional (LFT) and linear parameter-varying (LPV) form, and synthesis reduces to convex programs in linear matrix inequalities. Recent work includes attitude control of multirotors, robustness margins of Kalman filters, and the largest actuator degradation consistent with a prescribed performance.
Optimal Control & Trajectory Generation
Trajectory generation, receding-horizon control, and optimal control of systems with probabilistic parameters.
We compute trajectories and feedback laws that minimise a cost subject to the dynamics and constraints. Direct methods parameterise trajectories with B-splines and collocation, as in the OPTRAGEN toolbox, and receding-horizon control applies them in feedback. When parameters are uncertain, polynomial chaos converts the stochastic problem into a deterministic one of larger dimension. Applications range from the F-16 and hypersonic guidance to spacecraft momentum management.
Sensor & Actuator Architecture
Co-design of controllers and estimators with the sparsest sensing and actuation, and the lowest precision, that still guarantee closed-loop performance.
We treat sensors and actuators as design variables. Each channel carries a precision or an authority to be chosen, and a sparsity-promoting penalty removes the channels that are not needed, so the architecture and the controller or estimator are designed together. The resulting convex programs return the sparsest and least precise configuration that still guarantees a prescribed or performance.
Scientific Machine Learning
Advancing and applying scientific machine learning to improve control-system design and analysis.
We use machine learning where it extends the analysis of dynamical systems. Physics-informed neural networks estimate invariant sets, active learning reduces the data required for verification, maximum-entropy basis functions yield surrogate models from sparse data, and Gaussian-process regression is made privacy-aware. Koopman spectral methods reconstruct the state-space geometry of the cislunar three-body problem.
Control of Computation
Control-theoretic analysis of numerical methods, asynchronous parallel algorithms, and control under limited computing resources.
We regard numerical algorithms as dynamical systems and analyse them with the tools of control. Asynchronous parallel iterations, in which processors proceed without waiting for one another, are modelled as switched systems whose stability and convergence can then be established. The same viewpoint yields optimised compact finite-difference schemes and anytime controllers that remain correct when the available computation varies.
Optimal Transport
Wasserstein geometry of probability distributions for nonlinear filtering, density tracking, and probabilistic robustness analysis.
We use the geometry of optimal transport to compare and evolve probability distributions. The Wasserstein distance measures the discrepancy between a model's predicted density and observed data, which yields probabilistic model validation and the robustness analysis of controllers such as those of the F-16. In estimation, transport maps perform the Bayesian update for non-Gaussian, constrained, and manifold-valued states.
Verification & Model Validation
Certifying stability, invariance, and model fidelity with sum-of-squares Lyapunov certificates, invariant-set estimation, and probabilistic model validation.
We certify properties of uncertain systems before they are flown. Sum-of-squares programming constructs Lyapunov certificates for stability and partial stability, physics-informed neural networks estimate invariant sets, and probabilistic model validation tests a model against data in the Wasserstein metric. Data-driven verification with active learning extends these certificates to systems characterised by data.
Applications
Space Domain Awareness
Tracking resident space objects in Earth orbit and cislunar space from sparse observations, including detection of evasive maneuvers.
Resident space objects in cislunar space are observed rarely and from great distances, so their states are poorly constrained between measurements. We develop filters for sparse bearing-only and range-only measurements, design the precision and placement of observing sensors, and detect evasive maneuvers with cooperating observers. The work also addresses tracking in Earth orbit and privacy in the exchange of tracking data.
- Cooperative tracking of evasive resident space objects in cislunar space with sparse observation constellationsAFOSR, 2023–2025
- Adaptive Markov inference game optimization for rapid discovery of evasive satellite behaviorsIntelligent Fusion Technology (STTR Phases I & II), 2018–2021
- Cloud-computing-based robust space situational awarenessAFOSR, 2015–2018
Hypersonic & Entry Vehicles
Trajectory generation, uncertainty propagation, and control for atmospheric reentry, planetary entry, and hypersonic vehicles with rapidly changing flight dynamics.
Entry vehicles traverse dynamics that change rapidly along the trajectory, with large uncertainty in the atmosphere and in the vehicle itself. We propagate this uncertainty to quantify landing dispersion, generate trajectories in real time, and design guidance and control for Mars entry and hypersonic flight. Current work develops multi-modal control for rapidly changing flight dynamics.
- Development and experimental validation of multi-modal control for rapidly changing flight dynamicsUCAH (with Georgia Tech), 2021–2024
- Beyond Monte Carlo — statistical verification and validation of space systemsNASA, 2009–2010
- Robust adaptive real-time 6-DOF trajectory generation for atmospheric reentry vehiclesNASA, 2006–2010
Aircraft, UAVs & Swarms
Flight control for aircraft and UAVs, air-traffic management, and cooperative control of autonomous vehicle teams.
We design flight controllers for aircraft and unmanned vehicles. The work includes nonlinear receding-horizon control of the F-16, and control of quadrotors and tailsitters, attitude estimation on low-power processors, and air-traffic management under uncertainty. For teams of vehicles, invariance arguments establish rendezvous and cooperative behaviour.
- Self-aware autonomous swarms (Land, Air & Space Robotics Lab collaboration)Boeing, 2009–2010
- Simulation evaluation of nonlinear flight control and air-traffic management systemsOptimal Synthesis Inc., 2008
Tensegrity Structures
Dynamics, sensing, and control of lightweight tensegrity structures, from wind-turbine blades to habitats built in space.
Tensegrity structures carry load through bars in compression and cables in tension, which makes them light and permits their shape to change. We model their constrained dynamics in a Lagrangian framework, released as the STEDY software, and study their use in wind-turbine blades, deformable sensors and actuators, and habitats assembled in space.
- Modeling, analysis, and diagnostics of high strength-to-weight wind turbine blades using tensegrity principlesNSF, 2018–2021
- Multi-axis deformable sensor/actuator systemNSF I-Corps, 2017
- Tensegrity approaches to in-space construction of a 1g growable habitatNASA NIAC Phase II, 2016–2018
High-Performance & Embedded Computing
Asynchronous algorithms for exascale simulation of turbulent flows, and control systems that remain reliable under limited or uncertain computing resources.
Exascale simulations of turbulent flow are limited by synchronisation among processors. We develop asynchronous algorithms that remove the wait and establish their convergence with switched-system and control-theoretic arguments. A related line of work concerns real-time embedded controllers that remain correct when their computational resources are limited or uncertain.
- Asynchronous PDE algorithms for turbulent flows at exascaleNSF, 2014–2017
- Asynchronous algorithms for exascale computing systemsNSF, 2013–2014
- Uncertainty management in real-time embedded control systemsNSF, 2010–2013
- Design of robust and energy-efficient cyber-physical systems using dynamical systems and control theoryNSF, 2007–2009
Digital Twins & Data Privacy
Quantifying the trade-off between utility and privacy when estimation and learning systems share data. Shown here, a Gaussian-process digital twin with a physics kernel plus a data kernel, whose posterior uncertainty is held between a privacy floor and a utility ceiling.
Data shared for estimation reveal more than the estimate requires. We add calibrated noise to the shared data and quantify the trade-off between the accuracy of the resulting estimate and the information it discloses. The analysis covers Kalman and ensemble filtering for space situational awareness, object tracking from video, and Gaussian-process regression for digital twins.
- Quantifying utility vs. privacy trade-offs in digital twinsTexas A&M Institute of Data Science, 2024–2026