Optimal Estimation-Aware Motion: A Control-Centric Optimization Framework

This talk focuses on the intersection of trajectory generation with estimation theory, specifically addressing the challenges of operating in uncertain or adversarial environments, such as GPS-denied scenarios. In such scenarios, trajectories must be aware of the estimation process and actively maximize information gain. However, coupling estimation metrics with high-fidelity nonlinear dynamics creates complex, nonconvex optimal control problems that challenge standard computational techniques, such as the popular pseudospectral methods. Generating sensor-based trajectories naturally requires uniform time spacing, which introduces well-known limitations such as the Runge phenomenon and the impossibility theorem. This talk outlines a unified research architecture that bridges the gap between high-level mission goals and efficient computational methods with theoretical guarantees.

First, to enable efficient planning in complex domains, we introduce the mixed Bernstein-Fourier approximants. This representation is specifically designed to encode the complex periodic behaviors inherent to missions such as observer trajectory design and mine countermeasures, significantly reducing the dimensionality of the search space without sacrificing accuracy.

Second, we present a control-centric optimization framework that fundamentally reinterprets optimization algorithms as continuous-time dynamical systems. This approach provides a general theory for synthesizing solvers with tunable convergence profiles, ranging from asymptotic to fixed and prescribed-time. By leveraging results from Lyapunov stability theory, this framework allows embedding constraints, ensuring strictly feasible trajectories. This establishes a theoretical foundation for scalable autonomy, demonstrated through constrained optimization, minimax problems, and generalized Nash equilibrium seeking. These results pave the way for future research in robust, scalable aerospace autonomy where real-time performance and safety guarantees are paramount.

Dr. Liraz Mudrik is currently a Postdoctoral Fellow in the Department of Mechanical and Aerospace Engineering at the Naval Postgraduate School. He received his Ph.D. in Aerospace Engineering (direct track) from the Technion–Israel Institute of Technology in 2023, where he also earned his B.Sc. (cum laude).