TR2024-173

Inscribing and separating an ellipsoid and a constrained zonotope: Applications in stochastic control and centering


Abstract:

Constrained zonotopes are equivalent representations for convex polytopes that have recently enabled tractable implementations of some set-based control methods. We con- sider the problems of inscribing an ellipsoid within and separating an ellipsoid from a constrained zonotope. Such problems arise in several applications, including in stochastic optimal control problems when enforcing chance constraints involving constrained zonotopes. Given a parameterized ellipsoid, we propose a set of sufficient conditions that are convex in the parameters and guarantee that the ellipsoid is inscribed within a constrained zonotope. We use these conditions to solve a two-stage, return-guaranteed spacecraft rendezvous problem under uncertainty. We also apply these conditions to tractably approximate the Chebyshev center and the maximum volume inscribed ellipsoid of a constrained zonotope using linear and second-order cone programming. We also propose a set of necessary and sufficient conditions that separate an ellipsoid from a constrained zonotope, which has applications in enforcing probabilistic exclusion from a constrained zonotope.

 

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      Date: December 16, 2024 - December 19, 2024
      Where: Milan, Italy
      MERL Contacts: Ankush Chakrabarty; Vedang M. Deshpande; Stefano Di Cairano; James Queeney; Abraham P. Vinod; Avishai Weiss; Gordon Wichern
      Research Areas: Artificial Intelligence, Control, Dynamical Systems, Machine Learning, Multi-Physical Modeling, Optimization, Robotics
      Brief
      • MERL researchers presented 7 papers at the recently concluded Conference on Decision and Control (CDC) 2024 in Milan, Italy. The papers covered a wide range of topics including safety shielding for stochastic model predictive control, reinforcement learning using expert observations, physics-constrained meta learning for positioning, variational-Bayes Kalman filtering, Bayesian measurement masks for GNSS positioning, divert-feasible lunar landing, and centering and stochastic control using constrained zonotopes.

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