Time-Varying Feedback for Robust Regulation in Prescribed Finite Time (Abstract)
Abstract
Starting from the idea of prescribed-time stabilization, present in the heuristic Proportional Navigation feedback law, which is a PD control law with gains that grow unbounded as the missile nears the target, in this project we generalized this idea to all linear and certain nonlinear ODE systems, extended it to PDEs, and developed disturbance-robust versions for prescribed-time stabilization under both deterministic and stochastic disturbances. Our generalization from second-order linear systems to general ODEs has entailed systematic scaling of gains on the state by powers of the function 1/(t0 +T - t), where t is time, t0 is the initial time, and T is the prescribed terminal time. To make our feedback laws implementable without a requirement of full-state measurement, we also developed prescribed-time observers, with a similar scaling of observer gains by powers of 1/(t0 + T - t). Generalization to PDEs requires an entirely different, back stepping-based approach, with damping that grows unbounded in the target system. With this approach, in spite of infinite sums with functions that grow to infinity at terminal time, the gains converge and the states and input not only remain bounded but converge to zero, with all their derivatives also converging to zero. Our approach achieves a perfect disturbance rejection at the terminal time T, regardless of the size of the disturbance. This exceeds the capability of sliding mode control and related time-invariant methods, which employ an infinite gain near the origin. Such methods require a known bound on the disturbance. In addition to perfect rejection of deterministic disturbances, with a suitable combination of stochastic backstepping and time-varying gains in the stochastic target systems, we achieve a perfect mean-square rejection of stochastic disturbances.
Document Details
- Document Type
- Technical Report
- Publication Date
- Jun 04, 2021
- Accession Number
- AD1230390
Entities
People
- Miroslav Krstić
Organizations
- University of California, San Diego