The Mixed-Observable Constrained Linear Quadratic Regulator Problem: The Exact Solution and Practical Algorithms

• 成果类型: Article
• 署名作者: Rosolia, Ugo; Chen, Yuxiao; Daftry, Shreyansh; Ono, Masahiro; Yue, Yisong; Ames, Aaron D.
• 署名单位: California Institute of Technology; California Institute of Technology; National Aeronautics & Space Administration (NASA); NASA Jet Propulsion Laboratory (JPL)
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2022.3210871
• 发表日期: 2023
• 页码: 4435-4442
• 关键词: Measurement uncertainty; observability; optimal control

摘要

This article studies the problem of steering a linear system subject to state and input constraints toward a goal location that may be inferred only through noisy partial observations. We assume mixed-observable settings, where the system's state is fully observable and the environment's state defining the goal location is only partially observed. In these settings, the planning problem is an infinite-dimensional optimization problem where the objective is to minimize the expected cost. We show how to reformulate the control problem as a finite-dimensional deterministic problem by optimizing over a trajectory tree. Leveraging this result, we demonstrate that when the environment is static, the observation model piecewise, and cost function convex, the original control problem can be reformulated as a mixed-integer convex program that can be solved to global optimality using a branch-and-bound algorithm. The effectiveness of the proposed approach is demonstrated on navigation tasks, where the goal location should be inferred through noisy measurements.