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

• Main Authors: Rosolia, Ugo, Chen, Yuxiao, Daftry, Shreyansh, Ono, Masahiro, Yue, Yisong, Ames, Aaron D
• Format: Journal Article
• Language: English
• Published: 26.08.2021
• Subjects: Mathematics - Optimization and Control
• DOI: 10.48550/arxiv.2108.12030

This paper studies the problem of steering a linear time-invariant system subject to state and input constraints towards a goal location that may be inferred only through 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 (MICP) 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 system has to reach a goal location identified from partial observations.