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

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