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

arXiv: https://arxiv.org/abs/2108.12030 · HTML: https://mlsanity.com/paper/2108.12030/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 26 Aug 2021.

## Built on by (most cited first, 1 of 1)

- [A hierarchical control framework for autonomous decision-making systems: Integrating HMDP and MPC](https://mlsanity.com/paper/2401.06833/) (2024)

## Abstract (arXiv)

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.