The Mixed-Observable Constrained Linear Quadratic Regulator Problem: The Exact Solution and Practical Algorithms
The Mixed-Observable Constrained Linear Quadratic Regulator Problem: The Exact Solution and Practical Algorithms
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DOI：
10.1109/tac.2022.3210871
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发表时间：
2021-08
影响因子：
6.8
通讯作者：
Ugo Rosolia;Yuxiao Chen;S. Daftry;M. Ono;Yisong Yue;A. Ames
中科院分区：
文献类型：
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作者：
Ugo Rosolia;Yuxiao Chen;S. Daftry;M. Ono;Yisong Yue;A. Ames
本文研究了将受状态和输入约束的线性系统转向目标位置的问题，该目标位置只能通过有噪的部分观测来推断。我们假设混合可观测设置，其中系统的状态是完全可观测的，而定义目标位置的环境状态仅部分可观测。在这些设置中，规划问题是一个无限维的优化问题，其目标是最小化预期成本。我们展示了如何重新制定的控制问题作为一个有限维的确定性问题，通过优化的轨迹树。利用这一结果，我们证明，当环境是静态的，观察模型分段，成本函数凸，原来的控制问题可以重新制定为一个混合整数凸规划，可以解决全局最优使用分支定界算法。所提出的方法的有效性证明了导航任务，目标位置应推断通过噪声测量。
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.