论文标题
具有离散时间高阶控制屏障功能的模型预测控制的迭代凸优化
Iterative Convex Optimization for Model Predictive Control with Discrete-Time High-Order Control Barrier Functions
论文作者
论文摘要
安全是控制理论中的基本挑战之一。最近，制定了离散时间动力学系统的多步最佳控制问题，以实施稳定性，而在模型预测控制（MPC）框架内使用离散时间控制障碍功能受到输入约束以及关键要求。现有的工作通常集中在优化问题的可行性或安全性上，而现有工作的大多数将讨论限制在相对程度的一个控制障碍功能上。此外，当在MPC问题中考虑相对度或高阶控制屏障函数的MPC问题中的大范围时，实时计算具有挑战性。在本文中，我们提出了一个框架，该框架在迭代优化中解决了安全至关重要的MPC问题，该框架适用于任何相对度控制屏障函数。在提出的公式中，在每个时间步骤中都将非线性系统动力学以及建模为离散时间高阶控制屏障函数（DHOCBF）的安全约束。我们的公式通常对于具有任意相对度的任何控制屏障函数有效。通过数值结果对快速计算性能和安全保证的优势进行了分析和验证。
Safety is one of the fundamental challenges in control theory. Recently, multi-step optimal control problems for discrete-time dynamical systems were formulated to enforce stability, while subject to input constraints as well as safety-critical requirements using discrete-time control barrier functions within a model predictive control (MPC) framework. Existing work usually focus on the feasibility or the safety for the optimization problem, and the majority of the existing work restrict the discussions to relative-degree one control barrier functions. Additionally, the real-time computation is challenging when a large horizon is considered in the MPC problem for relative-degree one or high-order control barrier functions. In this paper, we propose a framework that solves the safety-critical MPC problem in an iterative optimization, which is applicable for any relative-degree control barrier functions. In the proposed formulation, the nonlinear system dynamics as well as the safety constraints modeled as discrete-time high-order control barrier functions (DHOCBF) are linearized at each time step. Our formulation is generally valid for any control barrier function with an arbitrary relative-degree. The advantages of fast computational performance with safety guarantee are analyzed and validated with numerical results.
