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.
翻译:安全是控制理论中的基本挑战之一。最近,为稳定制定了离散时间动态系统的多步最佳控制问题,在模型预测控制(MPC)框架内使用离散时间控制屏障功能,同时受投入限制和安全关键要求的限制,现有工作通常侧重于优化问题的可行性或安全性,而大多数现有工作将讨论限制在相对度一个控制屏障功能上。此外,当对相对度一级或高度控制屏障功能的MPC问题考虑大视野时,实时计算具有挑战性。在本文件中,我们提议了一个框架,以迭代优化方式解决安全危急时间控制屏障问题,适用于任何相对度控制屏障功能。在拟议的拟订中,非线性系统动态以及作为离散时间高控制屏障功能模型的安全限制(DHOCBF)在每个阶段都具有线性。我们的设计通常适用于任何任意的相对度控制屏障功能。快速计算功能的优点与数字结果经过分析和验证。</s>