用终端CBF约束提升安全控制可行性，减少保守性。
Maximal Controlled Invariant-MPC: Enhancing Feasibility and Reducing Conservatism through Terminal CBF Constraint in Safety-Critical Control
- 以终端CBF作为MPC约束，优化安全控制的可行性。
- 仿真显示不可行点减少1.7至2.7倍，可达状态空间显著扩大。
- 适合需要高安全性与高效率的实时控制系统研究者。
安全关键系统的最优控制常受限于约束的保守性。控制屏障函数（CBF）用于表征此类约束，但构造最小保守性的CBF是计算上难以处理的问题。本文提出一种基于CBF作为终端约束的模型预测控制（MPC）方法，证明其在预测时域增加时能提升可行性与可达到的状态集。证明过程具有构造性，支持非线性优化问题的热启动，显著降低计算时间。针对一个简单非完整系统进行仿真验证，结果表明不可行点数量减少了1.7至2.7倍。通过系统能够跟踪完全位于CBF不安全区域内的轨迹，验证了可达状态空间的扩展效果。
原文摘要 · Abstract (English)
Optimal control for safety-critical systems is often dependent on the conservativeness of constraints. Control Barrier Functions (CBFs) serve as a medium to represent such constraints, but constructing a minimally conservative CBF is a computationally intractable problem. Therefore, approaches that can guarantee safety while reducing conservatism will help improve the optimality of the system under consideration. Here, we present a Model Predictive Control (MPC) formulation using CBF as a terminal constraint, which is proven to improve feasibility and reachable sets with increasing prediction horizon. The constructive nature of the proofs allows for warm-starting the nonlinear optimization problem, thereby reducing the computational time substantially. Simulations are set up for a simple nonholonomic system to numerically validate the results, and it is observed that the number of infeasible points decreased by a factor of 1.7 to 2.7. The increase in reachable state space was demonstrated by the ability of the system to track trajectories that are entirely inside the unsafe region of the control barrier function.
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