This paper studies control synthesis for a general class of nonlinear, control-affine dynamical systems under multiple constraints. We enforce forward invariance of static and dynamic safe sets to ensure safety of the system trajectories, and furthermore enforce convergence to a given goal set within a user-defined time in the presence of input constraints. We use robust variants of control barrier functions (CBF) and control Lyapunov functions (CLF) to incorporate a class of additive disturbances in the system dynamics, and sensing errors in the system states. To solve the underlying constrained control problem, we formulate a quadratic program and use the proposed robust CBF-CLF conditions to compute the control input. Finally, we showcase the efficacy of the proposed method on a numerical case study involving multiple underactuated marine vehicles.

中文翻译：

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具有固定时间收敛保证的鲁棒控制障碍和控制 Lyapunov 函数

本文研究了多约束下一类非线性、控制仿射动力系统的控制综合。我们强制静态和动态安全集的前向不变性以确保系统轨迹的安全性，并且在存在输入约束的情况下，在用户定义的时间内强制收敛到给定的目标集。我们使用控制势垒函数 (CBF) 和控制李雅普诺夫函数 (CLF) 的稳健变体，将一类加性扰动纳入系统动力学，并在系统状态中检测误差。为了解决潜在的约束控制问题，我们制定了一个二次程序并使用建议的鲁棒 CBF-CLF 条件来计算控制输入。最后，