We study how to safely control nonlinear control-affine systems that are corrupted with bounded non-stochastic noise, i.e., noise that is unknown a priori and that is not necessarily governed by a stochastic model. We focus on safety constraints that take the form of time-varying convex constraints such as collision-avoidance and control-effort constraints. We provide an algorithm with bounded dynamic regret, i.e., bounded suboptimality against an optimal clairvoyant controller that knows the realization of the noise a prior. We are motivated by the future of autonomy where robots will autonomously perform complex tasks despite real-world unpredictable disturbances such as wind gusts. To develop the algorithm, we capture our problem as a sequential game between a controller and an adversary, where the controller plays first, choosing the control input, whereas the adversary plays second, choosing the noise's realization. The controller aims to minimize its cumulative tracking error despite being unable to know the noise's realization a prior. We validate our algorithm in simulated scenarios of (i) an inverted pendulum aiming to stay upright, and (ii) a quadrotor aiming to fly to a goal location through an unknown cluttered environment.

翻译：我们研究如何安全控制受限于有界非随机噪声（即先验未知且不一定服从随机模型的噪声）的非线性控制仿射系统。本文聚焦于形式为时变凸约束的安全约束，例如碰撞规避与控制能耗约束。我们提出一种具有有界动态遗憾的算法，即相对于预知噪声实现的最优先验控制器的有界次优性。这项研究的动机源于未来自主系统需在真实世界不可预测的扰动（如阵风）中自主完成复杂任务。为设计该算法，我们将问题建模为控制器与对手之间的序贯博弈：控制器先行选择控制输入，而对手后行选择噪声实现。尽管无法预知噪声实现，控制器仍致力于最小化累积跟踪误差。我们通过两种仿真场景验证所提算法：（i）倒立摆的直立稳定控制；（ii）四旋翼飞行器穿越未知杂乱环境抵达目标位置。