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：我们研究如何安全地控制受有界非随机噪声干扰的非线性控制仿射系统，即这种噪声是事先未知的，且不一定服从随机模型。我们关注于具有时变凸约束形式的安全约束，例如避碰约束和控制力约束。我们提出了一种具有有界动态遗憾的算法，即相对于已知噪声实现的最优预见控制器，其性能次优性是有界的。我们的研究动机源于自主系统的未来前景，即机器人将在现实世界不可预测的干扰（如阵风）下自主执行复杂任务。为了开发该算法，我们将问题建模为控制器与对手之间的序贯博弈，其中控制器先行动，选择控制输入；对手后行动，选择噪声的实现。控制器的目标是在无法事先获知噪声实现的情况下最小化其累积跟踪误差。我们在仿真场景中验证了我们的算法：（i）旨在保持直立的倒立摆，以及（ii）旨在通过未知杂乱环境飞向目标位置的四旋翼飞行器。