标题： 非线性鲁棒优化在规划与控制中的应用 显示英文标题

标题： Nonlinear Robust Optimization for Planning and Control

摘要： 本文提出了一种新颖的鲁棒轨迹优化方法，用于受未知有界干扰影响的约束非线性动态系统。 特别是，我们寻求最优控制策略，使其相对于规定不确定性集内的所有可能干扰实现鲁棒可行。 为了解决这个问题，我们引入了一种双层优化算法。 外层采用基于信任域的逐次凸化方法，该方法依赖于非线性动力学和鲁棒约束的线性化。 内层涉及求解由此产生的线性化鲁棒优化问题，为此我们推导了可处理的凸重新表述，并提出了增广拉格朗日方法以高效求解这些问题。 为了进一步增强我们方法在非线性系统的鲁棒性，我们还展示了潜在的线性化误差可以有效建模为未知干扰。 仿真结果验证了我们的方法在未知干扰下以鲁棒方式控制非线性系统的适用性。 此外，从鲁棒优化的角度强调了在这种逐次线性化方案中有效处理近似误差的潜力。 显示英文摘要

摘要： This paper presents a novel robust trajectory optimization method for constrained nonlinear dynamical systems subject to unknown bounded disturbances. In particular, we seek optimal control policies that remain robustly feasible with respect to all possible realizations of the disturbances within prescribed uncertainty sets. To address this problem, we introduce a bi-level optimization algorithm. The outer level employs a trust-region successive convexification approach which relies on linearizing the nonlinear dynamics and robust constraints. The inner level involves solving the resulting linearized robust optimization problems, for which we derive tractable convex reformulations and present an Augmented Lagrangian method for efficiently solving them. To further enhance the robustness of our methodology on nonlinear systems, we also illustrate that potential linearization errors can be effectively modeled as unknown disturbances as well. Simulation results verify the applicability of our approach in controlling nonlinear systems in a robust manner under unknown disturbances. The promise of effectively handling approximation errors in such successive linearization schemes from a robust optimization perspective is also highlighted.