Learning-based optimal control algorithms control unknown systems using past trajectory data and a learned model of the system dynamics. These controllers use either a linear approximation of the learned dynamics, trading performance for faster computation, or nonlinear optimization methods, which typically perform better but can limit real-time applicability. In this work, we present a novel nonlinear controller that exploits differential flatness to achieve similar performance to state-of-the-art learning-based controllers but with significantly less computational effort. Differential flatness is a property of dynamical systems whereby nonlinear systems can be exactly linearized through a nonlinear input mapping. Here, the nonlinear transformation is learned as a Gaussian process and is used in a safety filter that guarantees, with high probability, stability as well as input and flat state constraint satisfaction. This safety filter is then used to refine inputs from a flat model predictive controller to perform constrained nonlinear learning-based optimal control through two successive convex optimizations. We compare our method to state-of-the-art learning-based control strategies and achieve similar performance, but with significantly better computational efficiency, while also respecting flat state and input constraints, and guaranteeing stability.

翻译：基于学习的最优控制算法利用过往轨迹数据及系统动力学学习模型来控制未知系统。这类控制器要么采用学习动力学的线性近似（以性能换取更快计算），要么采用非线性优化方法（通常性能更优但可能限制实时应用）。本文提出一种新型非线性控制器，通过利用微分平坦性，在显著降低计算量的同时达到与主流学习型控制器相当的性能。微分平坦性是动力系统的一种特性，使得非线性系统可通过非线性输入映射实现精确线性化。我们将非线性变换学习为高斯过程，并用于安全滤波器，该滤波器能以高概率保证稳定性、输入约束及平坦状态约束的满足。随后，该安全滤波器用于优化来自平坦模型预测控制器的输入，通过两次连续凸优化实现受约束的非线性学习型最优控制。与主流的基于学习的控制策略相比，我们的方法在实现相似性能的同时，不仅具有显著更高的计算效率，还能满足平坦状态与输入约束，并保证系统稳定性。