As control engineering methods are applied to increasingly complex systems, data-driven approaches for system identification appear as a promising alternative to physics-based modeling. While the Bayesian approaches prevalent for safety-critical applications usually rely on the availability of state measurements, the states of a complex system are often not directly measurable. It may then be necessary to jointly estimate the dynamics and the latent state, making the quantification of uncertainties and the design of controllers with formal performance guarantees considerably more challenging. This paper proposes a novel method for the computation of an optimal input trajectory for unknown nonlinear systems with latent states based on a combination of particle Markov chain Monte Carlo methods and scenario theory. Probabilistic performance guarantees are derived for the resulting input trajectory, and an approach to validate the performance of arbitrary control laws is presented. The effectiveness of the proposed method is demonstrated in a numerical simulation.

翻译：随着控制工程方法应用于日益复杂的系统，数据驱动的系统辨识方法作为基于物理建模的替代方案展现出巨大潜力。尽管适用于安全关键场景的贝叶斯方法通常依赖于状态测量的可用性，但复杂系统的状态往往无法直接测量。此时需联合估计动力学特性与潜状态，使得不确定性量化及具有形式化性能保证的控制器设计面临更大挑战。本文提出一种新颖方法，通过结合粒子马尔可夫链蒙特卡洛方法与场景理论，为具有潜状态的未知非线性系统计算最优输入轨迹。针对所得输入轨迹推导了概率性能保证，并提出了一种验证任意控制律性能的方法。数值仿真实验验证了所提方法的有效性。