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，基于数据驱动的系统辨识方法正成为物理建模的有前途替代方案。尽管在安全关键应用中广泛采用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，需要同时估计系统动力学和潜状态，这使得不确定性量化以及具有形式化性能保证的控制器设计变得更具挑战性。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，计算具有潜状态的未知非线性系统的最优输入轨迹。推导了所得输入轨迹的概率性能保证，并给出了一种验证任意控制律性能的方法。数值仿真验证了所提方法的有效性。