A hierarchical learning approach for generalized trajectory tracking validated on a magnetic bearing system

A hierarchical learning framework (HLF) was proposed recently, for enabling control systems to generalize a learned optimal tracking behaviour to new unseen trajectories. The idea is inspired by the generalization capacity of intelligent beings (humans in particular) in solving new tasks by extrapolating and combining skills from an existing knowledge base. The HLF uses the so-called primitive pairs which are in fact pairs of reference inputs-controlled outputs. While these pairs are learnable over a lower-level closed-loop control system (CLCS) with the goal of a desired trajectory following, this is not mandatory as long as the primitive output has sufficient approximation capability and the CLCS is almost linearized. This paper shows that the primitive pairs can be employed to infer the optimized CLCS reference input which forces the CLCS’s output to track a new targeted trajectory with better accuracy than in the case without exploiting the primitive-based prediction. The explanation resides in that the primitives indirectly encode the CLCS’s model within the trajectory data. All the HLF’s features ranging from the primitive’s database construction, to database enrichment with extended, delayed and padded pairs, up to the decomposition of the new desired trajectory into output primitives and to the recomposition of the optimal reference, are detailed in this work, on a multivariable real-time magnetic bearing system (MBS). The HLF shows intelligent behaviour features: learning, memorization and generalization of the learned behaviour.