Learning Output Reference Model Tracking for Higher-Order Nonlinear Systems with Unknown Dynamics

Abstract

Linearly and nonlinearly parameterized approximate dynamic programming approaches used for output reference model (ORM) tracking control are proposed. The ORM tracking problem is of significant interest in practice since, with a linear ORM, the closed-loop control system is indirectly feedback linearized and value iteration (VI) offers the means to achieve ORM tracking without using process dynamics. Ranging from linear to nonlinear parameterizations, a successful approximate VI implementation for continuous state-action spaces depends on several key parameters such as: problem dimension, exploration of the state-action space, the state-transitions dataset size, and suitable selection of the function approximators. We show that using the same transitions dataset and under a general linear parameterization of the Q-function, high performance ORM tracking can be achieved with an approximate VI scheme, on the same performance level as that of a neural-network (NN)-based implementation that is more complex and takes significantly more time to learn. However, the latter proves to be more robust to hyperparameters selection, dataset size, and to exploration strategies, recommending it as the de facto practical implementation. The case study is aimed at ORM tracking of a real-world nonlinear two inputs−two outputs aerodynamic process with ten internal states, as a representative high order system.

Keywords

• approximate dynamic programming
• reinforcement learning
• data-driven control
• model-free control
• reference trajectory tracking
• output reference model
• multivariable control
• aerodynamic rotor system
• neural networks
• learning systems