In this paper, a novel Virtual State-feedback Reference Feedback Tuning (VSFRT) and Approximate Iterative Value Iteration Reinforcement Learning (AI-VIRL) are applied for learning linear reference model output (LRMO) tracking control of observable systems with unknown dynamics. For the observable system, a new state representation in terms of input/output (IO) data is derived. Consequently, the Virtual State Feedback Tuning (VRFT)-based solution is redefined to accommodate virtual state feedback control, leading to an original stability-certified Virtual State-Feedback Reference Tuning (VSFRT) concept. Both VSFRT and AI-VIRL use neural networks controllers. We find that AI-VIRL is significantly more computationally demanding and more sensitive to the exploration settings, while leading to inferior LRMO tracking performance when compared to VSFRT. It is not helped either by transfer learning the VSFRT control as initialization for AI-VIRL. State dimensionality reduction using machine learning techniques such as principal component analysis and autoencoders does not improve on the best learned tracking performance however it trades off the learning complexity. Surprisingly, unlike AI-VIRL, the VSFRT control is one-shot (non-iterative) and learns stabilizing controllers even in poorly, open-loop explored environments, proving to be superior in learning LRMO tracking control. Validation on two nonlinear coupled multivariable complex systems serves as a comprehensive case study.

This paper applies three classical and very popular discrete-time model-based sliding mode controllers, namely the Furuta controller, the Gao controller, and the quasi-relay controller due to Milosavljević, to the position control of tower crane systems. Three single input-single output (SISO) control systems are considered, for cart position control, arm angular position control and payload position control, and separate SISO controllers are designed in each control system. Experimental results are included to support the comparison of the three plus three plus three sliding mode controllers.