Model Predictive Control and Transfer Learning of Hybrid Systems Using Lifting Linearization Applied to Cable Suspension Systems

Model Predictive Control (MPC) of nonlinear hybrid systems using lifting linearization underpinned by Koopman Operator is presented. Unlike standard linearization, which is valid only locally, lifting linearization provides a global linear representation of a nonlinear system in a lifted space. This allows us to obtain a unified linear model for a class of hybrid systems, which are otherwise modeled as a collection of dynamic modes that are constantly switching. This linear model created with lifting linearization is utilized to control a multi-cable robot exhibiting hybrid dynamics due to switching between taut and slack conditions of each cable. Applying MPC to the cable suspension robot, we show that even though the highly complex computation is reduced to a straightforward convex optimization, MPC can still find dexterous control actions for manipulating an object by taking into account the hybrid nature of the dynamics. A drawback of lifting linearization is that the learned model must be relearned when parameters of the system change. Here, we exploit the linearity of the model for transfer learning of a tuned model, adapted to a similar system with different parameters. Using a recursive updating method for the linear model, we demonstrate that the transferred model is able to adapt to the dynamics of the new nonlinear system and decrease prediction error over time. The resulting prediction error is comparable to that of the original model trained on its original dataset.