Learning Exactly Linearizable Deep Dynamics Models

In recent years, there has been a growing interest in using machine learning (particularly deep learning) for modeling dynamical systems (Kocijan et al., 2004; Hedjar, 2013; Lenz et al., 2015; Moriyasu et al., 2019). Unlike the traditional modeling approach, machine learning can be used to create highly accurate models more easily without the need for detailed domain knowledge. However, control design using such models can become challenging because of the strong nonlinearity of the machine-learning models. Model predictive control (MPC) is a typical control method that can handle nonlinearity, wherein the model is used to optimize the predicted future behavior of the system; however, the optimal control problem solved each time is often nonconvex (Ławryńczuk, 2008; Nghiem, 2019; Gros, 2019) when the model is highly nonlinear, thereby making it difficult to ensure the uniqueness and optimality of the numerically obtained solution and the continuity of the control law (Moriyasu et al., 2022). Various nonlinear control theories besides MPC cannot be easily applied to general machine learning models because the model structures to which the theories can be applied are often limited to specific systems, such as input-affine systems.