Control-Coherent Koopman Modeling: A Physical Modeling Approach

Understand

The modeling of nonlinear dynamics based on Koopman operator theory, which is originally applicable only to autonomous systems with no control, is extended to non-autonomous control system without approximation to input matrix B.

• Prevailing methods using a least square estimate of the B matrix may result in an erroneous input matrix, misinforming the controller about the structure of the input matrix in a lifted space.
• Here, a new method for constructing a Koopman model that comprises the exact input matrix B is presented.
• A set of state variables are introduced so that the control inputs are linearly involved in the dynamics of actuators.