  This paper addresses a learning problem for nonlinear dynamical systems with
incorporating any specified dissipativity property. The nonlinear systems are
described by the Koopman operator, which is a linear operator defined on the
infinite-dimensional lifted state space. The problem of learning the Koopman
operator under specified quadratic dissipativity constraints is formulated and
addressed. The learning problem is in a class of the non-convex optimization
problem due to nonlinear constraints and is numerically intractable. By
applying the change of variable technique and the convex overbounding
approximation, the problem is reduced to sequential convex optimization and is
solved in a numerically efficient manner. Finally, a numerical simulation is
given, where high modeling accuracy achieved by the proposed approach including
the specified dissipativity is demonstrated.
