Seminar Details
2019-08-27 (15:00) : Koopman Based Control: Bilinearization, Controllability and Optimal Control of Control-Affine Nonlinear Systems
At Euler building (room A.002)
Organized by Mathematical Engineering
Speaker :
Debdipta Goswami (University of Maryland)
Abstract :
Note the unusual time of this talk (15:00).
Nonlinear systems are ubiquitous in real world applications, but the control design for them is
not an easy task. Hence, methods are sought to transform a control-affine nonlinear system into linear
or bilinear forms to alleviate the problem of nonlinear controllability and control design. While
there are linearization techniques like Carleman linearization for embedding a finite-dimensional
nonlinear system into an infinite-dimensional space, they depend on the analytic property of the
vector fields and work only on polynomial space. The Koopman-based approach described here
utilizes the Koopman Canonical Transform (KCT) to transform the dynamics and ensures bilinearity
from the projection of the Koopman operator associated with the control vector fields on
the eigenspace of the drift Koopman operator. The sufficient conditions for exact bilinearization
are derived. Even if the conditions are not fully met, the approximate bilinearization can also be
posed as an optimization problem. The resulting bilinear system is then subjected to controllability
analysis using the Myhill semigroup method and Lie algebraic structures. Using the same Myhill
semigroup structure, we also seek to prove the existence of an energy-only optimal control.