Moad Abudia

Moad Abudia, Opeyemi Owolabi, Joel A. Rosenfeld et al.

This paper presents a data-driven algorithm for simultaneous system identification and parameter estimation in control-affine nonlinear systems. Parameter estimation is achieved by training a data-driven predictive model using state-action measurements and various known values at the parameters of interest. The predictive model is then used in conjunction with state-action data corresponding to unknown values of the parameters to estimate the said unknown value. Numerical experiments on the controlled Duffing oscillator with unknown damping, stiffness, and nonlinearity coefficients demonstrate accurate recovery of both the system trajectories and the unknown parameter values from data collected under open-loop excitation.

Efrain Gonzalez, Moad Abudia, Michael Jury et al.

This manuscript revisits theoretical assumptions concerning dynamic mode decomposition (DMD) of Koopman operators, including the existence of lattices of eigenfunctions, common eigenfunctions between Koopman operators, and boundedness and compactness of Koopman operators. Counterexamples that illustrate restrictiveness of the assumptions are provided for each of the assumptions. In particular, this manuscript proves that the native reproducing kernel Hilbert space (RKHS) of the Gaussian RBF kernel function only supports bounded Koopman operators if the dynamics are affine. In addition, a new framework for DMD, that requires only densely defined Koopman operators over RKHSs is introduced, and its effectiveness is demonstrated through numerical examples.

Moad Abudia, Tejasvi Channagiri, Joel A. Rosenfeld et al.

This manuscript presents an algorithm for obtaining an approximation of a nonlinear high order control affine dynamical system. Controlled trajectories of the system are leveraged as the central unit of information via embedding them in vector-valued reproducing kernel Hilbert space (vvRKHS). The trajectories are embedded as the so-called higher order control occupation kernels which represent an operator on the vvRKHS corresponding to iterated integration after multiplication by a given controller. The solution to the system identification problem is then the unique solution of an infinite dimensional regularized regression problem. The representer theorem is then used to express the solution as finite linear combination of these occupation kernels, which converts an infinite dimensional optimization problem to a finite dimensional optimization problem. The vector valued structure of the Hilbert space allows for simultaneous approximation of the drift and control effectiveness components of the control affine system. Several experiments are performed to demonstrate the effectiveness of the developed approach.