Data-Driven Identification and Output Regulation Using Partially Observed Actuated Trajectories : A Koopman Bilinear Approach

Debdipta Goswami (Ohio State University)

Data-driven Koopman-theoretic approaches have proven effective in output prediction, state estimation, and control of nonlinear dynamical systems. For control-affine systems, the Koopman generator’s affine dependence on inputs enables finite-dimensional bilinear approximations. However, selecting appropriate basis functions remains a challenge in noisy, partially observed settings. Although time-delayed observables help under partial observations, their efficacy diminishes in actuated systems. To overcome this, we model control-affine dynamics as a bilinear Hidden Markov Model defined by Koopman generators with a nonlinear observation map parameterized by a multilayer perceptron. We learn the HMM and decoder parameters via expectation-maximization, using an extended Kalman filter and smoother in the E-step and least-squares and gradient-based optimization in the M-step. We apply model-predictive control using the learned HMM for regulation. We demonstrate our method’s effectiveness on: (1) an actuated polynomial system with a slow manifold, (2) a forced Duffing oscillator, and (3) the Kuramoto–Sivashinsky equation with noisy observations.