Deep Koopman Operator With Control for Nonlinear Systems

Recently Koopman operator has become a promising data-driven tool to facilitate real-time control for unknown nonlinear systems. It maps systems into equivalent linear in embedding space, ready methods. However, designing an appropriate function remains challenging task. Furthermore, most Koopman-based algorithms only consider with input, resulting lousy prediction and performance when the system is fully input. In this work, we propose end-to-end deep learning framework learn Operator together alleviate such difficulties. We first parameterize neural network train them K-steps loss function. Then, auxiliary augmented encode state-dependent term model nonlinearity This encoded considered new variable instead ensure linearity of modeled system. next deploy Linear Quadratic Regulator (LQR) on space derive optimal policy decode actual input from net. Experimental results demonstrate that our approach outperforms other existing methods, reducing error by order magnitude achieving superior several dynamic like damping pendulum, CartPole, seven DOF robotic manipulator.