Optimal control of a dynamical system requires knowledge about control inputs and corresponding controllable states and observables. For complex, nonlinear systems with multiple actuators and sensors, such as aircraft and spaceships, the identification of sparse, effective controller inputs and useful observable outputs is a challenge. In this contribution, we show how such low-dimensional, effective, nonlinear features can be found by constructing jointly smooth functions between control input and state observations. The construction relies on spectral methods from manifold learning and a special definition of smoothness of functions with respect to individual kernels. We illustrate the approach on simple examples such as the control of an inverted, nonlinear pendulum and demonstrate its feasibility in a real-world scenario by extracting the relevant features for the control of a landing spaceship.      «

Optimal control of a dynamical system requires knowledge about control inputs and corresponding controllable states and observables. For complex, nonlinear systems with multiple actuators and sensors, such as aircraft and spaceships, the identification of sparse, effective controller inputs and useful observable outputs is a challenge. In this contribution, we show how such low-dimensional, effective, nonlinear features can be found by constructing jointly smooth functions between control input...     »