Bayesian nonparametrics and feedback-linearisation of discretised control-affine systems - Calliess, J; Papachristodoulou, A; Roberts, S (Institute of Electrical and Electronics Engineers, 2019)
We propose random field system identification and inversion control (RF-SIIC) as a method for simultaneous probabilistic identification and control of time-discretised control-affine systems. Identification is achieved by conditioning random field priors on observations of configurations and noisy estimates of configuration derivatives. In contrast to previous work that has utilised random fields for identification, we leverage the structural knowledge afforded by Lagrangian mechanics and learn both the drift and control input matrix functions of a control-affine system. We employ feedback-linearisation to reduce, in expectation, the uncertain nonlinear control problem to one that is easy to regulate. Our method combines the flexibility of nonparametric Bayesian learning with epistemological guarantees on the expected closed-loop trajectory. We illustrate the viability of our approach in the context of a discretised, fully-actuated mechanical system. Our simulations suggest that our approach can adapt rapidly to a priori uncertain dynamics sufficiently well to succeed in feedback-linearising and controlling the plant as desired.