Gaussian Process Based Dual Adaptive Control of Nonlinear Stochastic Systems

The paper proposes a suboptimal adaptive control for a nonlinear stochastic system subject to functional uncertainty. The problem of a real-time identification of the unknown nonlinear system is tackled by using the Gaussian process based non-parametric model. The covariance function of the Gaussian process is chosen in such a way that allows deriving the control law in a closed form. The control action stems from the bicriterial dual approach that uses two separate criteria to introduce both of the mutually opposing aspects between estimation and control. Properties of the novel dual controller are tested and validated in a numerical example by Monte Carlo analysis.