Gaussian process based dual adaptive control of nonlinear stochastic systems

Abstract

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.

Functional Dual Adaptive Control with Recursive Gaussian Process Model

“…The equations (6)- (13) describe model of the system (1) and provide a procedure how to obtain an one-step predictionŷ k+1 and variance var(y k+1 ), which may be useful component in the control law derivation [27]. Note that, the equations (7)- (8) show that the prediction is calculated using all the currently available data.…”

“…The equations (27) and (32) represent the final BD adaptive control law, where the first term is the cautious control component and second term denotes probing control component. The probing part is a function of variable µ k and ν k which represent the uncertainty in the system functions f (x a k ) and g(x a k ).…”

“…So far, GP modelling was utilised in functional adaptive approach only in a few pioneering works [3,27]. It should be noted, that the GP models were implemented exclusively in a nonrecursive form, causing a continuous increase of the computational demands with time, which significantly reduces their practical applicability.…”

“…Based on the motivation point, the main goal of the paper is twofold: 1) Design a functional adaptive control using the recursive GP model suggested in [28] and 2) Compare the proposed solution with the non-recursive case presented in [27] through extensive Monte-Carlo analysis in a numerical example.…”

Anticipating the Long-Term Effect of Online Learning in Control

“…Within the control community, the idea of anticipating and exploiting learning effects in control design has been explored in the form of dual control [13], [14]. So far, dual control has been investigated mostly within the context of structured models with parametric uncertainties, with few exceptions [15], [16]. However, [16] requires the true system to be affine in the control, and both [16] and [15] employ approximations that yield no theoretical guarantees.…”