A probabilistic indirect adaptive controller is proposed for the general nonlinear multivariate class of discrete time system. The proposed probabilistic framework incorporates input–dependent noise prediction parameters in the derivation of the optimal control law. Moreover, because noise can be nonstationary in practice, the proposed adaptive control algorithm provides an elegant method for estimating and tracking the noise. For illustration purposes, the developed method is applied to the affine class of nonlinear multivariate discrete time systems and the desired result is obtained: the optimal control law is determined by solving a cubic equation and the distribution of the tracking error is shown to be Gaussian with zero mean. The efficiency of the proposed scheme is demonstrated numerically through the simulation of an affine nonlinear system.
|Number of pages||20|
|Journal||International Journal of Adaptive Control and Signal Processing|
|Early online date||28 Jul 2010|
|Publication status||Published - Jan 2011|
Bibliographical noteHerzallah, R. (2011). A probabilistic indirect adaptive control for systems with input-dependent noise. International Journal of Adaptive Control and Signal Processing, 25(1), 48–67, which has been published in final form at http://dx.doi.org/10.1002/acs.1198. This article may be used for non-commercial purposes in accordance With Wiley Terms and Conditions for self-archiving.
- neural networks
- stochastic systems
- nonstationary noise
- distribution modelling