Adaptive control of stochastic Hammerstein systems with dead-zone input non-linearity

Abstract

This article presents a new control scheme for H systems with symmetric dead-zone input non-linearity and coloured noise. Based on the parameterized H model, we derive a dead-zone compensating control law and a recursive estimator. Theoretical analysis shows that global convergence and closed-loop stability can be guaranteed using the proposed algorithms. What is more, theoretical results show that the output tracking error is convergent with a specific residue, which is related to the variance of the noise and the parameter estimate. Simulation results confirm that the proposed method leads to satisfactory output tracking performance.

Intelligent control for Hammerstein nonlinear systems with arbitrary deadzone input

“…This work is an extension of the results of Kung and Womack (1984a, 1984b) and Zhang and Mao (2014), since it deals with asymmetric deadzone input.…”

“…In order to derive the deadzone compensating control law, we introduce a new function as follows (Zhang and Mao, 2014):…”

“…However, for a parameterized H model (11), it is not always possible to generate an input such that y ^ i ( t + 1 ) is equal to y * ( t + 1 ) (Zhang and Mao, 2014). In other words, due to the nonsmooth properties of deadzone, the certainty equivalent principle (Goodwin and Sin, 1984) is not appropriate for the derivation of the control law.…”

“…Due to the nonsmooth properties of deadzone, there may be no solution for (27). Similar to Kung and Womack (1984a, 1984b) and Zhang and Mao (2014), we choose a u 1 ( t ) (that is, u ( t ) ) so that y ^ i ( t + 1 ) is as close to y * ( t + 1 ) as possible.…”

“…To overcome the need for precise model parameters, an adaptive controller can operate successfully in environments with large uncertainties. However, as was reported by Zhang and Mao (2014), in the literature of discrete adaptive control of H nonlinear systems with nonsmooth input, very few approaches are available: Kung and Womack (1984a, 1984b) studied symmetric preload nonlinearity and two-segment piecewise-linear nonlinearity; recently, Zhang and Mao (2014) considered symmetric deadzone nonlinearity. As far as we know, no discrete adaptive control approach has yet been reported for H models with arbitrary deadzone input.…”