Adaptive Control of Uncertain Linear Systems With Uncertain Hysteretic Input Nonlinearities

Abstract

We apply retrospective cost adaptive control (RCAC) with auxiliary nonlinearities to a command-following problem for uncertain Hammerstein systems with rate-dependent hysteretic input nonlinearities. The only required modeling information of the linear plant is a single Markov parameter. To account for the hysteretic input nonlinearity, RCAC uses auxiliary nonlinearities that reflect the monotonicity properties of the input nonlinearity. The hysteresis nonlinearity is modeled using the rate-dependent Prandtl-Ishlinskii model.

Retrospective-Cost Adaptive Control of Uncertain Hammerstein-Wiener Systems with Memoryless and Hysteretic Nonlinearities

“…[9][10][11][12] The present paper extends the application of RCAC to Hammerstein systems in. 13,15 In 13,15 the adaptive control is instantaneously linear, and thus converges to a linear time-invariant controller. Consequently, RCAC seeks a linear controller that is effective in reducing the distortion due to the input and output nonlinearities.…”