Adaptive output feedback command filter controlbased on extreme learning machine for nonaffine time delay systems with input saturation

Abstract

This paper is concerned with extreme learning machine (ELM)-approximation-based command filter control for nonaffine pure-feedback time delay systems with input saturation. To begin with, a mean value theorem and an implicit function theorem are exploited to transform the system under consideration into an affine form. Afterwards, a state observer is developed to estimate the state variables that cannot be measured directly. By using the approximation capability and inherent adaptive features of an ELM, the unknown functions in time delay systems are successfully solved. The outputs of the command filter are applied to approximate the virtual control signals’ derivative, thereby circumventing the problem of "explosion of complexity" that can occur due to the presence of multiple differentiation of the virtual control signals. Meanwhile, the compensation signals are introduced to eliminate the filtering errors in a dynamic surface control (DSC). The Lyapunov-Krasovskii functionals are utilized to mitigate the time delay terms. An error constraint transformation method is consumed to guarantee the fulfillment of prescribed performance for a tracking error. Combining a prescribed performance control (PPC) with a command filter control, the target of a tracking error converges to a prescribed arbitrary small interval can be realized. Additionally, the effect of input saturation is eliminated with the aid of an auxiliary system. Finally, the effectiveness of the presented control approach is further proved by taking an electromechanical system as an application object.