Robust Extremum Seeking for a Second Order Uncertain Plant Using a Sliding Mode Controller

Abstract

This paper suggests a novel continuous-time robust extremum seeking algorithm for an unknown convex function constrained by a dynamical plant with uncertainties. The main idea of the proposed method is to develop a robust closed-loop controller based on sliding modes where the sliding surface takes the trajectory around a zone of the optimal point. We assume that the output of the plant is given by the states and a measure of the function. We show the stability and zone-convergence of the proposed algorithm. In order to validate the proposed method, we present a numerical example.

Global Asymptotic Stability of Nonlinear Strict Feedback System via Backstepping Control Approach

“…Most often, useful nonlinear terms may be canceled due to the feedback linearization method used to stabilize the strict feedback control system (6). However, since the backstepping approach does not necessitate that the fnal input-output dynamics is a linear system, it demonstrates greater fexibility compared to the feedback linearization approach [17].…”

“…Sliding mode control, a well-liked variable structure control technique, alters the dynamics of a nonlinear system by applying a discontinuous control signal which makes the system move along a surface known as the sliding manifold, and this is a cross section representation of the system's typical behavior (see Solis et al [6]; Armghan et al [7]; and Gang [8]).…”

Analytical Method for Mechanism Design in Partially Observable Markov Games

“…In relation to future work, there are several challenges that are left to address. One interesting technical challenge is that of addressing extremum seeking in the context of mechanism design [31][32][33]. Another interesting challenge would be to consider the observer design approach in order to extend the mechanism design theory [23] .…”

Extremum Seeking Control for a Class of Nonholonomic Systems

“…to (20), where λ, µ are real constants which are be specified later in (24), ω is a positive real control parameter, y is the measured signal (21), and η is the high-pass filter (10). Using well-known trigonometric identities, we obtain the coordinate representation…”

“…On the other hand, measurements of the system state are not assumed to be available. Research on this type of optimization problem is motivated by various applications, such as spacecraft attitude optimization [27], optimal alignment of solar panels [20], and environmental source seeking [14].…”