Non-gradient Extremum Seeking Control of Feedback Linearizable Systems with Application to ABS Design

Abstract

In this paper, the extremum seeking control problem is treated as a real time optimization problem with dynamic system constraints. We propose a non-gradient trust regionbased extremum seeking control scheme for state feedback linearizable systems, then extend to input-output feedback linearizable systems with some minor modifications. The main contribution of the trust region-based extremum seeking control is that we no longer require gradient information of the performance function and is of global convergence. We also present the convergence and robustness analysis. Simulation study of antilock braking system (ABS) design is addressed to illustrate the feasibility of the proposed scheme.

Extremum Seeking Control based on Numerical Optimization and State Regulation - Part I: Theory and Framework

“…Moreover, such framework can be extended to more general nonlinear systems as long as one can successfully design a state regulator. Also we can design non-gradient extremum seeking control [17] by using a non-derivative optimization algorithm such as the trust region method or gradient estimation, Future research will include the design of output feedback state regulator and the exploration of other robust numerical optimization algorithms.…”

“…Then we apply controller (10) to perform output tracking of the reference r k (t). In the Section III-C, we have shown how to obtain the upper boundδ k of the regulation time δ k by solving inequality (17). Thus the controller will regulate the state to the desired neighborhood (15) in a finite time, and therefore ensure the state trajectory interpolate among the descent sequence {x k } every δ k time.…”

“…Moreover, we can relax the gradient requirement by considering non-derivative numerical optimization algorithms, related research on nongradient extremum seeking can be found in [17].…”

“…The estimated bound b k ∇J(x k ) is proportional to the last gradient measurement and can be computed in the beginning of the current regulation. Moreover, the step length α k is generally converging to zero as k → ∞, then we have b k → (14) and (16), we can solve the following inequality (17) to obtain the upper bound of the regulation timeδ k :…”

Numerical Optimization-Based Extremum Seeking Control With Application to ABS Design

“…Some modifications of the above scheme are required in order to use the trust region methods due to the need to obtain the ratio in (9), where we may need additional regulation time to drive the state back to if . Please refer to [28] for the details of trust region-based extremum seeking control.…”