Numerical optimization‐based extremum seeking control of a class of constrained nonlinear systems via finite‐time state transition.

This article studies the extremum seeking control (ESC) problem for a class of constrained nonlinear systems. Specifically, we focus on a family of constraints that allows to reformulate the original nonlinear system in the so‐called input–output normal form. To steer the system to optimize a performance function without knowing its explicit form, we propose a novel numerical optimization‐based extremum seeking control (NOESC) design consisting of a constrained numerical optimization method and an inversion‐based feedforward controller. In particular, a projected gradient descent algorithm is exploited to produce the state sequence to optimize the performance function, whereas a suitable boundary value problem accommodates the finite‐time state transition between each two consecutive points of the state sequence. Compared to available NOESC methods, the proposed approach (i) can explicitly deal with output constraints; (ii) can consider a direct dependence on the states of the internal dynamics in the performance function; (iii) the internal dynamics do not have to be necessarily stable. The effectiveness of the proposed ESC scheme is shown through extensive numerical simulations and design of antilock braking systems. [ABSTRACT FROM AUTHOR]