Solving smooth and nonsmooth multivariable extremum seeking problems by the methods of nonlinear programming

Contains an analysis of the dynamics associated with the interconnection of a dynamical system with a discrete-time approximate nonlinear programming algorithm designed to locate an extremum on the steady-state output map (readout map) of the dynamical system. Very few assumptions on the dynamical system, the readout map, and the nonlinear programming algorithm are imposed. Taking a nonlinear programming approach to the extremum seeking problem readily allows: 1) readout maps that depend on many input parameters in a highly coupled manner, 2) nonsmooth readout maps, 3) nonexponential convergence to attractors that determine the steady-state, and 4) attractors in infinite dimensions. Several simulation examples are provided to illustrate the theory and demonstrate the flexibility of the approach.