Abstract
AbstractIn this paper a method for generating periodic orbits for a class of non‐linear systems is presented. A periodic Hamiltonian system is defined as the target equilibrium for non‐linear systems in strict feedback form. A parameter dependent non‐linear periodic system description is introduced for a two‐dimensional subsystem and extended to higher dimensions using backstepping. Extremum seeking is used as a parameter update law that guarantees the convergence of the system to the optimal periodic orbit with respect to a given parameterization. The procedure resulted in an on‐line feedback control implementation that typically steers the system to a suboptimal solution that nevertheless improves the static optimization solution. Typical examples from optimal periodic control literature are used to illustrate the application of this approach.
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