Canadian Journal of Chemical Engineering, Vol.85, No.4, 479-489, 2007
On-line feedback control for optimal periodic control problems
In 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.