Control of complex peak-to-peak dynamics

The paper illustrates a method for the design of suitable controllers of chaotic systems characterized by complex peak-to-peak dynamics, namely by a recursive relationship between consecutive peaks (relative maxima) of a scalar output variable. For such systems, a reduced model can be defined which, in general, is a hybrid model composed of a one-dimensional map and a finite-state automaton. The issues related to the identification and control of such a reduced model are discussed with the help of three applications: the Chua's circuit, a market with advertizing, and a CO2 laser.