Flatness-Based Control in Successive Loops for Business Cycles of Finance Agents

Flatness-based control implemented in successive loops is proposed for modifying the business cycles of interacting finance agents. The dynamics of the business cycle of each individual agent is described as a nonlinear oscillator, while interaction terms exist between such oscillators denoting transactions in the form of goods trade or services hiring. A state-space description for the dynamics of the interacting business cycles is obtained. The differential flatness properties of this model are proven. It is demonstrated that each row of the state-space model is a differentially flat subsystem and that a stabilizing feedback controller can be designed for it. Actually, local control is achieved by considering specific state variables of the model as virtual control inputs. From the last row of the model, the control input that is actually exerted on the system is found and this is shown to contain recursively the virtual control inputs associated with the individual rows of the state-space description. The global stability properties of the control method are confirmed through Lyapunov analysis. The method comes to confirm that exogenous investements appearing as control inputs to the system can provide the impetus for growth to the interconnected finance agents. Consequently, changes of the business cycles of the individual agents (reflecting growth or recession) can be centrally controlled.