A Nonlinear Optimal Control Approach to Stabilization of Business Cycles of Finance Agents

The article proposes a new nonlinear optimal control method for the stabilization of the business cycles of interconnected finance agents. First, the dynamics of the interacting finance agents and of the associated business cycles is described by a model of coupled nonlinear oscillators. Next, this dynamic model undergoes approximate linearization round a temporary operating point which is defined by the present value of the system’s state vector and the last value of the control inputs vector that was exerted on it. The linearization procedure is based on Taylor series expansion of the dynamic model and on the computation of Jacobian matrices. Next, for the linearized model of the interacting finance agents, an H-infinity feedback controller is designed. The computation of the feedback control gain requires the solution of an algebraic Riccati equation at each iteration of the control algorithm. Through Lyapunov stability analysis it is proven that the control scheme is globally asymptotically stable. © 2017, Springer Science+Business Media, LLC, part of Springer Nature.