A Nonlinear Optimal Control Approach for Industrial Production under an Oligopoly Model

A nonlinear optimal (H-infinity) control method is proposed for industrial production under an oligopoly model. First, the dynamics of the oligopoly undergoes approximate linearization around a temporary operating point (equilibrium), which is recomputed at each time step of the control method. The equilibrium comprises the present value of the production system's state vector and the last value of the control inputs vector that was exerted on it. The linearization procedure makes use of the first-order Taylor series expansion and of the computation of the Jacobian matrices of the state-space description of the system. For the approximately linearized model of the system, an H-infinity (optimal) feedback controller is designed. For the computation of the controller's feedback gain, an algebraic Riccati equation is solved at each time step of the control method. The global asymptotic stability properties of the control scheme are analyzed with the use of the Lyapunov method.