Tailoring the bifurcation Diagram of Nonlinear Dynamical Systems: an Optimization Based Approach

Bifurcation tailoring is a method developed to design control laws modifying the bifurcation diagram of a nonlinear dynamical system to a desired one. In its original formulation, this method does not account for the possible presence of constraints on state and/or manipulated inputs. In this paper, a novel formulation of the bifurcation tailoring method overcoming this limitation is presented. In accordance with the proposed approach, a feedforward control law generating an optimal bifurcation diagram is computed by constrained minimization of an objective functional. Then, a feedback control system enforcing stability of the computed equilibrium branch is designed. In this context, bifurcation analysis is exploited to select feedback controller parameters ensuring desired output behavior and, at the same time, preventing the occurrence of multistability. The method is numerically validated on the problem of tailoring the bifurcation diagram of an exothermic chemical reactor.