Bifurcations, catastrophes, and optimal control

An approach to the problem of determining bifurcation-free optimal control laws is presented using the theory of catastrophes. Under the assumption that the linearized system dynamics in the neighborhood of the equilibrium are of gradient type, conditions are given to ensure that a linear feedback law simultaneously minimize a quadratic objective and generate a bifurcation-free trajectory. Explicit results are presented for the case of two system inputs (the cusp catastrophe). Extensions to the case of nongradient dynamics and/or nonquadratic costs are also discussed.