Nonlinear Control of Gradient Dynamics with Shifted Passivity

A nonlinear control framework is developed for constrained gradient dynamics in real-time convex optimization. To counter the effect of the input constraints, an existing linear controller is augmented with an artificial nonlinearity such that the equilibrium conditions of the resulting closed loop are exactly the KKT optimality conditions for the corresponding optimization problem. Global asymptotic stability of the equilibrium is established from the shifted passivity property of the modified dynamics. The utility of the proposed control algorithm for neural circuit implementation is illustrated for quadratic programming.