Dynamic inverse optimization

While system identification has traditionally concentrated on identifying systems driven by explicit ordinary differential equations, the recent explosion in computational power has made feasible systems whose dynamics are partly driven by real-time optimization processes. Identification algorithms which could pinpoint the optimization parameters used to drive these closed-loop control systems would clearly find application to receding horizon controllers and other control processes which incorporate online optimization. This work describes a procedure which identifies the optimization parameters at work in many types of receding horizon controllers. If all the control and state constraints are known, then the problem may be recast as identification of objective parameters of a real-time, static optimization problem. Using the necessary conditions of optimality in some cases of interest, this problem is shown to be equivalent to solving a feasibility semidefinite program. In alternate setups, the necessary conditions of optimality lead to a formulation of the identification problem as a feasibility linear or integer program.