Every Continuous Nonlinear Control System Can be Obtained by Parametric Convex Programming

In this short note, we define parametric convex programming (PCP) in a slightly different manner than it is usually done by extending convexity not only to variables but also to the parameters, and we show that the widely applied model predictive control (MPC) technique is a particular case of PCP. The main result of the note is an answer to the inverse question of PCP: which feedback laws can be generated by PCP? By employing results of convex analysis, we provide a constructive proof-yet not computational-that allows us to conclude that every continuous feedback law can be obtained by PCP.