The aim is to predict the future inputs to the system in such a way that the outputs follow a reference trajectory as good as possible. Constraints on inputs, outputs and states can be added. Convex problems Convex optimization problems are optimization problems that exist of a convex objective function and convex constraints.
Convex functions are functions with only a global optimum.
These convex problems have been shown to have very nice properties. First of all, because they only have global optima, algorithms have been developed that solve convex problems in polynomial time. Last but not least when the problem is convex, stability and robustness properties can be deduced. Especially with the introduction of Linear Matrix Inequalities, a wealth of potential objective functions and constraints have been introduced, which are largely unexplored in industrial applications. Although MPC is used widely in chemical industry, some things are still unclear and a lot of improvement is still possible.