called receding horizon control. Although this approach is not optimal, in practice it has given very good results. Much academic research has been done to find fast methods of solution of Euler–Lagrange type equations, to understand the global stability properties of MPC's local optimization, and in general to improve the MPC method. Principles of MPC Model predictive control is a multivariable control algorithm that uses: an internal dynamic model of the process a cost function J over the receding horizon an optimization algorithm minimizing the cost function J using the control input u An example of a quadratic cost function for optimization is given by: without violating constraints (low/high limits) with : th controlled variable (e.g. measured temperature) : th reference variable (e.g. required temperature) : th manipulated variable (e.g. control valve) : weighting coefficient reflecting the relative importance of : weighting coefficient penalizing relative big changes in etc. Nonlinear MPC Nonlinear model predictive control, or NMPC, is a variant of model predictive control that is characterized by the use of nonlinear system models in the prediction. As in linear MPC, NMPC requires the iterative solution of optimal control problems on a finite prediction horizon. While these problems are convex in linear MPC, in nonlinear MPC they are not necessarily convex anymore. This poses challenges for both NMPC stability theory and numerical solution. The numerical solution of the NMPC optimal control problems is typically based on direct optimal control methods using Newton-type optimization schemes, in one of the variants: direct single shooting, direct multiple shooting methods, or direct collocation. NMPC algorithms typically exploit the fact that consecutive optimal control problems are similar to each other. This allows to initialize the Newton-type solution procedure efficiently by a suitably shifted guess from the previously computed optimal solution, saving considerable amounts of computation time. The similarity of subsequent problems is even further exploited by path following algorithms (or "real-time iterations") that never attempt to iterate any optimization problem to convergence, but instead only take a few iterations towards the solution of the most current NMPC problem, before proceeding to the next one, which is suitably initialized; see, e.g.,.. Another promising candidate for the nonlinear optimization problem is to use a randomized optimization method. Optimum solutions are found by generating random samples that satisfy the constraints in the solution space and finding the optimum one based on cost function. While NMPC applications have in