Nonlinear Model Predictive Control, or NMPC, is a variant of Model Predictive Control (MPC) that is characterized by the use of nonlinear system models in prediction. As in linear MPC, NMPC requires the iterative solution of control problems as optimization over a finite prediction horizon. While these problems are convex in linear MPC, in NMPC they are no longer so. This poses challenges both for the stability theory in NMPC and for the numerical solution.[5]​.

The numerical solution of optimal control problems in NMPC is typically based on optimal control methods that use Newton-type optimization schemes: isolated direct shooting methods, multiple direct shooting methods, or direct placement methods.[6] Likewise, NMPC algorithms typically take advantage of the fact that consecutive optimal control problems are similar to each other.

This allows the Newton-type solution procedure to be initialized with a suitably shifted estimate that comes from the previously computed optimal solution, saving a considerable amount of computing time. The similarity in subsequent problems is exploited even further by means of path tracking algorithms (also "real-time iterations") that never attempt to iterate an optimization problem towards convergence, but only to perform an iteration towards the solution of the most recent NMPC problem, before moving on to the next one, which will also be properly initialized.

While NMPC applications have in the past been used primarily in the chemical and process industries that have comparatively slow sampling rates, it is increasingly common to see NMPC in applications with faster sampling rates, for example in the automotive industry, or even when states are distributed in space (distributed parameter systems).[7] As an application in aerospace engineering, NMPC has recently been used to achieve real-time terrain-trackers/evasion-trajectories.[6]​.

Robust variants of Model Predictive Control (MPC) are capable of considering bounded and fixed perturbations while ensuring that state constraints are still met. There are three main approaches in the search for robust MPC:

Model predictive control has been applied for the optimal development of projects in oil and gas deposits.[12]​.

Several commercial MPC software packages are available and typically contain tools that assist in model identification and analysis, controller design and tuning, and performance evaluation.

[1] A list of the technologies available in MPC has been provided by S.J. Qin and T.A. Badgwell in “Control Engineering Practice 11” (2003) 733–764.

Nonlinear Model Predictive Control, or NMPC, is a variant of Model Predictive Control (MPC) that is characterized by the use of nonlinear system models in prediction. As in linear MPC, NMPC requires the iterative solution of control problems as optimization over a finite prediction horizon. While these problems are convex in linear MPC, in NMPC they are no longer so. This poses challenges both for the stability theory in NMPC and for the numerical solution.[5]​.

The numerical solution of optimal control problems in NMPC is typically based on optimal control methods that use Newton-type optimization schemes: isolated direct shooting methods, multiple direct shooting methods, or direct placement methods.[6] Likewise, NMPC algorithms typically take advantage of the fact that consecutive optimal control problems are similar to each other.

This allows the Newton-type solution procedure to be initialized with a suitably shifted estimate that comes from the previously computed optimal solution, saving a considerable amount of computing time. The similarity in subsequent problems is exploited even further by means of path tracking algorithms (also "real-time iterations") that never attempt to iterate an optimization problem towards convergence, but only to perform an iteration towards the solution of the most recent NMPC problem, before moving on to the next one, which will also be properly initialized.

While NMPC applications have in the past been used primarily in the chemical and process industries that have comparatively slow sampling rates, it is increasingly common to see NMPC in applications with faster sampling rates, for example in the automotive industry, or even when states are distributed in space (distributed parameter systems).[7] As an application in aerospace engineering, NMPC has recently been used to achieve real-time terrain-trackers/evasion-trajectories.[6]​.

Robust variants of Model Predictive Control (MPC) are capable of considering bounded and fixed perturbations while ensuring that state constraints are still met. There are three main approaches in the search for robust MPC:

Model predictive control has been applied for the optimal development of projects in oil and gas deposits.[12]​.

Several commercial MPC software packages are available and typically contain tools that assist in model identification and analysis, controller design and tuning, and performance evaluation.

[1] A list of the technologies available in MPC has been provided by S.J. Qin and T.A. Badgwell in “Control Engineering Practice 11” (2003) 733–764.