Nonlinear MPC Design

Design model predictive controllers with nonlinear prediction models, costs, and constraints

As in traditional linear MPC, nonlinear MPC calculates control actions at each control interval, using a combination of model-based prediction and constrained optimization. The key differences are:

The prediction model can be nonlinear and include time-varying parameters
The equality and inequality constraints can be nonlinear
The scalar cost function to be minimized can be a nonquadratic (linear or nonlinear) function of the decision variables.

By default, nonlinear MPC controllers solve a nonlinear programming problem using the fmincon function, which requires Optimization Toolbox™ software. If you do not have Optimization Toolbox software you can specify your own custom nonlinear solver.

For more information, see Nonlinear MPC.

Functions

`nlmpc`	Nonlinear model predictive controller
`nlmpcMultistage`	Multistage nonlinear model predictive controller (Since R2021a)
`validateFcns`	Examine prediction model and custom functions of `nlmpc` or `nlmpcMultistage` objects for potential problems
`generateJacobianFunction`	Generate MATLAB Jacobian functions for multistage nonlinear MPC using automatic differentiation (Since R2023a)
`nlmpcmove`	Compute optimal control action for nonlinear MPC controller
`nlmpcmoveopt`	Option set for `nlmpcmove` function
`getSimulationData`	Create data structure to simulate multistage MPC controller with `nlmpcmove` (Since R2021a)
`convertToMPC`	Convert `nlmpc` object into one or more `mpc` objects
`createParameterBus`	Create Simulink bus object and configure Bus Creator block for passing model parameters to Nonlinear MPC Controller block

Blocks

Nonlinear MPC Controller	Simulate nonlinear model predictive controllers
Multistage Nonlinear MPC Controller	Simulate multistage nonlinear model predictive controllers (Since R2021a)

Topics

Nonlinear MPC Basics

Nonlinear MPC
Nonlinear model predictive controllers control plants using nonlinear prediction models, cost functions, or constraints.
Specify Prediction Model for Nonlinear MPC
To define a prediction model for a nonlinear MPC controller, specify the state and output functions.
Specify Cost Function for Nonlinear MPC
Nonlinear MPC controllers support generic cost functions, such as a combination of linear or nonlinear functions of the system states, inputs, and outputs.
Specify Constraints for Nonlinear MPC
You can specify custom linear and nonlinear constraints for your nonlinear MPC controller in addition to standard linear MPC constraints.
Configure Optimization Solver for Nonlinear MPC
By default, nonlinear MPC controllers optimize their control move using the fmincon function from the Optimization Toolbox. You can also specify your own custom nonlinear solver.
Trajectory Optimization and Control of Flying Robot Using Nonlinear MPC
You can use nonlinear MPC for both optimal trajectory planning and closed-loop control applications.
Landing a Vehicle Using Multistage Nonlinear MPC
Plan an optimal rocket lander trajectory and perform closed-loop control of landing process using multistage nonlinear MPC.

Feedback Control

Nonlinear Model Predictive Control of Exothermic Chemical Reactor
Control a nonlinear plant as it transitions between operating points.
Swing-Up Control of Pendulum Using Nonlinear Model Predictive Control
Achieve swing-up and balancing control of an inverted pendulum on a cart using a nonlinear model predictive controller.
Nonlinear and Gain-Scheduled MPC Control of an Ethylene Oxidation Plant
You can generate one or more linear MPC controllers from a nonlinear MPC controller and use these controllers for gain-scheduled control applications.
Optimization and Control of Fed-Batch Reactor Using Nonlinear MPC
Simulate nonlinear MPC controller as adaptive and time-varying MPC controller, and compare performance.

Optimal Planning

Optimizing Tuberculosis Treatment Using Nonlinear MPC with Custom Solver
You can use nonlinear MPC controllers for optimal planning applications that require a nonlinear model with nonlinear costs or constraints.
Generate Code to Plan and Execute Collision-Free Trajectories Using KINOVA Gen3 Manipulator
Use nonlinear MPC to plan and execute trajectories for a robot manipulator.

Economic MPC

Economic MPC
Economic model predictive controllers optimize control actions to satisfy generic economic or performance cost functions.
Economic MPC Control of Ethylene Oxide Production
Maximize production of an ethylene oxide plant for profit using a nonlinear cost function and nonlinear constraints.

Use Neural and Grey-Box Prediction Models

Control House Heating Using Nonlinear MPC with Neural State-Space Prediction Model
Design a Multistage MPC controller using a neural state space prediction model.
Swing-Up Control of a Pendulum on a Cart using Multistage Nonlinear MPC with Nonlinear Grey-Box Model
Design a Multistage MPC controller using a nonlinear grey-box prediction model.

Passivity-Based MPC

Control Robot Manipulator Using Passivity-Based Nonlinear MPC
Enforce stability of a robotic manipulator by implementing passivity-based constraints in a nonlinear MPC controller.
Control Quadruple-Tank Using Passivity-Based Nonlinear MPC
Control a system of four water tanks using passivity-based MPC.