Nonlinear Control Systems

Nonlinear models naturally occur in most areas of engineering (mechanical, electrical, chemical, ) and are traditionally dealt with by linear approximations. However, by using the nonlinear model, better controllers can be designed that take into account the nonlinear behavior.  The Wolfram Language provides full support for affine and general nonlinear models. For affine models, you can automatically find a transformation that makes the system linear, allowing for the full suite of linear analysis and design functionality to be used. For general nonlinear models, automatic approximation schemes allow one to reduce to linear or affine systems or directly design a full information regulator.

ReferenceReference

Modeling & Simulation

AffineStateSpaceModel affine model and

NonlinearStateSpaceModel nonlinear model and

SystemsModelSeriesConnect  ▪  SystemsModelFeedbackConnect  ▪  ...

OutputResponse  ▪  StateResponse  ▪  ...

Design by Approximate Linearization

StateSpaceModel Taylor linearize a model to a StateSpaceModel

CarlemanLinearize Carleman bilinearize a model to an AffineStateSpaceModel

StateFeedbackGains  ▪  EstimatorRegulator  ▪  ...

Design by Exact Linearization

FeedbackLinearize linearization through nonlinear feedback and state transformation

StateTransformationLinearize linearization through state transformation

StateSpaceTransform change of variables for state space models

StateFeedbackGains  ▪  EstimatorRegulator  ▪  LinearizingTransformationData  ▪  ...

Nonlinear Design

FullInformationOutputRegulator regulate output with full information state feedback

AsymptoticOutputTracker tracker with state feedback

Nonlinear Analysis

SystemsModelVectorRelativeOrders vector relative orders for affine models

ControllableModelQ  ▪  ObservableModelQ  ▪  ControllableDecomposition  ▪  ObservableDecomposition  ▪  MinimalStateSpaceModel  ▪  SystemsModelLinearity