# CONSTRAINTS

Object describing linear inequality constraints on states and inputs of a dynamical system

## Contents

Class of MOBY-DIC TOOLBOX.

## Description

The constraints object describes linear inequality constraints in the form , where x and u are the state and input variables (respectively) of a dynamical system and p is a vector of parameters. Such formulation allows to describe saturation constraints on states and inputs as well as mixed state-parameters-input constraints. This object is thought to be used with Model Predictive Control, in which constraints on input and states are imposed also in future istants within a certain time horizon. Given a prediction horizon N, it is possible to set input (or mixed) constraints from istant k to instant k+N-1, and state constraints from istant k to instant k+N (this because constraints on can be written as constraints on , by knowing the matrices defining the linear system). NOTE: state constraints on time k can be written but they cannot be imposed in MPC because the current state cannot be controlled by the input. The constraints are set with method setConstraints.

## Syntax

**constr = constraints()**

Builds an empty *constraints* object.

**constr = constraints(nx,nu,np,N)**

Builds a constraints object defining the number of state variables (nx), the number of input variables (nu), the number of parameters (np) and the prediction horizon (N).

## Properties

- nx - number of state variables.
- nu - number of input variables.
- np - number of parameters.
- N - prediction horizon
- H, K - matrices defining the linear inequality constraints . H and K are cell arrays of N+2 elements: each element corresponds to a time instant (from k to k+N+1)

## Methods

- disp - displays some information about the constraints object.
- getMatrices - gets the H and K matrices defining the constraints.
- getNumberOfInputConstraints - Gets the number of constraints involving only input variables.
- getNumberOfInputs - gets the number of input variables.
- getNumberOfMixedConstraints - Gets the number of mixed constraints.
- getNumberOfParameterConstraints - Gets the number of constraints involving only parameters.
- getNumberOfParameters - gets the number of parameters.
- getNumberOfStates - gets the number of state variables.
- getPredictionHorizon - gets the prediction horizon.
- setConstraints - sets state, input and mixed constraints.

## Acknowledgements

Contributors:

- Alberto Oliveri (alberto.oliveri@unige.it)

Copyright is with:

- Copyright (C) 2011 University of Genoa, Italy.