CONSTRAINTS

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

Description
Syntax
Properties
Methods
Acknowledgements

Description

The constraints object describes linear inequality constraints in the form $H [x \ u \ p]' <= K$ , 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 $x_{k+N}$ can be written as constraints on $u_{k+N\textrm{--}-1}$ , 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 $H [x \ u \ p]' <= K$ . 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)