Drake
ExpPlusPPTrajectory Class Reference

useful for solutions to linear systems driven by pptrajectory inputs in interval j, we have y(t) = K * exp(A*(t-tj)) * alpha(:,j) + sum_i gamma(:,j,i) (t-tj)^i More...

Inheritance diagram for ExpPlusPPTrajectory:
Collaboration diagram for ExpPlusPPTrajectory:

## Public Member Functions

function ExpPlusPPTrajectory (breaks, K, A, alpha, gamma)

function fasteval (obj, t)
no error checking. numeric scalar t only. More...

function eval (obj, t)

function fnder (obj, order)

function getBreaks (obj)

Public Member Functions inherited from Trajectory
function Trajectory (dim)

function getInitialState (obj)

function dynamics (obj, t, x, u)

function update (obj, t, x, u)

function output (obj, t, x, u)

function fasteval (obj, t)
derived classes should overload this to provide a fast, no-error-checking, eval method which supports only scalar numeric t inputs. More...

function fnder (obj)

function deriv (obj, t)

function dderiv (obj, t)

function inFrame (obj, frame)

Public Member Functions inherited from DrakeSystem
function DrakeSystem (num_xc, num_xd, num_u, num_y, direct_feedthrough_flag, time_invariant_flag)
Construct a DrakeSystem. More...

function zeroCrossings (obj, t, x, u)
Placeholder for the zeroCrossings method: a method phi = zeroCrossings(t,x,u) which triggers a zero crossing event when phi transitions from positive to negative. More...

function getNumContStates (obj)
Returns the number of continuous states. More...

function getNumDiscStates (obj)
Returns the number of discrete states. More...

function getNumInputs (obj)
Returns the number of inputs to the system. More...

function getNumOutputs (obj)
Returns the number of outputs from the system. More...

function getInitialStateWInput (obj, t, x, u)
Hook in case a system needs to initial state based on current time and/or input. More...

function getSampleTime (obj)
As described at http://www.mathworks.com/help/toolbox/simulink/sfg/f6-58760.html to set multiple sample times, specify one column for each sample time/offset pair. More...

function getInputSampleTimes (obj)
Returns getSampleTime - a DrakeSystem can only have a single same time associated with it. More...

function getOutputSampleTimes (obj)
Returns getSampleTime - a DrakeSystem can only have a single same time associated with it. More...

function setSampleTime (obj, ts)
robust method for setting default sample time More...

function isDirectFeedthrough (obj)
Check if the system is direct feedthrough (e.g., if the output depends on the immediate input) More...

function setDirectFeedthrough (obj, tf)
Set the direct feedthrough flag. More...

function getModel (obj)
Constructs a simulink system block for this system to be used by the simulink engine. More...

function findFixedPoint (obj, x0, u0)
attempts to find a fixed point (xstar,ustar) which also satisfies the constraints, using (x0,u0) as the initial guess. More...

function getDefaultInput (obj)
Define the default initial input so that behavior is well-defined if no controller is specified or if no control messages have been received yet. More...

function setNumContStates (obj, num_xc)
Guards the num_states variable. More...

function setNumDiscStates (obj, num_xd)
Guards the num_states variable. More...

function setNumInputs (obj, num_u)
Guards the num_u variable. More...

function setInputLimits (obj, umin, umax)
Guards the input limits to make sure it stay consistent. More...

function setNumOutputs (obj, num_y)
Guards the number of outputs to make sure it's consistent. More...

function getNumZeroCrossings (obj)
Returns the number of zero crossings. More...

function setNumZeroCrossings (obj, num_zcs)
Guards the number of zero crossings to make sure it's valid. More...

function getNumStateConstraints (obj)

function getNumUnilateralConstraints (obj)

function updateStateConstraint (obj, id, con, xind)

function displayStateConstraints (obj)

function removeAllStateConstraints (obj)

adds state constraints and unilateral constraints to the program on the specified indices. More...

add bounding box constraint todo: consider whether it makes sense to a list of constraints objects instead of just input limits. More...

function stateConstraints (obj, x)
Provides the old interface of a single constraint function which evaluates all of the equality constraints on the state (which should be == 0) More...

function linearize (obj, t0, x0, u0)
Uses the geval engine to linearize the model around the nominal point, at least for the simple case. More...

function simulate (obj, varargin)

function simulateODE (obj, tspan, x0, options)
Simulates the system using the ODE45 suite of solvers instead of the simulink solvers. More...

function feedback (sys1, sys2)
Constructs a feedback combination of sys1 and sys2. More...

Constructs a cascade combination of sys1 and sys2. More...

function extractPolynomialSystem (obj)
Attempts to symbolically extract the extra structure of a polynomial system from the Drake system Will throw an error if the system is not truly polynomial. More...

function extractAffineSystem (obj)
Attempts to symbolically extract the extra structure of an affine system from the Drake system Will throw an error if the system is not truly affine. More...

function extractLinearSystem (obj)
Attempts to symbolically extract the extra structure of a linear system from the Drake system Will throw an error if the system is not truly linear. More...

function makeTrigPolySystem (obj, options)

function systemGradTest (obj, t, x, u, options)
Compare numerical and analytical derivatives of dynamics,update,and output. More...

function extractAffineSystem (obj)

function extractTrigPolySystem (sys, options)
tries to convert the current system into a trig-poly system More...

function taylorApprox (sys, varargin)
performs a taylorApproximation around a point or trajectory usage: taylorApprox(sys,t0,x0,u0,order[,ignores]) or taylorApprox(sys,x0traj,u0traj,order[,ignores]) it returns a polynomial system (or polynomial trajectory system) More...

function transverseLQR (obj, xtraj, utraj, Q, R, Qf, transSurf)
Compute LQR control for transversal system. More...

function transverseLQRClosedLoop (obj, xtraj, utraj, Q, R, Vf, transSurf)

function tvlqr (obj, xtraj, utraj, Q, R, Qf, options)
implements the time-varying linear (or affine) quadratic regulator More...

Public Member Functions inherited from DynamicalSystem
function DynamicalSystem ()

function inInputFrame (sys, frame)
Ensures that sys has the specified input frame, by searching for and cascading a coordinate transformation to the existing input if necessary. More...

function inStateFrame (sys, frame)
Ensures that sys has the specified state frame. More...

function inOutputFrame (sys, frame)
Ensures that sys has the specified output frame, by searching for and cascading a coordinate transformation to the existing output if necessary. More...

Creates a new system with the output of system 1 connected to the input of system 2. More...

function feedback (sys1, sys2)
Creates a new systems with sys1 and sys2 in a feedback interconnect (with sys1 on the forward path, and sys2 on the return path). More...

function parallel (sys1, sys2)
Creates a new system that takes the inputs to both sys1 and sys2 as a single input (which is "demux"ed and passed independently to the two systems), and outputs the "mux"ed output of the two systems. More...

function sampledData (sys, tsin, tsout)
Creates a new system which is a sampled data (e.g. More...

function resolveConstraints (obj, x0, v, constraints)
attempts to find a x which satisfies the constraints, using x0 as the initial guess. More...

adds state constraints and unilateral constriants to the program on the specified indices. More...

function getNumStates (obj)
Returns the total number of states (discrete + continuous) in the system. More...

function getInputSampleTimes (obj)
Returns the sample time of the input See getSampleTime for more details about sample times. More...

function getOutputSampleTimes (obj)
Returns the sample time of the output See getSampleTime for more details about sample times. More...

function isDT (obj)
Returns true if the system has no states, or has states and only one sample time [a b], with a>0. More...

function isCT (obj)
Returns true if the system has only one sample time [a b], with a==0. More...

function isInheritedTime (obj)
Returns true if the system has only one sample time [a b], with b==-1. More...

function isTI (obj)
Returns true if the system is time-invariant. More...

function setTIFlag (obj, bval)
Sets the time invariant flag. More...

function getInputFrame (obj)
Access the CoordinateFrame object that defines the input to this system. More...

function setInputFrame (obj, fr)
Set the CoordinateFrame object that defines the input of this system. More...

function getStateFrame (obj)
Access the CoordinateFrame object that defines the state of this system. More...

function setStateFrame (obj, fr)
Set the CoordinateFrame object that defines the state of this system. More...

function getOutputFrame (obj)
Access the CoordinateFrame object that defines the output to this system. More...

function setOutputFrame (obj, fr)
Set the CoordinateFrame object that defines the output of this system. More...

function getNumStateConstraints (obj)
Returns the scalar number of state constraints (of the form phi(x)=0) More...

function stateConstraints (obj, x)
defines state equality constraints in the form phi(x)=0 More...

function unilateralConstraints (obj, x)
defines state unilateral constraints in the form phi(x)>=0 More...

function getNumUnilateralConstraints (obj)
Returns the scalar number of state constraints (of the form phi(x)>=0) More...

function linearize (obj, t0, x0, u0)
Linearize the system about an operating point (continuous time) More...

function dlinearize (obj, ts, t0, x0, u0)
Linearize the system about an operating point (discrete time) More...

function setParams (obj, p)
This default setParams method attempts to set class properties of the system according to the coordinate names in the parameter frame. More...

function getParams (obj)
This default getParams method attempts to get class properties of the system according to the coordinate names in the parameter frame. More...

function getNumParams (obj)

function setParamFrame (obj, fr)
Set the CoordinateFrame object which describes any system parameters. More...

function getParamFrame (obj)
Returns the CoordinateFrame object which describes any system parameters. More...

function setParamLimits (obj, pmin, pmax)
Set lower and upper bounds on the system parameters. More...

function getParamLimits (obj)
Returns the current lower and upper bounds on the system parameters. More...

function parameterEstimation (obj, data, options)
Estimate parameter values from input-output data. More...

function runLCM (obj, x0, options)
Runs the system as an lcm node. More...

function simulate (obj, tspan, x0, options)
Simulates the dynamical system (using the simulink solvers) More...

function tiHinf (obj, x0, u0, Q, R, Bw, gamma)
Suboptimal state-feedback H-infinity controller for LTI system with bound gamma. More...

function tilqr (obj, x0, u0, Q, R, options)
Computes an LQR controller to stabilize the system around (x0,u0) More...

function tilyap (obj, x0, Q)
Linearizes the system about the state x0 and returns a candidate LyapunovFunction generated by solving the quadratic Lyapunov equation. More...

function tvlyap (obj, xtraj, Q, Qf)
Linearizes the system about the state trajectory xtraj and returns a candidate LyapunovFunction generated by integrating backwards the quadratic differential Lyapunov equation. More...

## Public Attributes

Property breaks

Property pporder

Property K

Property A

Property alpha

Property gamma

Property mex_ptr
higher speed eval in C++ More...

Public Attributes inherited from Trajectory
Property tspan

Public Attributes inherited from DynamicalSystem
Property warning_manager

Protected Member Functions inherited from DynamicalSystem
function stateIndicesForCombination (sys1, sys2)
Helper method to figure out the indices of the discrete and continuous states after sys1 and sys2 have been combined into a single system. More...

function stateVectorToStructure (obj, xv, mdl)
Converts the vector state xv to the structure xs for simulink state. More...

function stateStructureToVector (obj, xs)
Converts the simulink state structure representation back to the vector state. More...

Protected Attributes inherited from Trajectory
Property dim

## Detailed Description

useful for solutions to linear systems driven by pptrajectory inputs in interval j, we have y(t) = K * exp(A*(t-tj)) * alpha(:,j) + sum_i gamma(:,j,i) (t-tj)^i

## Constructor & Destructor Documentation

 function ExpPlusPPTrajectory ( breaks , K , A , alpha , gamma )
Return values
 obj

## Member Function Documentation

 function eval ( obj , t )
virtual
Return values
 y jj

Reimplemented from Trajectory.

 function fasteval ( obj , t )

no error checking. numeric scalar t only.

Return values
 y
 function fnder ( obj , order )
Return values
 dtraj
 function getBreaks ( obj )
virtual
Return values
 t

Reimplemented from Trajectory.

 static function loadobj ( a )
static
Return values
 obj

## Member Data Documentation

 Property A
 Property alpha
 Property breaks
 Property gamma
 Property K
 Property mex_ptr

higher speed eval in C++

 Property pporder

The documentation for this class was generated from the following file:
• /home/ubuntu/workspace/linux-gcc-continuous-matlab-documentation/drake/matlab/systems/trajectories/ExpPlusPPTrajectory.m