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AffineSystem Class Reference

Implements xcdot = Ac*x + Bc*u + xcdot0 xdn = Ad*x + Bd*u + xdn0 y = C*x + D*u + y0. More...

Inheritance diagram for AffineSystem:
Collaboration diagram for AffineSystem:

Public Member Functions

function AffineSystem (Ac, Bc, xcdot0, Ad, Bd, xdn0, C, D, y0)
 
function dynamicsRHS (obj, t, x, u)
 
function update (obj, t, x, u)
 
function output (obj, t, x, u)
 
function feedback (sys1, sys2)
 try to keep feedback between affine systems affine. More...
 
function cascade (sys1, sys2)
 try to keep cascade between affine systems affine. More...
 
function parallel (sys1, sys2)
 try to keep parallel combinations between affine systems affine. More...
 
function extractLinearSystem (obj)
 
function dirtranModelPredictiveControl (obj, N)
 sets up a Quadratic Program with the dynamics constraints x[n+1] = Ad*x[n] + Bd*u[n] + xdn0; More...
 
- Public Member Functions inherited from PolynomialSystem
function PolynomialSystem (num_xc, num_xd, num_u, num_y, direct_feedthrough_flag, time_invariant_flag, rational_flag)
 initialize PolynomialSystem More...
 
function dynamics (obj, t, x, u)
 
function dynamicsLHS (obj, t, x, u)
 
function dynamicsRHS (obj, t, x, u)
 
function setRationalFlag (obj, tf)
 
function isRational (obj)
 
function getPolyDynamics (obj, t)
 
function getPolyUpdate (obj, t)
 
function getPolyOutput (obj, t)
 
function getPolyStateConstraints (obj)
 
function setNumZeroCrossings (obj, num_zcs)
 
function timeReverse (obj)
 
function setInputFrame (obj, frame)
 
function setStateFrame (obj, frame)
 
function inStateFrame (sys, frame)
 
function feedback (sys1, sys2)
 try to keep feedback between polynomial systems polynomial. More...
 
function cascade (sys1, sys2)
 try to keep cascade between polynomial systems polynomial. More...
 
function extractAffineSystem (obj)
 
function plotVdot (sys, Vtraj, ts, options)
 
function regionOfAttraction (sys, varargin)
 Estimates the region of attraction. More...
 
function sampledFiniteTimeReachability (poly, ts, xtraj, gTmss, R, options)
 Implements Henrion and Korda's SOS relaxation for computing finite time funnels. More...
 
function sampledFiniteTimeReachabilityFunnel (sys, polyOrig, Vtraj0, G, R0, tv, ts, xtraj0, utraj, options, Phi, rho)
 % Implements time-varying reachability computation. More...
 
function sampledFiniteTimeVerification (sys, ts, G, varargin)
 Attempts to find the largest funnel, defined by the time-varying one-level set of V, which verifies (using SOS over state at finite sample points in time) initial conditions to end inside the one-level set of the goal region G at time ts(end). More...
 
function sampledTransverseVerification (sys, G, Vtraj0, ts, xtraj, utraj, transSurf, options)
 Attempts to find the largest funnel around xtraj using transverse surfaces. More...
 
- 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 getInitialState (obj)
 Return a (potentially random) state double (column) vector of initial conditions. 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 addStateConstraint (obj, con, xind)
 
function updateStateConstraint (obj, id, con, xind)
 
function displayStateConstraints (obj)
 
function removeAllStateConstraints (obj)
 
function addStateConstraintsToProgram (obj, prog, indices)
 adds state constraints and unilateral constraints to the program on the specified indices. More...
 
function addInputConstraintsToProgram (obj, prog, indices)
 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...
 
function cascade (sys1, sys2)
 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)
 deprecated method (due to refactoring): please use extractTrigPolySystem instead More...
 
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...
 
function cascade (sys1, sys2)
 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...
 
function addStateConstraintsToProgram (obj, prog, indices)
 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 setSimulinkParam (obj, varargin)
 Sets parameters of the simulink model Syntax setSimulinkParam(obj,param_name,param_value[,param_name,param_value,]) % Se. 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 Ac
 
Property Bc
 
Property xcdot0
 
Property Ad
 
Property Bd
 
Property xdn0
 
Property C
 
Property D
 
Property y0
 
- Public Attributes inherited from DynamicalSystem
Property warning_manager
 

Additional Inherited Members

- 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...
 

Detailed Description

Implements xcdot = Ac*x + Bc*u + xcdot0 xdn = Ad*x + Bd*u + xdn0 y = C*x + D*u + y0.

Constructor & Destructor Documentation

function AffineSystem ( Ac  ,
Bc  ,
xcdot0  ,
Ad  ,
Bd  ,
xdn0  ,
C  ,
D  ,
y0   
)
Return values
obj

Member Function Documentation

function cascade ( sys1  ,
sys2   
)

try to keep cascade between affine systems affine.

else, kick out to DrakeSystem

Return values
sys
function dirtranModelPredictiveControl ( obj  ,
 
)

sets up a Quadratic Program with the dynamics constraints x[n+1] = Ad*x[n] + Bd*u[n] + xdn0;

Return values
prog
x_inds
u_inds
function dynamicsRHS ( obj  ,
,
,
 
)
Return values
xcdot
df
function extractLinearSystem ( obj  )
Return values
sys
function feedback ( sys1  ,
sys2   
)

try to keep feedback between affine systems affine.

else, kick out to DrakeSystem

Return values
sys
function output ( obj  ,
,
,
 
)
virtual
Return values
y
dy

Reimplemented from DrakeSystem.

Reimplemented in ScopeSystem.

function parallel ( sys1  ,
sys2   
)

try to keep parallel combinations between affine systems affine.

else, kick out to DrakeSystem

Return values
sys
function update ( obj  ,
,
,
 
)
virtual
Return values
xdn
df

Reimplemented from DrakeSystem.

Member Data Documentation

Property Ac
Property Ad
Property Bc
Property Bd
Property C
Property D
Property xcdot0
Property xdn0
Property y0

The documentation for this class was generated from the following file: