Drake

Classes  
class  Adder< T > 
An adder for arbitrarily many inputs of equal size. More...  
class  AffineSystem< T > 
A discrete OR continuous affine system (with constant coefficients). More...  
class  ConstantValueSource< T > 
A source block that always outputs a constant value. More...  
class  ConstantVectorSource< T > 
A source block with a constant output port at all times. More...  
class  Demultiplexer< T > 
This system splits a vector valued signal on its input into multiple outputs. More...  
class  FirstOrderLowPassFilter< T > 
An elementwise first order low pass filter system that filters the ith input uᵢ into the ith output zᵢ. More...  
class  Gain< T > 
An elementwise gain block with input u and output y = k * u with k a constant vector. More...  
class  Integrator< T > 
An integrator for a continuous vector input. More...  
class  LinearSystem< T > 
A discrete OR continuous linear system. More...  
class  TimeVaryingLinearSystem< T > 
Base class for a discrete or continuous linear timevarying (LTV) system. More...  
class  MatrixGain< T > 
A system that specializes LinearSystem by setting coefficient matrices A , B , and C to all be zero. More...  
class  Multiplexer< T > 
This system combines multiple vectorvalued inputs into a vectorvalued output. More...  
class  PassThrough< T > 
A pass through system with input u and output y = u . More...  
class  PiecewisePolynomialAffineSystem< T > 
A continuous or discretetime Affine TimeVarying system described by a piecewise polynomial trajectory of system matrices. More...  
class  PiecewisePolynomialLinearSystem< T > 
A continuous or discretetime Linear TimeVarying system described by a piecewise polynomial trajectory of system matrices. More...  
class  RandomSource< Distribution, Generator > 
A source block which generates random numbers at a fixed sampling interval, with a zeroorder hold between samples. More...  
class  Saturation< T > 
An elementwise hard saturation block with inputs signal u , saturation values \( u_{min} \) and/or \( u_{max} \), and output y respectively as in: More...  
class  SignalLogger< T > 
A sink block which logs its input to memory. More...  
class  Sine< T > 
A sine system which outputs y = a * sin(f * t + p) and first and second derivatives w.r.t. More...  
class  TrajectorySource< T > 
A source block that generates the value of a Trajectory for a given time. More...  
class  WrapToSystem< T > 
An elementwise wrapping block that transforms the specified indices of the input signal u into the interval [low, high) . More...  
class  ZeroOrderHold< T > 
A ZeroOrderHold block with input u , which may be vectorvalued (discrete or continuous) or abstract, and discrete output y , where the y is sampled from u with a fixed period. More...  
Typedefs  
typedef internal::RandomSource< std::uniform_real_distribution< double > >  UniformRandomSource 
Generates uniformly distributed random numbers in the interval [0,1]. More...  
typedef internal::RandomSource< std::normal_distribution< double > >  GaussianRandomSource 
Generates normally distributed random numbers with mean zero and unit covariance. More...  
typedef internal::RandomSource< std::exponential_distribution< double > >  ExponentialRandomSource 
Generates exponentially distributed random numbers with mean, standard deviation, and scale parameter (aka 1/λ) set to one. More...  
Functions  
std::unique_ptr< LinearSystem< double > >  Linearize (const System< double > &system, const Context< double > &context, int input_port_index=kUseFirstInputIfItExists, int output_port_index=kUseFirstOutputIfItExists, double equilibrium_check_tolerance=1e6) 
Takes the firstorder Taylor expansion of a System around a nominal operating point (defined by the Context). More...  
std::unique_ptr< AffineSystem< double > >  FirstOrderTaylorApproximation (const System< double > &system, const Context< double > &context, int input_port_index=kUseFirstInputIfItExists, int output_port_index=kUseFirstOutputIfItExists) 
A firstorder Taylor series approximation to a system in the neighborhood of an arbitrary point. More...  
typedef internal::RandomSource<std::exponential_distribution<double> > ExponentialRandomSource 
Generates exponentially distributed random numbers with mean, standard deviation, and scale parameter (aka 1/λ) set to one.
typedef internal::RandomSource<std::normal_distribution<double> > GaussianRandomSource 
Generates normally distributed random numbers with mean zero and unit covariance.
typedef internal::RandomSource<std::uniform_real_distribution<double> > UniformRandomSource 
Generates uniformly distributed random numbers in the interval [0,1].
std::unique_ptr< AffineSystem< double > > FirstOrderTaylorApproximation  (  const System< double > &  system, 
const Context< double > &  context,  
int  input_port_index = kUseFirstInputIfItExists , 

int  output_port_index = kUseFirstOutputIfItExists 

) 
A firstorder Taylor series approximation to a system
in the neighborhood of an arbitrary point.
When Taylorexpanding a system at a nonequilibrium point, it may be represented either of the form:
\[ \dot{x}  \dot{x0} = A (x  x0) + B (u  u0), \]
for continuous time, or
\[ x[n+1]  x0[n+1] = A (x[n]  x0[n]) + B (u[n]  u0[n]), \]
for discrete time. As above, we denote x0, u0 to be the nominal state and input at the provided context
. The system description is affine when the terms \( \dot{x0}  A x0  B u0 \) and \( x0[n+1]  A x0[n]  B u0[n] \) are nonzero.
More precisely, let x be a state and u be an input. This function returns an AffineSystem of the form:
\[ \dot{x} = A x + B u + f0, \]
(CT)
\[ x[n+1] = A x[n] + B u[n] + f0, \]
(DT) where \( f0 = \dot{x0}  A x0  B u0 \) (CT) and \( f0 = x0[n+1]  A x[n]  B u[n] \) (DT).
This method currently supports approximating around at most a single vector input port and at most a single vector output port. For systems with more ports, use input_port_index
and output_port_index
to select the input for the newly constructed system. Any additional input ports will be treated as constants (fixed at the value specified in context
).
system  The system or subsystem to linearize. 
context  Defines the nominal operating point about which the system should be linearized. 
input_port_index  A valid input port index for system or kNoInput or (default) kUseFirstInputIfItExists. 
output_port_index  A valid output port index for system or kNoOutput or (default) kUseFirstOutputIfItExists. 
std::runtime_error  if the system if the system is not (only) continuous or (only) discrete time with a single periodic update. 
Note that x, u and y are in the same coordinate system as the original system
, since the terms involving x0, u0 reside in f0.
std::unique_ptr< LinearSystem< double > > Linearize  (  const System< double > &  system, 
const Context< double > &  context,  
int  input_port_index = kUseFirstInputIfItExists , 

int  output_port_index = kUseFirstOutputIfItExists , 

double  equilibrium_check_tolerance = 1e6 

) 
Takes the firstorder Taylor expansion of a System around a nominal operating point (defined by the Context).
This method currently supports linearizing around at most a single vector input port and at most a single vector output port. For systems with more ports, use input_port_index
and output_port_index
to select the input for the newly constructed system. Any additional input ports will be treated as constants (fixed at the value specified in context
).
system  The system or subsystem to linearize. 
context  Defines the nominal operating point about which the system should be linearized. See note below. 
input_port_index  A valid input port index for system or kNoInput or (default) kUseFirstInputIfItExists. 
output_port_index  A valid output port index for system or kNoOutput or (default) kUseFirstOutputIfItExists. 
equilibrium_check_tolerance  Specifies the tolerance on ensuring that the derivative vector isZero at the nominal operating point. Default: 1e6. 
std::runtime_error  if the system the operating point is not an equilibrium point of the system (within the specified tolerance) 
std::runtime_error  if the system if the system is not (only) continuous or (only) discrete time with a single periodic update. 
Note: All inputs in the Context must be connected, either to the output of some upstream System within a Diagram (e.g., if system is a reference to a subsystem in a Diagram), or to a constant value using, e.g. context>FixInputPort(0,default_input);
Note: The inputs, states, and outputs of the returned system are NOT the same as the original system. Denote x0,u0 as the nominal state and input defined by the Context, and y0 as the value of the output at (x0,u0), then the created systems inputs are (uu0), states are (xx0), and outputs are (yy0).