ScalarInitialValueProblem< T > Class Template Reference

Detailed Description

template<typename T>
class maliput::drake::systems::ScalarInitialValueProblem< T >

A thin wrapper of the InitialValueProblem class to provide a simple interface when solving scalar initial value problems i.e.

when evaluating the x(t; 𝐤) solution function to the given ODE dx/dt = f(t, x; 𝐤), where f : t ⨯ x → ℝ , t ∈ ℝ, x ∈ ℝ, 𝐤 ∈ ℝᵐ, along with an initial condition x(t₀; 𝐤) = x₀. The parameter vector 𝐤 allows for generic IVP definitions, which can later be solved for any instance of said vector.

Note the distinction from general initial value problems where f : t ⨯ 𝐱 → ℝⁿ and 𝐱 ∈ ℝⁿ, addressed by the class being wrapped. While every scalar initial value problem could be written in vector form, this wrapper keeps both problem definition and solution in their scalar form with almost zero overhead, leading to clearer code if applicable. Moreover, this scalar form facilitates single-dimensional quadrature using methods for solving initial value problems.

See InitialValueProblem class documentation for information on caching support and dense output usage for improved efficiency in scalar IVP solving.

For further insight into its use, consider the following examples of scalar IVPs:

• The population growth of an hypothetical bacteria colony is described by dN/dt = r * N. The colony has N₀ subjects at time t₀. In this context, x ≜ N, x₀ ≜ N₀, 𝐤 ≜ [r], dx/dt = f(t, x; 𝐤) = 𝐤₁ * x.
• The charge Q stored in the capacitor of a (potentially equivalent) series RC circuit driven by a time varying voltage source E(t) can be described by dQ/dt = (E(t) - Q / Cs) / Rs, where Rs refers to the resistor's resistance and Cs refers to the capacitor's capacitance. In this context, and assuming an initial stored charge Q₀ at time t₀, x ≜ Q, 𝐤 ≜ [Rs, Cs], x₀ ≜ Q₀, dx/dt = f(t, x; 𝐤) = (E(t) - x / 𝐤₂) / 𝐤₁.

@tparam_nonsymbolic_scalar

#include <src/maliput/drake/systems/analysis/scalar_initial_value_problem.h>

Classes
struct	ScalarOdeContext
	A collection of values i.e. More...

Public Types
using	ScalarOdeFunction = std::function< T(const T &t, const T &x, const VectorX< T > &k)>
	Scalar ODE dx/dt = f(t, x; 𝐤) function type. More...

Public Member Functions
	DRAKE_NO_COPY_NO_MOVE_NO_ASSIGN (ScalarInitialValueProblem)
	ScalarInitialValueProblem (const ScalarOdeFunction &scalar_ode_function, const ScalarOdeContext &default_values)
	Constructs an scalar IVP described by the given scalar_ode_function, using given default_values.t0 and default_values.x0 as initial conditions, and parameterized with default_values.k by default. More...
T	Solve (const T &tf, const ScalarOdeContext &values={}) const
	Solves the IVP for time tf, using the initial time t₀, initial state x₀ and parameter vector 𝐤 present in values, falling back to the ones given on construction if not given. More...
std::unique_ptr< ScalarDenseOutput< T > >	DenseSolve (const T &tf, const ScalarOdeContext &values={}) const
	Solves and yields an approximation of the IVP solution x(t; 𝐤) for the closed time interval between the initial time t₀ and the given final time tf, using initial state x₀ and parameter vector 𝐤 present in values (falling back to the ones given on construction if not given). More...
template<typename Integrator , typename... Args>
Integrator *	reset_integrator (Args &&... args)
	Resets the internal integrator instance by in-place construction of the given integrator type. More...
const IntegratorBase< T > &	get_integrator () const
	Gets a reference to the internal integrator instance. More...
IntegratorBase< T > &	get_mutable_integrator ()
	Gets a mutable reference to the internal integrator instance. More...

Member Typedef Documentation

ScalarOdeFunction

using ScalarOdeFunction = std::function<T(const T& t, const T& x, const VectorX<T>& k)>

Scalar ODE dx/dt = f(t, x; 𝐤) function type.

Parameters

t	The independent variable t ∈ ℝ .
x	The dependent variable x ∈ ℝ .
k	The parameter vector 𝐤 ∈ ℝᵐ.

Returns

The derivative dx/dt ∈ ℝ.

Constructor & Destructor Documentation

ScalarInitialValueProblem()

ScalarInitialValueProblem	(	const ScalarOdeFunction &	scalar_ode_function,
		const ScalarOdeContext &	default_values
	)

Constructs an scalar IVP described by the given scalar_ode_function, using given default_values.t0 and default_values.x0 as initial conditions, and parameterized with default_values.k by default.

Parameters

scalar_ode_function	The ODE function f(t, x; 𝐤) that describes the state evolution over time.
default_values	The values specified by default for this IVP, i.e. default initial time t₀ ∈ ℝ and state x₀ ∈ ℝ, and default parameter vector 𝐤 ∈ ℝᵐ.

Precondition

An initial time default_values.t0 is provided.

An initial state default_values.x0 is provided.

An parameter vector default_values.k is provided.

Exceptions

std::exception

if preconditions are not met.

Member Function Documentation

DenseSolve()

std::unique_ptr<ScalarDenseOutput<T> > DenseSolve	(	const T &	tf,
		const ScalarOdeContext &	values = {}
	)		const

Solves and yields an approximation of the IVP solution x(t; 𝐤) for the closed time interval between the initial time t₀ and the given final time tf, using initial state x₀ and parameter vector 𝐤 present in values (falling back to the ones given on construction if not given).

To this end, the wrapped IntegratorBase instance solves this scalar IVP, advancing time and state from t₀ and x₀ = x(t₀) to tf and x(tf), creating a scalar dense output over that [t₀, tf] interval along the way.

Parameters

tf	The IVP will be solved up to this time. Usually, t₀ < tf as an empty dense output would result if t₀ = tf.
values	IVP initial conditions and parameters.

Returns

A dense approximation to x(t; 𝐤) with x(t₀; 𝐤) = x₀, defined for t₀ ≤ t ≤ tf.

Note

The larger the given tf value is, the larger the approximated interval will be. See documentation of the specific dense output technique in use for reference on performance impact as this interval grows.

Precondition

Given tf must be larger than or equal to the specified initial time t₀ (either given or default).

If given, the dimension of the initial state vector values.x0 must match that of the default initial state vector in the default specified values given on construction.

If given, the dimension of the parameter vector values.k must match that of the parameter vector in the default specified values given on construction.

Exceptions

std::exception

if any of the preconditions is not met.

DRAKE_NO_COPY_NO_MOVE_NO_ASSIGN()

DRAKE_NO_COPY_NO_MOVE_NO_ASSIGN

(

ScalarInitialValueProblem< T >

)

get_integrator()

const IntegratorBase<T>& get_integrator

(

)

const

Gets a reference to the internal integrator instance.

get_mutable_integrator()

IntegratorBase<T>& get_mutable_integrator

(

)

Gets a mutable reference to the internal integrator instance.

reset_integrator()

Integrator* reset_integrator

(

Args &&...

args

)

Resets the internal integrator instance by in-place construction of the given integrator type.

A usage example is shown below.

scalar_ivp.reset_integrator<RungeKutta2Integrator<T>>(max_step);

Parameters

args	The integrator type-specific arguments.

Returns

The new integrator instance.

Template Parameters

Integrator	The integrator type, which must be an IntegratorBase subclass.
Args	The integrator specific argument types.

Warning

This operation invalidates pointers returned by ScalarInitialValueProblem::get_integrator() and ScalarInitialValueProblem::get_mutable_integrator().

Solve()

T Solve	(	const T &	tf,
		const ScalarOdeContext &	values = {}
	)		const

Solves the IVP for time tf, using the initial time t₀, initial state x₀ and parameter vector 𝐤 present in values, falling back to the ones given on construction if not given.

Parameters

tf	The IVP will be solved for this time.
values	IVP initial conditions and parameters.

Returns

The IVP solution x(tf; 𝐤) for x(t₀; 𝐤) = x₀.

Precondition

Given tf must be larger than or equal to the specified initial time t₀ (either given or default).

If given, the dimension of the parameter vector values.k must match that of the parameter vector in the default specified values given on construction.

Exceptions

std::exception

if any of the preconditions is not met.

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

• scalar_initial_value_problem.h