Cost Function Interface

All cost functions are required to define the following methods

n = state_dim(cost)
m = control_dim(cost)
J = stage_cost(cost, x, u)
J = stage_cost(cost, xN)
gradient!(E::QuadraticCostFunction, cost, x, u)
gradient!(E::QuadraticCostFunction, cost, xN)
hessian!(E::QuadraticCostFunction, cost, x, u)
hessian!(E::QuadraticCostFunction, cost, xN)

and inherit from CostFunction. Note the it is good practice to use the method defined on the terminal state internal to the method defined for both the state and control, i.e. gradient!(E, cost, x, u) should call gradient!(E, cost, xN). They then inherit the following methods defined on knot points:

stage_cost(::CostFunction, ::KnotPoint)
gradient!(::QuadraticCostFunction, ::CostFunction, ::AbstractKnotPoint)
hessian!(::QuadraticCostFunction, ::CostFunction, ::AbstractKnotPoint)

Objective Interface

The objective interface is very simple. After inheriting from AbstractObjective, define the following methods:

Base.length(::NewObjective)       # number of knot points
get_J(::NewObjective)             # return vector of costs at each knot point
cost!(::NewObjective, Z::Traj)    # calculate the cost at each knot point and store in get_J(::NewSolver)
cost_expansion!(E::CostExpansion, obj::NewObjective, Z::Traj)

And inherits the single method

cost(::NewObjective, Z::Traj)

that simply returns the summed cost.