Riccati Solver

Data Structures
struct	RiccatiSolver
	Solver that uses Riccati recursion to solve an LQR problem. More...

Functions
int	ndlqr_SolveRiccati (RiccatiSolver *solver)
	Solve the LQR problem using Riccati recursion and a forward simulation of the linear dynamics. More...
int	ndlqr_BackwardPass (RiccatiSolver *solver)
	Run the Riccati solver backward pass. More...
int	ndlqr_ForwardPass (RiccatiSolver *solver)
	Run the Riccati forward pass to solve for the solution vector. More...
RiccatiSolver *	ndlqr_NewRiccatiSolver (LQRProblem *lqrprob)
	Initialize a new Riccati solver. More...
int	ndlqr_FreeRiccatiSolver (RiccatiSolver *solver)
	Free the memory for a Riccati solver. More...
int	ndlqr_PrintRiccatiSummary (RiccatiSolver *solver)
	Prints a summary of the solve. More...
Matrix	ndlqr_GetRiccatiSolution (RiccatiSolver *solver)
	Get the solution vector. More...
int	ndlqr_GetNumVarsRiccati (RiccatiSolver *solver)
int	ndlqr_CopyRiccatiSolution (RiccatiSolver *solver, double *soln)
	Copies the solution to a user-supplied array. More...
int	ndlqr_GetRiccatiSolveTimes (RiccatiSolver *solver, double *t_solve, double *t_bp, double *t_fp)
	Get the Riccati solve times. More...

Detailed Description

Function Documentation

ndlqr_BackwardPass()

int ndlqr_BackwardPass

(

RiccatiSolver *

solver

)

Run the Riccati solver backward pass.

Uses backward Riccati recursion to solve for the feedback and feedforward LQR gains along the trajectory. Also computes the quadratic cost-to-go and the expansions of the action-value function. All the data is stored in the solver.

Parameters

solver

An initialized RiccatiSolver

Returns

0 if successful

ndlqr_CopyRiccatiSolution()

int ndlqr_CopyRiccatiSolution	(	RiccatiSolver *	solver,
		double *	soln
	)

Copies the solution to a user-supplied array.

See ndlqr_CopyRiccatiSolution() for variable ordering

Precondition

ndlqr_SolveRiccati() has already been called

Parameters

solver	An initialized RiccatiSolver that has been solved but not freed
soln	Destination for solution vector. Must have length at least equal to solver.nvars.

Returns

0 if successful

ndlqr_ForwardPass()

int ndlqr_ForwardPass

(

RiccatiSolver *

solver

)

Run the Riccati forward pass to solve for the solution vector.

Computes the solution vector by simulating the linear dynamics forward using the the feedback law \( u = -K x + d \).

Precondition

The LQR gains must have been computed using ndlqr_BackwardPass()

Parameters

solver

An initialized RiccatiSolver

Returns

0 if successful

ndlqr_FreeRiccatiSolver()

int ndlqr_FreeRiccatiSolver

(

RiccatiSolver *

solver

)

Free the memory for a Riccati solver.

Parameters

solver

Initialized Riccati solver.

Returns

0 if successful

Postcondition

solver will be NULL

ndlqr_GetRiccatiSolution()

Matrix ndlqr_GetRiccatiSolution

(

RiccatiSolver *

solver

)

Get the solution vector.

Returns the solution vector as a Matrix object, which is a simple wrapper around a raw pointer which points to the data actually stored by the solver. The user must not free the data, as it is owned by the solver. To get a solution vector owned by the caller, use ndlqr_CopySolution() instead.

Variable ordering

The variabled are ordered as follows:

\[ \begin{bmatrix} \lambda_1^T & x_1^T & u_1^T & \lambda_2^T & \dots & x_{N-1}^T & u_{N-1}^T & \lambda_N^T & x_N^T \end{bmatrix}^T \]

Precondition

ndlqr_SolveRiccati() has already been called

Parameters

solver

Returns

ndlqr_GetRiccatiSolveTimes()

int ndlqr_GetRiccatiSolveTimes	(	RiccatiSolver *	solver,
		double *	t_solve,
		double *	t_bp,
		double *	t_fp
	)

Get the Riccati solve times.

Writes the solve times to the given pointers.

Precondition

ndlqr_SolveRiccati() has already been called

Parameters

	solver	An initialized RiccatiSolver
[out]	t_solve	Total solve time, in milliseconds
[out]	t_bp	Backward pass time, in milliseconds
[out]	t_fp	Forward pass time, in milliseconds

Returns

0 if successful

ndlqr_NewRiccatiSolver()

RiccatiSolver* ndlqr_NewRiccatiSolver

(

LQRProblem *

lqrprob

)

Initialize a new Riccati solver.

Create a new Riccati solver, provided the problem data given by lqrprob.

Parameters

lqrprob

Contains all the data to describe the LQR problem to be solved.

Returns

An initialized Riccati solver.

ndlqr_PrintRiccatiSummary()

int ndlqr_PrintRiccatiSummary

(

RiccatiSolver *

solver

)

Prints a summary of the solve.

Sample output

NDLQR Riccati Solve Summary
Solve time:    1.24 ms
Backward Pass: 1.13 ms (91.1 % of total)
Foward Pass:   0.11 ms (8.9 % of total)
Final error: 5.05696e-12
Final error after 2nd solve: 5.05696e-12

Precondition

ndlqr_SolveRiccati() has already been called

Parameters

solver

An initialized solver

Returns

0 if successful

ndlqr_SolveRiccati()

int ndlqr_SolveRiccati

(

RiccatiSolver *

solver

)

Solve the LQR problem using Riccati recursion and a forward simulation of the linear dynamics.

Parameters

solver

An initialized RiccatiSolver

Returns

0 if successful