Riccati Solver

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

Functions
int	ulqr_SolveRiccati (RiccatiSolver *solver)
	Solve the LQR problem using Riccati recursion and a forward simulation of the linear dynamics. More...
int	ulqr_BackwardPass (RiccatiSolver *solver)
	Run the Riccati solver backward pass. More...
int	ulqr_ForwardPass (RiccatiSolver *solver)
	Run the Riccati forward pass to solve for the solution vector. More...
RiccatiSolver *	ulqr_NewRiccatiSolver (int nstates, int ninputs, int nhorizon)
	Initialize a new Riccati solver. More...
int	ulqr_FreeRiccatiSolver (RiccatiSolver **solver)
	Free the memory for a Riccati solver. More...
int	ulqr_PrintRiccatiSummary (RiccatiSolver *solver)
	Prints a summary of the solve. More...
int	ulqr_GetNumVars (RiccatiSolver *solver)
enum ulqr_ReturnCode	ulqr_SetInitialState (RiccatiSolver *solver, double *x0)
	Set the initial state. More...
enum ulqr_ReturnCode	ulqr_SetCost (RiccatiSolver *solver, const double *Q, const double *R, const double *H, const double *q, const double *r, double c, int k_start, int k_end)
enum ulqr_ReturnCode	ulqr_SetDynamics (RiccatiSolver *solver, const double *A, const double *B, const double *f, int k_start, int k_end)
Matrix *	ulqr_GetA (RiccatiSolver *solver, int k)
	Get (n,n) state transition matrix.
Matrix *	ulqr_GetB (RiccatiSolver *solver, int k)
	Get (n,m) control input matrix.
Matrix *	ulqr_Getf (RiccatiSolver *solver, int k)
	Get (n,) affine dynamice term.
Matrix *	ulqr_GetQ (RiccatiSolver *solver, int k)
	Get state cost Hessian.
Matrix *	ulqr_GetR (RiccatiSolver *solver, int k)
	Get control cost Hessian.
Matrix *	ulqr_GetH (RiccatiSolver *solver, int k)
	Get cost Hessian cross-term (m,n)
Matrix *	ulqr_Getq (RiccatiSolver *solver, int k)
	Get affine state cost.
Matrix *	ulqr_Getr (RiccatiSolver *solver, int k)
	Get affine control cost.
double	ulqr_Getc (RiccatiSolver *solver, int k)
	Get cost constant.
Matrix *	ulqr_GetFeedbackGain (RiccatiSolver *solver, int k)
	Get (m,n) feedback gain.
Matrix *	ulqr_GetFeedforwardGain (RiccatiSolver *solver, int k)
	Get (m,) feedforward gain.
Matrix *	ulqr_GetCostToGoHessian (RiccatiSolver *solver, int k)
	Get (n,n) Hessian of the cost-to-go.
Matrix *	ulqr_GetCostToGoGradient (RiccatiSolver *solver, int k)
	Get (n,) Gradient of the cost-to-go.
Matrix *	ulqr_GetQxx (RiccatiSolver *solver, int k)
	Get (n,n) Action-value state Hessian.
Matrix *	ulqr_GetQuu (RiccatiSolver *solver, int k)
	Get (m,m) Action-value control Hessian.
Matrix *	ulqr_GetQux (RiccatiSolver *solver, int k)
	Get (m,n) Action-value Hessian cross-term.
Matrix *	ulqr_GetQx (RiccatiSolver *solver, int k)
	Get (n,) Action-value state gradient.
Matrix *	ulqr_GetQu (RiccatiSolver *solver, int k)
	Get (m,) Action-value conrol gradient.
Matrix *	ulqr_GetState (RiccatiSolver *solver, int k)
	Get (n,) state vector.
Matrix *	ulqr_GetInput (RiccatiSolver *solver, int k)
	Get (m,) input vector.
Matrix *	ulqr_GetDual (RiccatiSolver *solver, int k)
	Get (n,) dual vector.
double	ulqr_CalcCost (RiccatiSolver *solver)

Detailed Description

Function Documentation

ulqr_BackwardPass()

int ulqr_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

ulqr_ForwardPass()

int ulqr_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 ulqr_BackwardPass()

Parameters

solver

An initialized RiccatiSolver

Returns

0 if successful

ulqr_FreeRiccatiSolver()

int ulqr_FreeRiccatiSolver

(

RiccatiSolver **

solver

)

Free the memory for a Riccati solver.

Parameters

solver

Pointer to initialized Riccati solver.

Postcondition

solver will be NULL

Returns

0 if successful

ulqr_NewRiccatiSolver()

RiccatiSolver* ulqr_NewRiccatiSolver	(	int	nstates,
		int	ninputs,
		int	nhorizon
	)

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.

ulqr_PrintRiccatiSummary()

int ulqr_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

ulqr_SolveRiccati() has already been called

Parameters

solver

An initialized solver

Returns

0 if successful

ulqr_SetInitialState()

enum ulqr_ReturnCode ulqr_SetInitialState	(	RiccatiSolver *	solver,
		double *	x0
	)

Set the initial state.

Parameters

solver	Initialized RiccatiSolver
x0	Initial state. Length must be at least solver->nstates

Returns

Info code

ulqr_SolveRiccati()

int ulqr_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