RiccatiSolver Struct Reference

Solver that uses Riccati recursion to solve an LQR problem. More...

#include <riccati_solver.h>

Data Fields
LQRProblem *	prob
	Problem data.
int	nhorizon
	length of the time horizon
int	nstates
	size of state vector (n)
int	ninputs
	number of control inputs (m)
int	nvars
	total number of decision variables, including the dual variables
double *	data
	pointer to the beginning of the single block of memory allocated by the solver
Matrix *	K
	N-1 feedback gain matrices of size (m,n)
Matrix *	d
	N-1 feedforward gains of size (m,)
Matrix *	P
	N cost-to-go Hessians of size (n,n)
Matrix *	p
	N cost-to-go gradients of size (n,)
Matrix *	X
	State trajectory. N vectors of size (n,)
Matrix *	U
	Control trajectory. N-1 vectors of size (m,)
Matrix *	Y
	Lagrange multipliers. N vectors of size (n,)
Matrix *	Qx
	Gradient of the action-value function with respect to the state. N vectors of size (n,).
Matrix *	Qu
	Gradient of the action-value function with respect to the control. N vectors of size (m,).
Matrix *	Qxx
	Hessian of the action-value function with respect to the state. N vectors of size (n,n).
Matrix *	Qux
	Cross-term Hessian of the action-value function. N vectors of size (m,n).
Matrix *	Quu
	Hessian of the action-value function with respect to the control. N vectors of size (m,m).
double	t_solve_ms
	Total solve time in milliseconds.
double	t_backward_pass_ms
	Time spent in the backward pass in milliseconds.
double	t_forward_pass_ms
	Time spent in the forward pass in milliseconds.

Detailed Description

Solver that uses Riccati recursion to solve an LQR problem.

Solves the generic LQR problem with affine terms using Riccati recursion and a forward simulation of the linear dynamics. Assumes problems are of the following form:

\begin{align*} \underset{x_{1:N}, u_{1:N-1}}{\text{minimize}} &&& \frac{1}{2} x_N^T Q_N + x_N + q_N^T x_N + \sum_{k-1}^{N-1} \frac{1}{2} x_k^T Q_k + x_k + q_k^T x_k + u_k^T R_k + u_k + r_k^T u_k \\ \text{subject to} &&& x_{k+1} = A_k x_k + B_k u_k + f_k \\ &&& x_1 = x_\text{init} \end{align*}

All the memory required by the solver is initialized upon the creation of the solver to avoid any dynamic memory allocations during the solve.

Construction and destruction

Use ndlqr_NewRiccatiSolver() to initialize a new solver, which much be paired with a single call to ndlqr_FreeRiccatiSolver() to free all of solver's memory.

Typical Usage

Standard usage will typically look like the following:

LQRProblem* lqrprob = ndlqr_ReadTestLQRProblem();  // your data here
RiccatiSolver* solver = ndlqr_NewRiccatiSolver(lqrprob);
ndlqr_SolveRiccati(solver);
ndlqr_PrintRiccatiSummary(solver);
double* soln = (double*) malloc(solver->nvars * sizeof(double));
ndlqr_CopyRiccatiSolution(solver, soln);
ndlqr_FreeRiccatiSolver();
ndlqr_FreeLQRProblem();
free(soln);

Methods

• ndlqr_NewRiccatiSolver()
• ndlqr_FreeRiccatiSolver()
• ndlqr_PrintRiccatiSummary()
• ndlqr_GetRiccatiSolution()
• ndlqr_CopyRiccatiSolution()
• ndlqr_GetRiccatiSolveTimes()

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

• src/riccati_solver.h