Using the Riccati Solver

This page provides some details on how to use the rsLQR solver to solve an LQR problem.

Part I: Defining the problem

First, create a new LQRProblem with ndlqr_NewLQRProblem

LQRProblem* lqrprob = ndlqr_NewLQRProblem(nstates, ninputs, nhorizon);

Next, fill in the LQRProblem data. You can choose to define an array of LQRData structs and use ndlqr_InitializeLQRProblem(), or loop over time steps and do it yourself

lqrprob->nhorizon = nhorizon;
for (int i = 0; i < nstates; ++i) {
    lqrprob->x0[i] = x0[i];  // assumes x0 is defined somewhere
}
for (int k = 0; i < nhorizon; ++k) {
    // Assumes all of the following data is defined
    LQRData* data = lqrprob->lqrdata[k];
    ndlqr_InitializeLQRData(data, Q, R, q, r, c, A, B, d);
}

Part II: Setting up the solver

Initialize a new solver:

RiccatiSolver* solver = rdlqr_NewRiccatiSolver(lqrprob);

Part III: Solving

Call the ndlqr_SolveRiccati() method to solve the system using Riccati recursion:

ndlqr_SolveRiccati(solver);

Part IV: Getting the solution and post-processing

A summary of the solve can be printed using:

ndlqr_PrintRiccatiSummary(solver);

Like the rsLQR solver, the solution can vector can be obtained either one of two ways:

int nvars = ndlqr_GetNumVarsRiccati(solver);  // can also use solver->nvars
double* soln = (double*) malloc(nvars * sizeof(double));
ndlqr_CopyRiccatiSolution(solver, soln);

or

Matrix soln = ndlqr_GetRiccatiSolution(solver);

Note that the second method return a Matrix whose data is still owned by the solver (avoids a memory allocation or copy). Do not free this memory and be aware that editing it will edit the data stored in the solver.

Part V: Freeing the solver

Don't forget to free the solver!

ndlqr_FreeRiccatiSolver(solver);