GNU Octave - Local Sector 7 web page

Chapter 29: Control Theory 277syssigwsigvqrin idxsystem data structureintensities of independent Gaussian noise processes (as above)state, control weighting respectively. Control are isnames or indices of controlled inputs (see sysidx, cellidx)default: last dim(R) inputs are assumed to be controlled inputs, all othersare assumed to be noise inputs.Outputskp1q1eeessystem data structure format lqg optimal controller (Obtain A, B, Cmatrices with sys2ss, sys2tf, or sys2zp as appropriate).Solution of control (state feedback) algebraic Riccati equation.Solution of estimation algebraic Riccati equation.Estimator poles.Controller poles.[k, p, e] = lqr (a, b, q, r, z)construct the linear quadratic regulator for the continuous time systemFunction Filedxdt= Ax + Buto minimize the cost functionalJ =z omitted orJ =z included.∫ ∞The following values are returned:0∫ ∞0x T Qx + u T Rux T Qx + u T Ru + 2x T ZukpeThe state feedback gain, (A − BK) is stable and minimizes the costfunctionalThe stabilizing solution of appropriate algebraic Riccati equation.The vector of the closed loop poles of (A − BK).Reference Anderson and Moore, Optimal control: linear quadratic methods, Prentice-Hall, 1990, pp. 56–58.