GNU Octave - Local Sector 7 web page

Chapter 29: Control Theory 273[k, p, e] = dlqr (a, b, q, r, z)Construct the linear quadratic regulator for the discrete time systemFunction Filex k+1 = Ax k + Bu kto minimize the cost functionalJ = ∑ x T Qx + u T Ruz omitted orJ = ∑ x T Qx + u T Ru + 2x T Zuz included.The following values are returned:k The state feedback gain, (A − BK) is stable.p The solution of algebraic Riccati equation.e The closed loop poles of (A − BK).[Lp, Lf, P, Z] = dkalman (A, G, C, Qw, Rv, S)Function FileConstruct the linear quadratic estimator (Kalman predictor) for the discrete timesystemx k+1 = Ax k + Bu k + Gw ky k = Cx k + Du k + v kwhere w, v are zero-mean gaussian noise processes with respective intensities Qw =cov (w, w) and Rv = cov (v, v).If specified, S is cov (w, v). Otherwise cov (w, v) = 0.The observer structure is x k+1|k = Ax k|k−1 + Bu k + L p (y k − Cx k|k−1 − Du k ) x k|k =x k|k + L f (y k − Cx k|k−1 − Du k )The following values are returned:LpLfThe predictor gain, (A − L p C). is stable.The filter gain.P The Riccati solution. P = E{(x − x n|n−1 )(x − x n|n−1 ) ′ }Z The updated error covariance matrix. Z = E{(x − x n|n )(x − x n|n ) ′ }[K, gain, kc, kf, pc, pf ] = h2syn (asys, nu, ny, tol)Function FileDesign H 2 optimal controller per procedure in Doyle, Glover, Khargonekar, Francis,State-Space Solutions to Standard H 2 and H ∞ Control Problems, ieee tac August1989.Discrete-time control per Zhou, Doyle, and Glover, Robust and optimal control,Prentice-Hall, 1996.Inputs