TY - JOUR
T1 - Delay sensitivity of quadratic controllers
T2 - A singular perturbation approach
AU - Ndiaye, Papa Momar
AU - Sorine, Michel
PY - 2000/6
Y1 - 2000/6
N2 - We study the variations of the quadratic performance associated to a linear differential system of retarded type for small values of the delays. From an interpretation of delays as singular perturbations of abstract evolution operators, we revisit the usual theory of representation and optimal control of retarded systems. This leads to a new parameterization of associated Riccati operators for which insight is gained in the dependence on the delays. This explicit parameterization of Riccati operators by the delays enables us to prove differentiability at zero for performance viewed as a function of the delays, in the LQ-optimal or H∞ suboptimal control. In each case, the gradient is explicitly computed in terms of the nonnegative solution of the finite dimensional Riccati equation associated to the nondelay control problem. A thorough treatment is stated for the linear quadratic optimal case, and the H∞ suboptimal control is presented as an application.
AB - We study the variations of the quadratic performance associated to a linear differential system of retarded type for small values of the delays. From an interpretation of delays as singular perturbations of abstract evolution operators, we revisit the usual theory of representation and optimal control of retarded systems. This leads to a new parameterization of associated Riccati operators for which insight is gained in the dependence on the delays. This explicit parameterization of Riccati operators by the delays enables us to prove differentiability at zero for performance viewed as a function of the delays, in the LQ-optimal or H∞ suboptimal control. In each case, the gradient is explicitly computed in terms of the nonnegative solution of the finite dimensional Riccati equation associated to the nondelay control problem. A thorough treatment is stated for the linear quadratic optimal case, and the H∞ suboptimal control is presented as an application.
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U2 - 10.1137/S0363012997329858
DO - 10.1137/S0363012997329858
M3 - Article
AN - SCOPUS:0034539376
SN - 0363-0129
VL - 38
SP - 1655
EP - 1682
JO - SIAM Journal on Control and Optimization
JF - SIAM Journal on Control and Optimization
IS - 6
ER -