Moelja, Agoes A.; Meinsma, Gjerrit \(H_{2}\) control of preview systems. (English) Zbl 1117.93327 Automatica 42, No. 6, 945-952 (2006). Summary: The \(H_{2}\)-optimal controller for systems with preview, in which the knowledge of external input is available in advance for the controller, is derived. The single input case is first considered and solved by transforming the problem into a non-standard LQR problem. Based on the single input result, the multiple inputs case and the multiple preview times case are treated. In every case considered, the controller consists of a static state feedback plus a finite impulse response block. The paper also provides a formula for the optimal \(H_{2}\)-norm that clearly shows how the performance gain owing to the previewed input varies as the preview time increases. Cited in 10 Documents MSC: 93B52 Feedback control 93B17 Transformations 49N05 Linear optimal control problems Keywords:\(H_{2}\)-optimal control; preview systems PDF BibTeX XML Cite \textit{A. A. Moelja} and \textit{G. Meinsma}, Automatica 42, No. 6, 945--952 (2006; Zbl 1117.93327) Full Text: DOI References: [1] Anderson, B.D.O.; Moore, J.B., Optimal filtering, (1979), Prentice-Hall Englewood Cliffs, NJ · Zbl 0758.93070 [2] Anderson, B.D.O.; Moore, J.B., Optimal control linear quadratic methods, (1989), Prentice-Hall Englewood Cliffs, NJ · Zbl 0176.07602 [3] Cohen, A.; Shaked, U., Linear discrete-time \(H_\infty\)-optimal tracking with preview, IEEE transactions on automatic control, 42, 270-276, (1997) · Zbl 0878.93023 [4] Kojima, A. (2004). \(H_2\) performance on preview feedforward action. In Proceedings of the 16th MTNS, Leuven, Belgium. [5] Kojima, A.; Ishijima, S., LQ preview synthesis: optimal control and worst case analysis, IEEE transactions on automatic control, 44, 352-356, (1999) · Zbl 1056.93643 [6] Kojima, A., & Ishijima, S. (2003a). Formulas on preview and delayed \(H_\infty\) control. In Proceedings of the 42nd IEEE CDC (pp. 6532-6538). Maui, Hawaii, USA. [7] Kojima, A.; Ishijima, S., \(H_\infty\) performance of preview control systems, Automatica, 39, 393-701, (2003) · Zbl 1029.93021 [8] Kučera, V., Analysis and design of discrete linear control systems, (1991), Prentice-Hall London [9] Marro, G.; Zattoni, E., \(H_2\)-optimal rejection with preview in the continuous-time domain, Automatica, 41, 815-821, (2005) · Zbl 1093.93008 [10] Mirkin, L., On the \(H_\infty\) fixed-lag smoothing: how to exploit the information preview, Automatica, 39, 1495-1504, (2003) · Zbl 1033.93066 [11] Mirkin, L., & Tadmor, G. (2004). Fixed-lag smoothing as a constrained version of the fixed-interval case. In Proceedings of the 2004 American control conference. [12] Moelja, A.A.; Meinsma, G., \(H_2\)-optimal control of systems with multiple i/o delays: time domain approach, Automatica, 41, 7, 1229-1238, (2005) · Zbl 1085.93009 [13] Mosca, E., Optimal, predictive, and adaptive control, (1995), Prentice-Hall Englewood Cliffs, NJ [14] Mosca, E.; Casavola, A., Deterministic LQ preview tracking design, IEEE transactions on automatic control, 40, 1278-1281, (1995) · Zbl 0825.93199 [15] Mosca, E.; Casavola, A.; Giarre, L., Minimax LQ stochastic tracking and servo problems, IEEE transactions on automatic control, 35, 95-97, (1990) · Zbl 0709.93081 [16] Mosca, E.; Zappa, G., Matrix fraction solution to the discrete-time LQ stochastic tracking and servo problems, IEEE transactions automatic control, 34, 240-242, (1989) · Zbl 0676.93066 [17] Samson, C., An adaptive LQ controller for non-minimum-phase systems, International journal of control, 35, 1-28, (1982) · Zbl 0473.93050 [18] Shaked, U.; de Souza, C.E., Continuous-time tracking problems in an \(H_\infty\) setting: A game theory approach, IEEE transactions on automatic control, 40, 841-852, (1995) · Zbl 0834.93019 [19] Tadmor, G., Robust control in the gap: A state-space solution in the presence of a single input delay, IEEE transactions on automatic control, 42, 1330-1335, (1997) · Zbl 0889.93009 [20] Tadmor, G.; Mirkin, L., \(H^\infty\) control and estimation with preview—part I: matrix ARE solutions in continuous time, IEEE transactions on automatic control, 50, 19-28, (2005) · Zbl 1365.93149 [21] Tadmor, G.; Mirkin, L., \(H^\infty\) control and estimation with preview—part II: fixed-size ARE solutions in discrete time, IEEE transactions on automatic control, 50, 29-40, (2005) · Zbl 1365.93150 [22] Theodor, Y.; Shaked, U., Game theory approach to \(H_\infty\)-optimal discrete-time fixed point and fixed-lag smoothing, IEEE transactions on automatic control, 39, 1944-1948, (1994) · Zbl 0818.93074 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.