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Linear quadratic regulation for linear time-varying systems with multiple input delays
- Source :
-
Automatica . Sep2006, Vol. 42 Issue 9, p1465-1476. 12p. - Publication Year :
- 2006
-
Abstract
- Abstract: This paper studies the classic linear quadratic regulation (LQR) problem for both continuous-time and discrete-time systems with multiple input delays. For discrete-time systems, the LQR problem for systems with single input delay has been studied in existing literature, whereas a solution to the multiple input delay case is not known to our knowledge. For continuous-time systems with multiple input delays, the LQR problem has been tackled via an infinite dimensional system theory approach and a frequency/time domain approach. The objective of the present paper is to give an explicit solution to the LQR problem via a simple and intuitive approach. The main contributions of the paper include a fundamental result of duality between the LQR problem for systems with multiple input delays and a smoothing problem for an associated backward stochastic system. The duality allows us to obtain a solution to the LQR problem via standard projection in linear space. The LQR controller is simply constructed by the solution of one backward Riccati difference (for the discrete-time case) or differential (for the continuous-time case) equation of the same order as the plant (ignoring the delays). [Copyright &y& Elsevier]
Details
- Language :
- English
- ISSN :
- 00051098
- Volume :
- 42
- Issue :
- 9
- Database :
- Academic Search Index
- Journal :
- Automatica
- Publication Type :
- Academic Journal
- Accession number :
- 21666079
- Full Text :
- https://doi.org/10.1016/j.automatica.2006.04.007