| Title:
|
A simple solution to the finite-horizon LQ problem with zero terminal state (English) |
| Author:
|
Ntogramatzidis, Lorenzo |
| Language:
|
English |
| Journal:
|
Kybernetika |
| ISSN:
|
0023-5954 |
| Volume:
|
39 |
| Issue:
|
4 |
| Year:
|
2003 |
| Pages:
|
[483]-492 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
This short paper deals with the classical finite-horizon linear-quadratic regulator problem with the terminal state constrained to be zero, for both continuous and discrete-time systems. Closed-form expressions for the optimal state and costate trajectories of the Hamiltonian system, as well as the corresponding control law, are derived through the solutions of two infinite- horizon LQ problems, thus avoiding the use of the Riccati differential equation. The computation of the optimal value of the performance index, as a function of the initial state, is also presented. (English) |
| Keyword:
|
finite-horizon LQ problems |
| Keyword:
|
Hamiltonian system |
| Keyword:
|
Riccati differential equation |
| Keyword:
|
algebraic Riccati equation |
| Keyword:
|
optimal value of the quadratic cost |
| MSC:
|
49N10 |
| MSC:
|
93C15 |
| idZBL:
|
Zbl 1249.49048 |
| idMR:
|
MR2024527 |
| . |
| Date available:
|
2009-09-24T19:55:50Z |
| Last updated:
|
2015-03-24 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/135547 |
| . |
| Reference:
|
[1] Anderson B. D. O., Moore J. B.: Optimal Control: Linear Quadratic Methods.Prentice Hall, London 1989 Zbl 0751.49013 |
| Reference:
|
[2] Brunovský P., Komorník J.: LQ preview synthesis: optimal control and worst case analysis.IEEE Trans. Automat. Control 26 (1981), 2, 398–402 |
| Reference:
|
[3] Dorea C. E. T., Milani B. E. A.: Design of L-Q regulators for state constrained continuous-time systems.IEEE Trans. Automat. Control 40 (1995), 3, 544–548 Zbl 0827.49023, MR 1319262, 10.1109/9.376078 |
| Reference:
|
[4] Grimble M. J.: S-domain solution for the fixed end-point optimal-control problem.Proc. IEE 124 (1977), 9, 802–808 |
| Reference:
|
[5] Ionescu V., Oară, C., Weiss M.: Generalized Riccati Theory and Robust Control: a Popov Function Approach.Wiley, New York 1999 Zbl 0915.34024, MR 1681732 |
| Reference:
|
[6] Juang J. N., Turner J. D., Chun H. M.: Closed-form solutions for a class of optimal quadratic regulator problems with terminal constraints.Trans. ASME, J. Dynamic Systems, Measurement Control 108 (1986), 1, 44–48 Zbl 0596.49002, 10.1115/1.3143741 |
| Reference:
|
[7] Kojima A., Ishijima S.: LQ preview synthesis: optimal control and worst case analysis.IEEE Trans. Automat. Control 44 (1999), 2, 352–357 Zbl 1056.93643, MR 1668996, 10.1109/9.746265 |
| Reference:
|
[8] Kwakernaak H., Sivan R.: Linear Optimal Control Systems.Wiley, New York 1972 Zbl 0276.93001, MR 0406607 |
| Reference:
|
[9] Lewis F. L., Syrmos V.: Optimal Control.Wiley, New York 1995 |
| Reference:
|
[10] Marro G., Prattichizzo, D., Zattoni E.: A geometric insight into the discrete time cheap and singular LQR problems.IEEE Trans. Automat. Control 47 (2002), 1, 102–107 MR 1879695, 10.1109/9.981727 |
| Reference:
|
[11] Marro G., Prattichizzo, D., Zattoni E.: A nested computational scheme for discrete-time cheap and singular LQ control.SIAM J. Control Optim. 2002 (to appear) |
| Reference:
|
[12] Marro G., Prattichizzo, D., Zattoni E.: Previewed signal ${H}_2$ optimal decoupling by finite impulse response compensators.Kybernetika 38 (2002), 4, 479–492 MR 1937142 |
| . |
