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finite-horizon LQ problems; Hamiltonian system; Riccati differential equation; algebraic Riccati equation; optimal value of the quadratic cost
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.
[1] Anderson B. D. O., Moore J. B.: Optimal Control: Linear Quadratic Methods. Prentice Hall, London 1989 Zbl 0751.49013
[2] Brunovský P., Komorník J.: LQ preview synthesis: optimal control and worst case analysis. IEEE Trans. Automat. Control 26 (1981), 2, 398–402
[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 DOI 10.1109/9.376078 | MR 1319262 | Zbl 0827.49023
[4] Grimble M. J.: S-domain solution for the fixed end-point optimal-control problem. Proc. IEE 124 (1977), 9, 802–808
[5] Ionescu V., Oară, C., Weiss M.: Generalized Riccati Theory and Robust Control: a Popov Function Approach. Wiley, New York 1999 MR 1681732 | Zbl 0915.34024
[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 DOI 10.1115/1.3143741 | Zbl 0596.49002
[7] Kojima A., Ishijima S.: LQ preview synthesis: optimal control and worst case analysis. IEEE Trans. Automat. Control 44 (1999), 2, 352–357 DOI 10.1109/9.746265 | MR 1668996 | Zbl 1056.93643
[8] Kwakernaak H., Sivan R.: Linear Optimal Control Systems. Wiley, New York 1972 MR 0406607 | Zbl 0276.93001
[9] Lewis F. L., Syrmos V.: Optimal Control. Wiley, New York 1995
[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 DOI 10.1109/9.981727 | MR 1879695
[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)
[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
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