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Journal of Applied Mathematics and Stochastic Analysis
Volume 2006 (2006), Article ID 41926, 22 pages
http://dx.doi.org/10.1155/JAMSA/2006/41926

Existence and uniqueness of constrained globally optimal feedback controls in a linear-quadratic framework

Institute of Mathematics, Fudan University, Shanghai 200433, China

Received 14 January 2006; Revised 5 March 2006; Accepted 15 March 2006

Copyright © 2006 Yashan Xu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. B. D. O. Anderson and J. B. Moore, Linear Optimal Control, Prentice-Hall, New Jersey, 1971. View at Zentralblatt MATH · View at MathSciNet
  2. L. D. Berkovitz, Convexity and Optimization in Rn, Pure and Applied Mathematics (New York), John Wiley & Sons, New York, 2002. View at Zentralblatt MATH · View at MathSciNet
  3. P. Brunovský, “Regular synthesis for the linear-quadratic optimal control problem with linear control constraints,” Journal of Differential Equations, vol. 38, no. 3, pp. 344–360, 1980. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  4. J. Casti, “The linear-quadratic control problem: some recent results and outstanding problems,” SIAM Review, vol. 22, no. 4, pp. 459–485, 1980. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  5. L. Cesari, “Existence of solutions and existence of optimal solutions,” in Mathematical Theories of Optimization (Genova, 1981), vol. 979 of Lecture Notes in Math., pp. 88–107, Springer, Berlin, 1983. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  6. G. R. Chen, “Closed-form solutions of a general inequality-constrained LQ optimal control problem,” Applicable Analysis, vol. 41, no. 1–4, pp. 257–279, 1991. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  7. Y. Z. Chen, “Linear quadratic problems for time-varying systems: the cases without constraints and with the control energy constraint,” Control Theory & Applications, vol. 16, no. 4, pp. 474–477, 1999. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  8. Z. Emirsajłow, “Linear-quadratic control problem with terminal state constraints,” Systems Analysis Modelling Simulation, vol. 4, no. 3, pp. 227–240, 1987. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  9. Z. Emirsajłow, “A unified approach to optimal feedback in the infinite-dimensional linear-quadratic control problem with an inequality constraint on the trajectory or terminal state,” IMA Journal of Mathematical Control and Information, vol. 8, no. 2, pp. 179–208, 1991. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  10. H. Jaddu, “Spectral method for constrained linear-quadratic optimal control,” Mathematics and Computers in Simulation, vol. 58, no. 2, pp. 159–169, 2002. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  11. R. Kalman, “When is a linear control law optimal?” Transactions of the ASME Journal of Basic Engineering, vol. 86D, pp. 51–60, 1964. View at Google Scholar
  12. Y. Liu, S. Ito, H. W. J. Lee, and K. L. Teo, “Semi-infinite programming approach to continuously-constrained linear-quadratic optimal control problems,” Journal of Optimization Theory and Applications, vol. 108, no. 3, pp. 617–632, 2001. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  13. D. H. Martin and D. H. Jacobson, “Optimal control laws for a class of constrained linear-quadratic problems,” Automatica, vol. 15, no. 4, pp. 431–440, 1979. View at Publisher · View at Google Scholar
  14. A. Matveev and V. Yakubovich, “Nonconvex problems of global optimization: linear-quadratic control problems with quadratic constraints,” Dynamics and Control, vol. 7, no. 2, pp. 99–134, 1997. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  15. F. W. Sears, An Introduction to Thermodynamic: The Kinetic Theory of ASES, and Statistical Mechanics, Addison-Wesley, Massachusetts, 1956.
  16. G. Stefani and P. Zezza, “Constrained regular LQ-control problems,” SIAM Journal on Control and Optimization, vol. 35, no. 3, pp. 876–900, 1997. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  17. D. D. Thompson and R. A. Volz, “The linear quadratic cost problem with linear state constraints and the nonsymmetric Riccati equation,” SIAM Journal on Control and Optimization, vol. 13, no. 1, pp. 110–145, 1975. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  18. Y. Xu, “A linear quadratic control problem with constrained state feedback matrix,” submitted to Journal of Optimization Theory and Applications.
  19. J. Yong and X. Y. Zhou, Stochastic Controls. Hamiltonian Systems and HJB Equations, vol. 43 of Applications of Mathematics (New York), Springer, New York, 1999. View at Zentralblatt MATH · View at MathSciNet