A number of problems in control can be reduced to finding suitable real solutions of algebraic equations. In particular, such a problem arises in the context of switching surfaces in optimal control. Recently, a powerful new methodology for doing symbolic manipulations with polynomial data has been developed and tested, namely the use of Gröbner bases. In this paper, we apply the Gröbner basis technique to find effective solutions to the classical problem of time-optimal control.
Bibliographical noteFunding Information:
Manuscript received March 17, 1999; revised June 6, 2000. Recommended by Associate Editor P. Voulgaris. The work of U. Walther was supported by the A.P. Sloan Foundation. The work of T. T. Georgiou and A. Tan-nenbaum was supported by Grants from the National Science Foundation ECS-99700588, ECS-9505995, NSF-LIS, Air Force Office of Scientific Research AF/F49620-98-1-0168, AF/F49620-96-1-0094 by the Army Research Office DAAG55-98-1-0169, and MURI Grant.
- Computation algebraic geometry
- Gröbner bases
- Optimal control
- Switching surfaces