Parametric variational solution of linear-quadratic optimal control problems with control inequality constraints.
- Resource Type
- Article
- Authors
- Peng, Hai-jun; Gao, Qiang; Zhang, Hong-wu; Wu, Zhi-gang; Zhong, Wan-xie
- Source
- Applied Mathematics & Mechanics. Sep2014, Vol. 35 Issue 9, p1079-1098. 20p.
- Subject
- *LINEAR systems
*OPTIMAL control theory
*NUMERICAL analysis
*HAMILTON'S equations
*PROBLEM solving
- Language
- ISSN
- 0253-4827
A parametric variational principle and the corresponding numerical algorithm are proposed to solve a linear-quadratic (LQ) optimal control problem with control inequality constraints. Based on the parametric variational principle, this control problem is transformed into a set of Hamiltonian canonical equations coupled with the linear complementarity equations, which are solved by a linear complementarity solver in the discrete-time domain. The costate variable information is also evaluated by the proposed method. The parametric variational algorithm proposed in this paper is suitable for both time-invariant and time-varying systems. Two numerical examples are used to test the validity of the proposed method. The proposed algorithm is used to astrodynamics to solve a practical optimal control problem for rendezvousing spacecrafts with a finite low thrust. The numerical simulations show that the parametric variational algorithm is effective for LQ optimal control problems with control inequality constraints. [ABSTRACT FROM AUTHOR]