Parametric variational solution of linear-quadratic optimal control problems with control inequality constraints

doi:10.1007/s10483-014-1858-6

Abstract

Abstract: 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.

Key words: linear-quadratic (LQ), inequality constraint, parametric variational principle, linear complementarity, astrodynamics, optimal control

2010 MSC Number:

Hai-jun PENG;Qiang GAO;Hong-wu ZHANG;Zhi-gang WU;Wan-xie ZHONG. Parametric variational solution of linear-quadratic optimal control problems with control inequality constraints. Applied Mathematics and Mechanics (English Edition), 2014, 35(9): 1079-1098.

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