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

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.