Satisficing Nonlinear Rendezvous Approach Under Control Magnitude and Direction Constraints

A rendezvous problem under thrust magnitude and direction constraints is considered. A constraint-satisficing scheme has been newly proposed by introducing two barrier functions. The constraint-satisficing set smoothly establishes an intersection between the unconstrained satisficing set and the input constraint set as the perturbation parameters of two barrier functions tend toward zero. For a simple nonlinear controller, a controller generated by projecting a constraint-free linearized optimal controller onto the input constraint is proposed and its stability is investigated. Some numerical simulations treating nonlinear relative orbit systems show that various control sets, which guide the orbit to the origin, can be generated, whereas the convergence property of the closed-loop system is analyzed by the proposed parameter design with the assistance of a graphical plot.

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