This paper focuses on the design of a quadratically-constrained Linear-QuadraticRegulator for finite-thrust orbital rendezvous. The original Linear-Quadraticoptimal control problem is subject to maximum thrust magnitude andquadratic collision avoidance constraints. Thrust arcs are approximated by impulsivevelocity increments and the Yamanaka-Ankersen transition matrixpropagates the state vector. An explicit closed-loop solution is obtained by performinghigh-order series expansions of the HJB equation on sub-regions ofthe state-space associated with specific sets of active constraints. A rendezvousin an elliptical orbit is considered to demonstrate the application of thismethod.
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