REACHING A TARGET WITHIN A GPS-DENIED OR COSTLY AREA: A TWO-STAGE OPTIMAL CONTROL APPROACH
Martins, Nuno C
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In this thesis, a new class of problem is studied where a mobile agent is controlled to reach a target. Especially, the target is enclosed within a special area. The presence of this area requires a controller to have two stages: the outer stage steers the mobile agent to enter such area while the inner stage steers the mobile agent towards the target. We consider two types of the special area: a time-costly area and a GPS-denied area. For the time-costly area, we formulate a two-stage optimal control problem where time is explicitly specified in the cost function. We solve the problem by solving its subproblems. The key subproblem is a nonconvex quadratic programming with two quadratic constraints (QC2QP). We study the QC2QP independently and prove the necessary and sufficient conditions for strong duality in a general QC2QP. Such conditions enable efficient solution methods for a QC2QP utilizing its dual and semidefinite relaxation. For the GPS-denied area, we formulate another two-stage optimal control problem where perturbation is considered. To deal with the perturbation, we propose a robust controller using the variable horizon model predictive control. The performance of the two-stage controller for each type of the special area is demonstrated in simulations. We construct and implement a two-stage controller that can steer a quadrotor to reach a target enclosed within a denied area. Such controller utilizes the formulation and solution methods in the theoretical study. We show experimental results where the controller can run in real-time using off-the-shelf fast optimization solvers. We also conduct a bat experiment to learn bat's strategy for target reaching inside a denied area.