Learning model predictive control with application to quadcopter trajectory tracking
Abstract: In thiswork, we develop a learning model predictive controller (LMPC) for energy-optimaltracking of periodic trajectories for a quadcopter. The main advantage of this controller isthat it is “reference-free”. Moreover, the controller is able to improve its performance overiterations by incorporating learning from the previous iterations. The proposed learningmodel predictive controller aims to learn the “best” energy-optimal trajectory over timeby learning a terminal constraint set and a terminal cost from the history data of previousiterations. We have shown howto recursively construct terminal constraint set and terminalcost as a convex hull and a convex piece-wise linear approximation of state and inputtrajectories of previous iterations, respectively. These steps allow us to formulate theonline planning problem for the controller as a convex optimization program, therebyavoiding the complex combinatorial optimization problems that alternative formulationsin the literature need to solve. The data-driven terminal constraint set and terminal costnot only ensure recursive feasibility and stability of LMPC but also guarantee convergenceto the neighbourhood of the optimal performance at steady state. Our LMPC formulationincludes linear time-varying system dynamics which is also learnt from stored state andinput trajectories of previous iterations.To show the performance of LMPC, a quadcopter trajectory learning problem in thevertical plane is simulated in MATLAB/SIMULINK. This particular trajectory learningproblem involves non-convex state constraints, which makes the resulting optimal controlproblem difficult to solve. A tangent cut method is implemented to approximate the nonconvexconstraints by convex ones, which allows the optimal control problem to be solvedby efficient convex optimization solvers. Simulation results illustrate the effectiveness ofthe proposed control strategy.
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