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Designing controllers to generate various trajectories has been studied foryears, while recently, recovering an optimal controller from trajectoriesreceives increasing attention. In this paper, we reveal that the inherentlinear quadratic regulator (LQR) problem of a moving agent can be reconstructedbased on its trajectory observations only, which enables one to learn theoptimal control law of the agent autonomously. Specifically, the reconstructionof the optimization problem requires estimation of three unknown parametersincluding the target state, weighting matrices in the objective function andthe control horizon. Our algorithm considers two types of objective functionsettings and identifies the weighting matrices with proposed novel inverseoptimal control methods, providing the well-posedness and identifiabilityproof. We obtain the optimal estimate of the control horizon using binarysearch and finally reconstruct the LQR problem with above estimates. Thestrength of learning control law with optimization problem recovery lies inless computation consumption and strong generalization ability. We apply ouralgorithm to the future control input prediction and the discrepancy loss isfurther derived. Numerical simulations and hardware experiments on aself-designed robot platform illustrate the effectiveness of our work.

Observation-based Optimal Control Law Learning with LQR Reconstruction