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J. Dyn. Sys., Meas., Control. 2017;139(7):071001-071001-8. doi:10.1115/1.4035459.

This paper examines the shaping of a drug's delivery—in this case, nicotine—to maximize its efficacy. Previous research: (i) furnishes a pharmacokinetic–pharmacodynamic (PKPD) model of this drug's metabolism; (ii) shows that the drug-delivery problem is proper, meaning that its optimal solution is periodic; (iii) shows that the underlying PKPD model is differentially flat; and (iv) exploits differential flatness to solve the problem by optimizing the coefficients of a truncated Fourier expansion of the flat output trajectory. In contrast, the work in this article provides insight into the structure of the theoretical solution to this optimal periodic control (OPC) problem. First, we argue for the existence of a bijection between feasible periodic input and state trajectories of the problem. Second, we exploit Pontryagin's maximum principle to show that the optimal periodic solution has a bang–singular–bang structure. Building on these insights, this article proposes two different numerical methods for solving this OPC problem. One method uses nonlinear programming (NLP) to optimize the states at which the optimal solution transitions between the different solution arcs. The second method approximates the control input trajectory as piecewise constant and optimizes the discrete values of the input sequence. The paper concludes by discussing the computational costs of these two algorithms as well as the importance of the associated insights into the structure of the optimal solution trajectory.

Commentary by Dr. Valentin Fuster
J. Dyn. Sys., Meas., Control. 2017;139(7):071002-071002-8. doi:10.1115/1.4035452.

Precise, robust, and consistent localization is an important subject in many areas of science such as vision-based control, path planning, and simultaneous localization and mapping (SLAM). To estimate the pose of a platform, sensors such as inertial measurement units (IMUs), global positioning system (GPS), and cameras are commonly employed. Each of these sensors has their strengths and weaknesses. Sensor fusion is a known approach that combines the data measured by different sensors to achieve a more accurate or complete pose estimation and to cope with sensor outages. In this paper, a three-dimensional (3D) pose estimation algorithm is presented for a unmanned aerial vehicle (UAV) in an unknown GPS-denied environment. A UAV can be fully localized by three position coordinates and three orientation angles. The proposed algorithm fuses the data from an IMU, a camera, and a two-dimensional (2D) light detection and ranging (LiDAR) using extended Kalman filter (EKF) to achieve accurate localization. Among the employed sensors, LiDAR has not received proper attention in the past; mostly because a two-dimensional (2D) LiDAR can only provide pose estimation in its scanning plane, and thus, it cannot obtain a full pose estimation in a 3D environment. A novel method is introduced in this paper that employs a 2D LiDAR to improve the full 3D pose estimation accuracy acquired from an IMU and a camera, and it is shown that this method can significantly improve the precision of the localization algorithm. The proposed approach is evaluated and justified by simulation and real world experiments.

Commentary by Dr. Valentin Fuster

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