Joint University Program for Air Transportation Research, 1989-1990

Research conducted during the academic year 1989-90 under the NASA/FAA sponsored Joint University Program for Air Transportation research is discussed. Completed works, status reports and annotated bibliographies are presented for research topics, which include navigation, guidance and control theory and practice, aircraft performance, human factors, and expert systems concepts applied to airport operations. An overview of the year's activities for each university is also presented

Adaptive deep learning for high-dimensional hamilton-jacobi-bellman equations

The article of record as published may be found at http://dx.doi.org/10.1137/19M1288802Computing optimal feedback controls for nonlinear systems generally requires solving Hamilton--Jacobi--Bellman (HJB) equations, which are notoriously difficult when the state dimension is large. Existing strategies for high-dimensional problems often rely on specific, restrictive problem structures or are valid only locally around some nominal trajectory. In this paper, we propose a data-driven method to approximate semiglobal solutions to HJB equations for general high-dimensional nonlinear systems and compute candidate optimal feedback controls in real-time. To accomplish this, we model solutions to HJB equations with neural networks (NNs) trained on data generated without discretizing the state space. Training is made more effective and data-efficient by leveraging the known physics of the problem and using the partially trained NN to aid in adaptive data generation. We demonstrate the effectiveness of our method by learning solutions to HJB equations corresponding to the attitude control of a six-dimensional nonlinear rigid body and nonlinear systems of dimension up to 30 arising from the stabilization of a Burgers'-type partial differential equation. The trained NNs are then used for real-time feedback control of these systems.Defense Advanced Research Projects Agency (DARPA)The work of the first and second authors was partially supported with funding from the Defense Advanced Research Projects Agency (DARPA) grant FA8650-18-1-7842

Adaptive Deep Learning for High-Dimensional Hamilton-Jacobi-Bellman Equations

Computing optimal feedback controls for nonlinear systems generally requires solving Hamilton-Jacobi-Bellman (HJB) equations, which are notoriously difficult when the state dimension is large. Existing strategies for high-dimensional problems often rely on specific, restrictive problem structures, or are valid only locally around some nominal trajectory. In this paper, we propose a data-driven method to approximate semi-global solutions to HJB equations for general high-dimensional nonlinear systems and compute candidate optimal feedback controls in real-time. To accomplish this, we model solutions to HJB equations with neural networks (NNs) trained on data generated without discretizing the state space. Training is made more effective and data-efficient by leveraging the known physics of the problem and using the partially-trained NN to aid in adaptive data generation. We demonstrate the effectiveness of our method by learning solutions to HJB equations corresponding to the attitude control of a six-dimensional nonlinear rigid body, and nonlinear systems of dimension up to 30 arising from the stabilization of a Burgers'-type partial differential equation. The trained NNs are then used for real-time feedback control of these systems.Comment: Added section on validation error computation. Updated convergence test formula and associated result

Indirect neural-enhanced integral sliding mode control for finite-time fault-tolerant attitude tracking of spacecraft

In this article, a neural integral sliding mode control strategy is presented for the finite-time fault-tolerant attitude tracking of rigid spacecraft subject to unknown inertia and disturbances. First, an integral sliding mode controller was developed by originally constructing a novel integral sliding mode surface to avoid the singularity problem. Then, the neural network (NN) was embedded into the integral sliding mode controller to compensate the lumped uncertainty and replace the robust switching term. In this way, the chattering phenomenon was significantly suppressed. Particularly, the mechanism of indirect neural approximation was introduced through inequality relaxation. Benefiting from this design, only a single learning parameter was required to be adjusted online, and the computation burden of the proposed controller was extremely reduced. The stability argument showed that the proposed controller could guarantee that the attitude and angular velocity tracking errors were regulated to the minor residual sets around zero in a finite time. It was noteworthy that the proposed controller was not only strongly robust against unknown inertia and disturbances, but also highly insensitive to actuator faults. Finally, the effectiveness and advantages of the proposed control strategy were validated using simulations and comparisons

Review of dynamic positioning control in maritime microgrid systems

For many offshore activities, including offshore oil and gas exploration and offshore wind farm construction, it is essential to keep the position and heading of the vessel stable. The dynamic positioning system is a progressive technology, which is extensively used in shipping and other maritime structures. To maintain the vessels or platforms from displacement, its thrusters are used automatically to control and stabilize the position and heading of vessels in sea state disturbances. The theory of dynamic positioning has been studied and developed in terms of control techniques to achieve greater accuracy and reduce ship movement caused by environmental disturbance for more than 30 years. This paper reviews the control strategies and architecture of the DPS in marine vessels. In addition, it suggests possible control principles and makes a comparison between the advantages and disadvantages of existing literature. Some details for future research on DP control challenges are discussed in this paper