ABSTRACT

This project will devise mathematical methods to control the behavior of dynamical systems that arise in the field of marine robotics and other engineering applications. The methods will entail event-triggered feedback control, whereby the systems use feedback about their states and their surroundings, help decide future optimizing courses of action, and where events like potential violations of constraints are used to determine when to change the controls. The project will seek finite-time control methods, which enable control objectives such as tracking and station keeping to be realized by prescribed finite-time deadlines. Using applied mathematics to control ecological robotic systems will promote scientific progress, by leading to more effective ways to understand the effects of pollutions, oil spills, or other environmental stresses in complex, dynamic, and unstructured marine environments. The work will be collaborative with two Ph.D. students whose research at the interface of engineering and mathematics will help prepare them for a wide variety of potential careers. The investigators will also deliver presentations on elementary aspects of the project to grade school students in Louisiana or New York. This outreach can help inspire a diverse, qualified cadre of students to consider pursuing careers in engineering or mathematics. The project's applied part will focus on algorithmic development and marine robots. Additionally, this research will have the potential for applications in other settings with event-triggered controls, safety or timing constraints, and uncertainties, such as renewable energy networks or intelligent transportation systems.

The project will help address significant challenges in control theory for nonlinear control systems with communication or state constraints or optimization requirements, using three strategies. The first will design event- or self-triggered feedback controls for systems with time deadlines, whose triggers are computed from output measurements, and which determine when to recompute the control to avoid undesirable operating modes, with the goal of ensuring finite time convergence. This will help overcome the obstacles to using standard feedback controls, which require the user to continuously or frequently recompute control values without optimizing cost criteria or meeting time deadlines, and which therefore are less suitable in engineering applications. This will build on the nonlead investigator's prior work in event-triggered nonlinear control theory that developed several constructive design tools for various classes of nonlinear systems. The second will develop robust forward invariance methods under event- or self-triggered controls, which help predict and quantify the degree of uncertainty that control systems can tolerate without violating tolerance and safety bounds. This will build on the lead investigator's prior work that computed bounds on allowable uncertainties in marine robotic curve tracking. The third involves finite time learning-based adaptive dynamic programming that approximates optimal policies, to help overcome the curse of dimensionality that arises in traditional dynamic programming. This will build on the nonlead investigator's prior work in adaptive dynamic programming that proposed computational algorithms to learn suboptimal controllers from input-state or input-output data. The work will include applications to, and experiments with, underwater marine robots, where event-triggering will cope with intermittent communication and constrained power resources. Real physical marine robotic platforms will be used to explore numerical aspects and to evaluate the mathematical algorithms.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

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