Collaborative Research: Designs and Theory of State-Constrained Nonlinear Feedback Controls for Delay and Partial Differential Equation Systems

点击翻译按钮获取中文摘要

Collaborative Research: Designs and Theory of State-Constrained Nonlinear Feedback Controls for Delay and Partial Differential Equation SystemsControl systems are used to model many important engineering systems, such as electronics manufacturing processes involving lasers, marine robots that can monitor water pollution, oil drilling and refining, and rehabilitation mechanisms for patients with mobility disorders. However, many of these engineering applications involve input delays, state constraints, and uncertainties that can put them outside the scope of existing controller designs and theory. State constraints occur when the control objectives include avoiding undesirable situations such as collisions with obstacles, while input delays often arise from sensor designs or transport phenomena that make it difficult to measure the current state of the system. Also, it is inherent in many engineering applications that the control mechanisms must be autonomous. One important technique for ensuring autonomy is by using feedback control, which means that the control values must be determined from past values of the state of the system. This project will develop cutting edge feedback control designs and theory that can help address the preceding challenges, and will demonstrate the techniques in real time experiments. One key technique will involve prediction, which provides a way to use past observations from the control system to compute future states of the dynamics and future control values, even when the system involves long input delays or considerable uncertainty. As reflected in the backgrounds of the PIs, the project combines insightful engineering with sophisticated mathematics, with the goal of producing practically useful controls that have rigorous performance guarantees under delays or state constraints. The problems to be addressed are among the most challenging and significant ones in the control engineering community. The project will strive for transformative methods, and will pursue three theoretical strategies. The first will seek generalized Lyapunov function constructions for partial differential equations, which can include extensions of current approach for building strict Lyapunov functions for ordinary differential equations to much more difficult hyperbolic partial differential equation cases. The second strategy will involve representing robust predictive controls as solutions of integral delay equations, and a dual representation in terms of perturbed first-order hyperbolic partial differential equations. Combined with the Lyapunov function constructions, this can provide robust tracking for predictively controlled nonlinear ordinary differential equations and robustness results for the corresponding partial differential equations. The third strategy will use robust forward invariance, which involves specifying the state constraints to facilitate computing maximal allowable perturbation sets to ensure safe operation under uncertainty. The project will be guided by cutting edge engineering applications, to help ensure the practical usefulness of all of the project results. The ordinary differential equation applications will involve neuromuscular electrical stimulation, which is a rehabilitation method that can help restore movement in humans with motor neuron disorders, and the control of a class of autonomous marine robots that are used for bathymetric surveys or to monitor water quality. The partial differential equation applications will involve laser pulse shaping systems that are used in the manufacture of flat panel displays or in photolithography, and a multi-phase flow system that can help mitigate the adverse effects of slugging in oil production.