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Hierarchical robust nonlinear switching control design for propulsion systems.

机译：推进系统的分层鲁棒非线性切换控制设计。

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The desire for developing an integrated control system-design methodology for advanced propulsion systems has led to significant activity in modeling and control of flow compression systems in recent years. In this dissertation we develop a novel hierarchical switching control framework for addressing the compressor aerodynamic instabilities of rotating stall and surge. The proposed control framework accounts for the coupling between higher-order modes while explicitly addressing actuator rate saturation constraints and system modeling uncertainty.; To develop a hierarchical nonlinear switching control framework, first we develop generalized Lyapunov and invariant set theorems for nonlinear dynamical systems wherein all regularity assumptions on the Lyapunov function and the system dynamics are removed. In particular, local and global stability theorems are given using lower semicontinuous Lyapunov functions. Furthermore, generalized invariant set theorems are derived wherein system trajectories converge to a union of largest invariant sets contained in intersections over finite intervals of the closure of generalized Lyapunov level surfaces. The proposed results provide transparent generalizations to standard Lyapunov and invariant set theorems.; Using the generalized Lyapunov and invariant set theorems, a nonlinear control-system design framework predicated on a hierarchical switching controller architecture parameterized over a set of moving system equilibria is developed. Specifically, using equilibria-dependent Lyapunov functions, a hierarchical nonlinear control strategy is developed that stabilizes a given nonlinear system by stabilizing a collection of nonlinear controlled subsystems. The switching nonlinear controller architecture is designed based on a generalized lower semicontinuous Lyapunov function obtained by minimizing a potential function over a given switching set induced by the parameterized system equilibria. The proposed framework provides a rigorous alternative to designing gain scheduled feedback controllers and guarantees local and global closed-loop system stability for general nonlinear systems. Furthermore, the hierarchical switching control framework is extended to include inverse optimality notions. Specifically, the hierarchical controller is parameterized with respect to a given system equilibrium manifold wherein an inverse optimal morphing strategy is constructed to coordinate the hierarchical switching. The overall approach is quite different from the quasivariational inequality methods for optimal switching systems developed in the literature in that our results provide hierarchical homotopic feedback controllers guaranteeing closed-loop stability via an underlying Lyapunov function. Finally, the proposed control framework is extended to account for system parametric uncertainty wherein the hierarchical switching architecture is parameterized over a set of moving nominal system equilibria.
机译：近年来，对于开发用于高级推进系统的集成控制系统设计方法的需求导致了在流动压缩系统的建模和控制方面的大量活动。在本文中，我们开发了一种新颖的分层切换控制框架，以解决压缩机旋转失速和喘振的气动不稳定性。拟议的控制框架考虑了高阶模式之间的耦合，同时明确解决了执行器速率饱和约束和系统建模不确定性。为了开发分层的非线性切换控制框架，首先我们为非线性动力学系统开发广义Lyapunov和不变集定理，其中所有关于Lyapunov函数和系统动力学的正则性假设都被删除。特别是，使用较低的半连续Lyapunov函数给出了局部和全局稳定性定理。此外，导出了广义不变集定理，其中系统轨迹收敛到在广义Lyapunov水平面闭合的有限区间的交点中包含的最大不变集的并集。拟议的结果为标准Lyapunov和不变集定理提供了透明的概括。利用广义的Lyapunov和不变集定理，开发了一种非线性控制系统设计框架，该框架基于在一组运动系统平衡上参数化的分层切换控制器架构进行了预测。具体而言，使用依赖于平衡的Lyapunov函数，开发了一种分级非线性控制策略，该策略通过稳定一组非线性受控子系统来稳定给定的非线性系统。开关非线性控制器体系结构是基于广义下半连续Lyapunov函数设计的，该函数通过将由参数化系统均衡引起的给定开关集上的势函数最小化而获得。所提出的框架为设计增益调度反馈控制器提供了一种严格的选择，并保证了通用非线性系统的局部和全局闭环系统稳定性。此外，分层切换控制框架被扩展为包括逆最优概念。具体地，相对于给定的系统平衡歧管来对分层控制器进行参数化，其中构造了逆最优变形策略以协调分层切换。总体方法与文献中开发的最优开关系统的拟变分不等式方法完全不同，因为我们的结果提供了分层的同质反馈控制器，可通过底层Lyapunov函数确保闭环稳定性。最后，扩展了所提出的控制框架以解决系统参数不确定性问题，其中，在一组移动的<标称>标称系统平衡点上对分层切换架构进行了参数化。

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