Active Sensing Approach to Output-Based Control of Nonsmooth Dynamical Systems with Controlled Singularities

PI和他的同事最近引入了一类新的系统，即具有主动或受控奇点的动力系统，以及相应的严格建模和最优控制框架。本类系统的主要特征是在其运动的奇异阶段（如不连续、非光滑、维度跳跃等）中允许脉冲控制作用。然而，这项工作揭示了一个基本的知识差距，需要弥合以允许实际的控制器实现：在具有受控奇点的系统中传感的新问题的正确陈述和解决方案，即在具有规则和非常短持续时间的奇异运动组合的系统中传感，两者都受控制。在进一步研究撞击类游戏时，我们会注意到，高级玩家会投入相当多的精力来维持两种感应模式的最佳组合：视觉追踪和球的接触“感觉”。因此，玩家在游戏的每个瞬间分别控制游戏的非冲击阶段和冲击阶段的感知环境。该策略在具有受控奇异点的系统中产生了主动感知的概念，其中两个阶段的控制都是为了使状态观测的信息内容最大化而选择的。主动感知在这类系统中是必不可少的，因为奇异相位持续时间很短，但对整个系统的行为影响很大。因此，所提出的概念是重要的，并且与上面指出的概念相结合，它提供了极大地提高具有奇点的系统性能的潜力。对整个两相系统运动的主动感知和基于输出的控制需要信息集、优化和多尺度动态小波网络方法来合成基于奇异相位短间隔非光滑实时测量的超高速时域状态估计器和控制器。并将多尺度模型严格嵌入到离散-连续方程中，该方程既能表示奇异运动阶段，也能表示平滑运动阶段的传感和控制。因此，本研究的目标是：a)为控制奇点系统中的主动传感开发一个数学框架；b)在此框架的基础上，开发利用包含平滑和脉冲数据的信号的主动超高速时间局部化状态观测器的设计程序；C)在a)和b)结果的基础上，开发获得全输入/状态/输出两相系统模型的技术，并设计基于输出的最优开环和反馈控制律，在规则和奇异运动中应用控制动作，d)将开发的程序应用于电网和具有快速阀控的锅炉-汽轮机机组的高速故障清除，以及具有脉冲端点返回运动的超高性能机电驱动器。以及MEMS中基于冲击运动的建模和控制。该研究提出的更广泛的影响源于这样一个事实，即系统运动中的奇点在广泛的技术意义重大的系统中至关重要，例如由故障引起的拓扑变化突然影响的电网、双足机器人、反向运动的快速定位系统、薄膜微致动器阵列、脉冲推进的太空飞行器、智能皮肤和其他系统。由于在快速传感/驱动方面的快速进展，提议的活动有可能在这些系统的性能上提供质的飞跃。

A new class of systems, dynamical systems with active, or controlled, singularities, and the corresponding rigorous modeling and optimal control framework have been recently introduced by the PI and his colleagues. The main characteristic of the systems in this class is the admission of impulsive control action during the singular phases of their motion, such as discontinuities and nonsmoothness, jumps in dimension, and others. This work, however, revealed a fundamental knowledge gap that needs to be bridged to permit practical controller implementation: correct statement and solution of the novel problem of sensing in systems with controlled singularities, i.e. sensing in systems with combined regular and very short duration singular motions, both controlled. Upon further examining the impact games, one notices that the advanced player puts considerable effort into maintaining the best possible combination of the two sensing modes: the visual tracking and the contact ``feel'' of the ball. Thereby, the player controls the sensing environment of the non-impact and impact phases of the game, respectively, at every instant of the game. This strategy gives rise to the concept of active sensing in the systems with controlled singularities, where the control in both phases is chosen with the added goal of maximizing the information content of the state observations. Active sensing in this class of systems is imperative, since singular phases have very short duration, but critically affect the entire system behavior. Thus, the concept proposed is important, and in combination with the concepts indicated above, it offers the potential of drastically improving the performance of systems with singularities. Active sensing and output-based control of the entire two-phase system motion are expected to require information-set, optimization, and multi-scale dynamic wavelet network methods for synthesis of the ultra-high-speed time-localized state estimators and controllers based on the short interval nonsmooth real-time measurements in the singular phase, and rigorous embedding of the multi-scale models into the discrete-continuous equations capable of representing sensing and control in both singular and smooth motion phases. Thus, the objectives of the proposed research are a) to develop a mathematical framework for active sensing in the systems with controlled singularities, b) on the basis of this framework to develop procedures for the design of active ultra-high-speed time-localized state observers that utilize signals containing both smooth and impulsive data, c) on the basis of the results of a) and b) to develop techniques\ for obtaining the full input/state/output two-phase system model and designing the optimal output-based open-loop and feedback control laws, with control actions applied during both regular and singular motion, and d) to apply the procedures developed to high speed fault clearing in power networks and boiler-turbine units with fast valving, ultra-high performance electromechanical drives with impulsive endpoint return motion, and modeling and control of impact-based motions in MEMS. The broader impact of the research proposed stems from the fact that singularities in system motion are critically important across a broad range of technologically significant systems, such as power networks abruptly affected by the fault-induced topological change, biped robots, fast positioning systems with reverse motion, thin-film microactuator arrays, space vehicles with impulsive propulsion, smart skins, and other systems. Due to rapid progress in fast sensing/actuation the proposed activity has a potential of providing qualitative jump in the performance of these systems.