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

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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.