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Feedback optimization aims at regulating the output of a dynamical system to a value that minimizes a cost function. This problem is beyond the reach of the traditional output regulation theory, because the desired value is generally unknown and the reference signal evolves according to a gradient flow using the system’s real-time output. This paper complements the output regulation theory with the nonlinear small-gain theory to address this challenge. Specifically, the authors assume that the cost function is strongly convex and the nonlinear dynamical system is in lower triangular form and is subject to parametric uncertainties and a class of external disturbances. An internal model is used to compensate for the effects of the disturbances while the cyclic small-gain theorem is invoked to address the coupling between the reference signal, the compensators, and the physical system. The proposed solution can guarantee the boundedness of the closed-loop signals and regulate the output of the system towards the desired minimizer in a global sense. Two numerical examples illustrate the effectiveness of the proposed method. 

This paper studies the distributed feedback optimization problem for linear multi-agent systems without precise knowledge of local costs and agent dynamics. The proposed solution is based on a hierarchical approach that uses upper-level coordinators to adjust reference signals toward the global optimum and lower-level controllers to regulate agents’ outputs toward the reference signals. In the absence of precise information on local gradients and agent dynamics, an extremum-seeking mechanism is used to enforce a gradient descent optimization strategy, and an adaptive dynamic programming approach is taken to synthesize an internal-model-based optimal tracking controller. The whole procedure relies only on measurements of local costs and input-state data along agents’ trajectories. Moreover, under appropriate conditions, the closed-loop signals are bounded and the output of the agents exponentially converges to a small neighborhood of the desired extremum. A numerical example is conducted to validate the efficacy of the proposed method. 

Abstract The distinct molecular states — single molecule, assembly, and aggregate — of two ionic macromolecules, TPPE‐APOSS and TPE‐APOSS, are easily distinguishable through their tunable fluorescence emission wavelengths, which reflect variations in intermolecular distances. Both ionic macromolecules contain aggregation‐induced emission (AIE) active moieties whose emission wavelengths are directly correlated to their mutual distances in solution: far away from each other as individual molecules, maintaining a tunable and relatively long distance in electrostatic interactions‐controlled blackberry‐type assemblies (microphase separation), or approaching van der Waals close distance in aggregates (macrophase separation). Furthermore, within the blackberry assemblies, the emission wavelength decreases monotonically with increasing assembly size, indicative of shorter intermolecular distances at nanoscale. The emission changes of TPPE‐APOSS blackberry assemblies can even be visually distinguishable by eyes when their sizes and intermolecular distances are tuned. Molecular dynamics simulations further revealed that macromolecules are confined in various conformations by controllable intermolecular distances within the blackberry structure, thereby resulting in fluorescence emission with tunable wavelength. 

Understanding the petrological and geochemical processes shaping the Moho transition zone (MTZ) is crucial for advancing our knowledge of thermal and chemical exchanges between the oceanic crust and the residual upper mantle. In this study, we systematically investigate the MTZ outcropped within the Zedong ophiolite, located in the eastern part of the Yarlung-Tsangpo Suture Zone (YTSZ), with the aim of at reconstructing the magmatic processes responsible for generating the petrological Moho. The Zedong MTZ comprises a sequence of dunite, wehrlite, pyroxenite, and gabbro, with frequent occurrences of clinopyroxene-rich lithologies. Cyclicity within the MTZ sequences is characterized by the recurrence of olivine-rich intervals and the presence of zig-zag patterns in both major and trace elements of clinopyroxenes. Zircon Usingle bondPb dating on the Zedong gabbros supports the coeval formation of the Zedong ophiolite with other YTSZ ophiolites. Clinopyroxene in the Zedong MTZ follows a differentiation sequence characterized by an increase in contents of Al2O3 and TiO2, coupled with a decrease in Mg#. This differentiation sequence along with frequent occurrences of amphibole suggest the evolution of a primitive hydrous melt depleted in Al2O3, TiO2, and Na2O. The depleted Ndsingle bondHf isotopes and rare earth element patterns of the MTZ rocks indicate that their parental magmas originated from fluid-enhanced re-melting of a previously depleted mantle. Additionally, we proposed that the initiation of a new subduction zone results in the re-melting of the mantle peridotite, leading to the formation of primitive hydrous basaltic melts. The variable lithologies observed in the Zedong MTZ arise from fractional crystallization and repeated replenishment of hydrous melts.