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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. 

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. 

The distributed optimization algorithm proposed by J. Wang and N. Elia in 2010 has been shown to achieve linear convergence for multi-agent systems with single-integrator dynamics. This paper extends their result, including the linear convergence rate, to a more complex scenario where the agents have heterogeneous multi-input multi-output linear dynamics and are subject to external disturbances and parametric uncertainties. Disturbances are dealt with via an internal-modelbased control design, and the interaction among the tracking error dynamics, average dynamics, and dispersion dynamics is analyzed through a composite Lyapunov function and the cyclic small-gain theorem. The key is to ensure a small enough stepsize for the convergence of the proposed algorithm, which is similar to the condition for time-scale separation in singular perturbation theory. 

Traditional traffic signal control focuses more on the optimization aspects whereas the stability and robustness of the closed-loop system are less studied. This paper aims to establish the stability properties of traffic signal control systems through the analysis of a practical model predictive control (MPC) scheme, which models the traffic network with the conservation of vehicles based on a store-and-forward model and attempts to balance the traffic densities. More precisely, this scheme guarantees the exponential stability of the closed-loop system under state and input constraints when the inflow is feasible and traffic demand can be fully accessed. Practical exponential stability is achieved in case of small uncertain traffic demand by a modification of the previous scheme. Simulation results of a small-scale traffic network validate the theoretical analysis. 

This paper presents a unified approach to the problem of learning-based optimal control of connected human-driven and autonomous vehicles in mixed-traffic environments including both the freeway and ring road settings. The stabilizability of a string of connected vehicles including multiple autonomous vehicles (AVs) and heterogeneous human-driven vehicles (HDVs) is studied by a model reduction technique and the Popov-Belevitch-Hautus (PBH) test. For this problem setup, a linear quadratic regulator (LQR) problem is formulated and a solution based on adaptive dynamic programming (ADP) techniques is proposed without a priori knowledge on model parameters. To start the learning process, an initial stabilizing control law is obtained using the small-gain theorem for the ring road case. It is shown that the obtained stabilizing control law can achieve general Lp string stability under appropriate conditions. Besides, to minimize the impact of external disturbance, a linear quadratic zero-sum game is introduced and solved by an iterative learning-based algorithm. Finally, the simulation results verify the theoretical analysis and the proposed methods achieve desirable performance for control of a mixed-vehicular network.