Quantile regression (QR) has become an important tool to measure dependence of response variable's quantiles on a number of predictors for heterogeneous data, especially heavy-tailed data and outliers. However, it is quite challenging to make statistical inference on distributed high-dimensional QR with missing data due to the distributed nature, sparsity and missingness of data and non-differentiable quantile loss function. To overcome the challenge, this paper develops a communication-efficient method to select variables and estimate parameters by utilizing a smooth function to approximate the non-differentiable quantile loss function and incorporating the idea of the inverse probability weighting and the penalty function. The proposed approach has three merits. First, it is both computationally and communicationally efficient because only the first- and second-order information of the approximate objective function are communicated at each iteration. Second, the proposed estimators possess the oracle property after a limited number of iterations without constraint on the number of machines. Third, the proposed method simultaneously selects variables and estimates parameters within a distributed framework, ensuring robustness to the specified response probability or propensity score function of the missing data mechanism. Simulation studies and a real example are used to illustrate the effectiveness of the proposed methodologies.

This article investigates the fuzzy adaptive resilient leader-following consensus control problem for a class of nonlinear heterogeneous multi-agent systems (HMASs) under denial-of-service (DoS) attacks. Since the considered leader's system contains unknown nonlinear dynamics and HMASs are subject to DoS attacks, the leader's states and output are inaccessible to followers, a stable distributed estimator is developed to estimate them. To solve the virtual controller non-differentiable problem in backstepping control design technique caused by DoS attacks, the command-filter is introduced into the backstepping control design process, and formulate a resilient leader-following consensus controller. It is proven that the proposed control scheme can guarantee that the controlled HMASs are stable, and the consensus errors converge to a small neighborhood of zero. Finally, a simulation example on unmanned aerial vehicle-unmanned ground vehicles (UAV-UGVs) is provided to verify the feasibility of the proposed control scheme.

In this paper, the asynchronously practical control is studied for discrete time switched systems with singular perturbations. Firstly, a novel Lyapunov function is constructed including the singular perturbation parameter and quasi-time parameter matrices. And then, quasi-time dependent criteria are achieved to study the practical stability and asynchronous stabilization; an allowable upper bound is expected to be obtained for the singular perturbation parameters; the asynchronous sampling controller is designed with quasi-time gains, and the application range of this controller is further widened via some constraints relaxed. At last, two simulation examples are utilized to illustrate that the proposed results are less conservative and effective.

This paper first proposes a distributed continuous-time Newton-Raphson algorithm for heterogeneous linear multi-agent systems over unbalanced digraphs. Then this approach extends to cases where the local cost functions and Hessian matrices are unknown. While local exponential stability of the inverse Hessian matrix estimator has been established for single-agent systems, this paper proves local exponential stability in multi-agent systems, ensuring the stability of the proposed distributed Newton-Raphson extremum seeking algorithm. A numerical example demonstrates the effectiveness of the proposed algorithms.

In this paper, we stumble upon that the normal ordering expansion for $\left(x\frac{\mathrm{d}}{\mathrm{d}x}\right)^n$ is equivalent to the expansion of $(bD_G)^n$, where $G$ is the context-free grammar defined by $G=\{a\rightarrow a, b\rightarrow 1\}$. Motivated by this fact, we introduce the definition of grammatical basis. We then study several grammatical bases generated by $G=\{a\rightarrow 1, b\rightarrow 1\}$. Using grammatical bases, we give a classification of grammars. In particular, we provide new grammatical descriptions for Ward numbers, Hermite polynomials, Bessel polynomials, Chebyshev polynomials and logarithmic polynomials arising from an integral. We end this paper by giving some applications of grammatical bases. One can see that if two or more polynomials share a grammatical basis, then they share the same coefficients, and it might be helpful for the detection of intrinsic relationship among superficially different structures.

In this paper, we are concerned with the problem of achieving Nash equilibrium in noncooperative games over networks. We propose two types of distributed projected gradient dynamics with accelerated convergence rates. The first type is a variant of the commonly-known consensus-based gradient dynamics, where the consensual terms for determining the actions of each player are discarded to accelerate the learning process. The second type is formulated by introducing the Nesterov's accelerated method into the distributed projected gradient dynamics. We prove convergence of both algorithms with at least linear rates under the common assumption of Lipschitz continuity and strongly monotonicity. Simulation examples are presented to validate the outperformance of our proposed algorithms over the well-known consensus-based approach and augmented game based approach. It is shown that the required number of iterations to reach the Nash equilibrium is greatly reduced in our proposed algorithms. These results could be helpful to address the issue of long convergence time in partial-information Nash equilibrium seeking algorithms.

This paper studies the adaptive mean-square output consensus problem of heterogeneous multi-agent systems with different multiplicative noises under a directed graph. Specifically, due to the presence of packet losses, the optimal estimator is first derived for the continuous-time stochastic system through discretization to estimate each agent's state. Based on this, we design an edge-based distributed adaptive control protocol that is independent of global information of the communication topology. With the aid of the distributed feedforward control approach and stochastic stability theory, the sufficient condition for achieving mean-square output consensus is derived. Moreover, the convergence of the optimal estimator is analyzed through rigorous mathematical derivation. Finally, a numerical simulation verifies the validity of the obtained results.

This paper proposes a factor model for interval-valued panel data. We exploit that the first $r$ largest eigenvalues of the sample covariance matrix divided by $N$ (i.e., $\frac{\langle s_Y^{\prime},s_Y\rangle_K}{NT}$) of interval-valued response variables are $O_p(1)$, while the rest are $o_p(1)$. Then the eigenvalue ratio-type estimators of the number of factors are proposed. Under certain conditions, the proposed estimators are all proven to be consistent. Moreover, the estimators of interval-valued factors and the loadings can be obtained by the principal components method. Monte Carlo simulation studies show that the proposed estimators have the desired finite sample properties. A real example is analysed for illustrations.

In this paper, we address the bounded leader-following consensus problem for linear multi-agent systems connected via undirected graphs, specifically in the presence of non-consistent time-varying communication delays. The periodic event-triggered scheme is proposed to mitigate the adverse effects of these delays, which ensures discrete data transmission only occurs at specific event instants. By leveraging the nature of periodic event-triggered schemes, Zeno-freeness can be guaranteed by discretely event-checking. Additionally, the appropriate design of the threshold range prevents the event-triggered consensus from degrading into sampled-data consensus. The numerical simulation is presented in the end to show the effectiveness of the provided approach.

This article explores the dynamic event-triggered (DET) ${H_\infty }$ load frequency control (LFC) for networked power systems (NPSs) subject to deception attacks. Firstly, a novel DET mechanism is proposed, which aims to improve the system control performance under deception attacks and save more network resources effectively. Compared with the existing DET mechanisms, the proposed DET mechanism involves an adaptive rule, which can be utilized to dynamically adjust the event-triggered threshold based on the relative rate of change and absolute difference of system state and the frequency of deception attacks. Then, considering the complexity of the actual power systems, a new DET-based LFC stochastic model is formulated, which integrates actuator failure, network-induced delay and deception attacks. Subsequently, by using Lyapunov theory, the sufficient conditions guaranteeing the asymptotic mean-square stability of the NPSs are derived. Finally, some simulation results are presented to validate the superiority of the designed approach.

The broad goal of the research surveyed in this article is to develop methods for understanding the aggregate behavior of interconnected dynamical systems, as found in mathematical physics, neuroscience, economics, power systems and neural networks. Questions concern prediction of emergent (often unanticipated) phenomena, methods to formulate distributed control schemes to influence this behavior, and these topics prompt many other questions in the domain of learning. The area of mean field games, pioneered by Peter Caines, are well suited to addressing these topics. The approach is surveyed in the present paper within the context of controlled coupled oscillators.

This paper addresses boundary control to input-to-state stabilization for fractional convection-diffusion-reaction (FCDR) systems governed by coupled time fractional partial differential equations (TFPDEs) under matched and unmatched disturbances over actuator/sensor networks using output feedback, fractional sliding mode (FSM) algorithm and sampled-in-space sensing. Here it is assumed that sensors provide discrete in space measurements, i.e., spatially averaged measurements (SAMs), and a limited number of sensors are allocated in a spatial domain. A sampled-data observation problem is first in investigation, which contains to design a FSM observer against boundary disturbances and to prove input-to-state stability (ISS) of the proposed observer. Using this observer and backstepping approach, we develop an output feedback FSM controller and establish the reaching condition to FSM surface. Using the fractional Lyapunov method, ISS of the closed-loop dynamics is achieved. Theoretical results are verified by numerical simulations.

The authors study an approximation method for partially observed Markov decision processes (POMDPs) with continuous spaces. Belief MDP reduction, which has been the standard approach to study POMDPs requires rigorous approximation methods for practical applications, due to the state space being lifted to the space of probability measures. Generalizing recent work, in this paper the authors present rigorous approximation methods via discretizing the observation space and constructing a fully observed finite MDP model using a finite length history of the discrete observations and control actions. The authors show that the resulting policy is near-optimal under some regularity assumptions on the channel, and under certain controlled filter stability requirements for the hidden state process. The authors also provide a Q learning algorithm that uses a finite memory of discretized information variables, and prove its convergence to the optimality equation of the finite fully observed MDP constructed using the approximation method.

This paper considers the practical fixed-time tracking control problem for a state constrained pure-feedback nonlinear system. A new barrier function is first proposed to handle various asymmetric time-varying constraints and unify the cases with and without state constraints. Then a low-cost neural network based adaptive fixed-time controller is constructed by further combining the dynamic surface control, which overcomes the technical problems of overparametrization and singularity in the backstepping procedure. Our design guarantees that the tracking error converges to a small neighbourhood of zero in a fixed time while satisfying the state constraints as a priority task without imposing feasibility conditions on the virtual controllers. Simulation results validate the effectiveness of the proposed adaptive fixed-time tracking control strategy.

With the development of the tourism industry, the associated carbon dioxide emissions have become considerable, significantly impacting global climate change. This study will compile relevant publications from various fields in recent years on sustainable tourism and climate change, and analyse the hot issues in this field based on the bidirectional relationship between the tourism industry and climate change. Firstly, based on the research framework of the bidirectional relationship between tourism and climate change, the impact of the tourism industry on climate change was measured from the perspective of tourist carbon footprint in four aspects. Simultaneously, the effects of climate change on the tourism industry were summarized. Subsequently, bibliometric methods are employed to analyse the literature in this field in recent years. Finally, combining qualitative and quantitative review results, the study presents feasible suggestions for future research directions, highlighting potential avenues for further investigation from both technical and policy perspectives.

This paper considers risk-sensitive linear-quadratic mean-field games. By the so-called direct approach via dynamic programming, we determine the feedback Nash equilibrium in an $N$-player game. Subsequently, we design a set of decentralized strategies by passing to the mean-field limit. We prove that the set of decentralized strategies constitutes an $O(1/N)$-Nash equilibrium when applied by the $N$ players, and hence obtain so far the tightest equilibrium error bounds for this class of models.

In this paper, the authors revisit decentralized control of linear quadratic (LQ) systems. Instead of imposing an assumption that the process and observation noises are Gaussian, the authors assume that the controllers are restricted to be linear. The authors show that the multiple decentralized control models, the form of the best linear controllers is identical to the optimal controllers obtained under the Gaussian noise assumption. The main contribution of the paper is the solution technique. Traditionally, optimal controllers for decentralized LQ systems are identified using dynamic programming, maximum principle, or spectral decomposition. The authors present an alternative approach which is based by combining elementary building blocks from linear systems, namely, completion of squares, state splitting, static reduction, orthogonal projection, (conditional) independence of state processes, and decentralized estimation.

Optimal feedback control of nonlinear system with free terminal time present many challenges including nonsmooth in the value function and control laws, and existence of multiple local or even global optimal trajectories. To mitigate these issues, the authors introduce an actor-critic method along with some enhancements. The authors demonstrate the algorithm's effectiveness on a prototypical example featuring each of the main pathological issues present in problems of this type as well as a higher dimensional example to show that the solution method presented can scale.

This study aims to solve the Nash equilibrium (NE) seeking problem for monotone $N$-coalition games. The authors assume that the gradient mapping of the game is monotone but not necessarily strictly or strongly monotone. Such a merely monotone assumption presents significant challenges to NE seeking, since the basic gradient descent method may fail to converge. The authors start with a regularization-based projected gradient dynamical system in a general non-cooperative game framework and analyze the convergence of the dynamics under different scenarios. Then, the authors develop NE seeking algorithms for monotone $N$-coalition games with undirected and connected inner-coalition communication graphs. Asymptotic convergence to the least-norm NE is proven. The convergence rate of the algorithm for an analytic mapping is provided. Furthermore, the authors propose a novel regularization-based dynamical system that allows different parameters among the coalitions. Rigorous analysis and a numerical example are provided to illustrate the effectiveness of the proposed method.

In this paper the authors consider the operational problem of optimal signalling and control, called control-coding capacity (with feedback), $C_{FB}$ in bits/second, of discrete-time nonlinear partially observable stochastic systems in state space form, subject to an average cost constraint. $C_{FB}$ is the maximum rate of encoding signals or messages into randomized controller-encoder strategies with feedback, which control the state of the system, and reproducing the messages at the output of the system using a decoder or estimator with arbitrary small asymptotic error probability. In the first part of the paper, the authors characterize $C_{FB}$ by an information theoretic optimization problem of maximizing directed information from the inputs to the outputs of the system, over randomized strategies (controller-encoders). The authors derive equivalent characterizations of $C_{FB}$, using randomized strategies generated by either uniform or arbitrary distributed random variables (RVs), sufficient statistics, and a posteriori distributions of nonlinear filtering theory. In the second part of the paper, the authors analyze $C_{FB}$ for linear-quadratic Gaussian partially observable stochastic systems (LQG-POSSs). The authors show that randomized strategies consist of control, estimation and signalling parts, and the sufficient statistics are, two Kalman-filters and an orthogonal innovations process. The authors prove a semi-separation principle which states, the optimal control strategy is determined explicitly from the solution of a control matrix difference Riccati equation (DRE), independently of the estimation and signalling strategies. Finally, the authors express the optimization problem of $C_{FB}$ in terms of two filtering matrix DREs, a control matrix DRE, and the covariance of the innovations process. Throughout the paper, the authors illustrate that the expression of $C_{FB}$ includes as degenerate cases, problems of stochastic optimal control and channel capacity of information transmission.

This paper considers the value iteration algorithms of stochastic zero-sum linear quadratic games with unkown dynamics. On-policy and off-policy learning algorithms are developed to solve the stochastic zero-sum games, where the system dynamics is not required. By analyzing the value function iterations, the convergence of the model-based algorithm is shown. The equivalence of several types of value iteration algorithms is established. The effectiveness of model-free algorithms is demonstrated by a numerical example.

This paper proposes a data-driven learning-based approach to predictive control for switched nonlinear systems subject to state and control constraints and external stochastic disturbances. A switched Koopman modeling framework is developed, where a multi-mode neural network for state lifting is trained simultaneously with Koopman operators and state reconstruction matrices for all the modes. This framework facilitates the construction of a switched linear Koopman model in a transformed space and effectively captures the dynamics of the original nonlinear system. A switched predictive control strategy is then designed to regulate the switched Koopman model with constrained state and control inputs against both the stochastic disturbances and the uncertainties introduced by the lifting neural network. The proposed control scheme ensures mean-square stability and guarantees boundedness during the online phase. Furthermore, boundedness analysis is performed to determine the reachable set of the original system state across all admissible switching sequences. The effectiveness of the proposed methodology is demonstrated through a case study of a gene regulatory network.

This paper focuses on solving the distributed optimization problem with binary-valued intermittent measurements of local objective functions. In this context, a binary-valued measurement represents whether the measured value is smaller than a fixed threshold. Meanwhile, the "intermittent|" scenario arises when there is a non-zero probability of not detecting each local function value during the measuring process. Using this kind of coarse measurement, we propose a discrete-time stochastic extremum seeking-based algorithm for distributed optimization over a directed graph. As is well-known, many existing distributed optimization algorithms require a doubly-stochastic weight matrix to ensure the average consensus of agents. However, in practical engineering, achieving double-stochasticity, especially for directed graphs, is not always feasible or desirable. To overcome this limitation, we design a row-stochastic matrix and a column-stochastic matrix as weight matrices in our algorithm instead of relying on doubly-stochasticity. Under some mild conditions, we rigorously prove that agents can reach the average consensus and ultimately find the optimal solution. Finally, we provide a numerical example to illustrate the effectiveness of our algorithm.

In this paper, we consider a wave-plate transmission system on Riemannian manifold with boundary controls on the plate equation. This model arises from the noise control and is extended to the broader context of the Riemannian manifold. By employing the semigroup method, we obtain the well-posedness of the system. Subsequently, under certain geometric conditions, we establish a polynomial energy decay estimate of type $t^{-1}$ by using the geometric multiplier method in which the conclusion proposed by Guo and Yao (J. Math. Anal. Appl. 2006, 317: 50-70.) plays a crucial role in our proof. It effectively addresses the challenge posed by curvature on the Riemannian manifold. Moreover, by employing the higher-order energy method, we overcome the technical difficulties caused by higher-order terms in boundary controls, which generalizes the results in the literature.

In this paper, we consider a class of linear quadratic optimal control problems of backward stochastic differential equations under partial information with initial value constraint. The main contribution is to obtain an explicitly optimal controller by using a Riccati equation and an optimal parameter characterized by a matrix equation. The key technique is to introduce Lagrange multiplier to transform the problem with initial value constraint into unconstrained optimal control problem and optimal parameter calculation problem, and solve the optimal parameter calculation by using the exact controllability of the system.

This paper addresses an indefinite linear-quadratic mean field games for stochastic large-population system, where the individual diffusion coefficients may depend on both the state and the control of the agents. Moreover, the control weights in the cost functionals could be indefinite. We employ a direct approach to derive the $\epsilon$-Nash equilibrium strategy. First, we formally solve an $N$-player game problem within a vast but finite population setting. Subsequently, by introducing two Riccati equations, we decouple or reduce the high-dimensional systems to yield centralized strategies, which depend on the state of a specific player and the average state of the population. As the population size $N$ goes infinity, the construction of decentralized strategies becomes feasible. Then, we demonstrate that these strategies constitute an $\epsilon$-Nash equilibrium. Finally, numerical examples are provided to demonstrate the effectiveness of the proposed strategies.

In this paper, the issues of both reconstructibility analysis and state estimation are investigated for locally reconstructible Boolean networks (BNs), where the pinning control is employed to design a special control sequence. First, this paper will focus on dealing with state unreconstructible cycle based on state set-estimation theory, and the concept of set-to-set reachability is proposed. Second, the locally reconstructible BNs are transformed to Boolean control networks (BCNs) by pinning control technique, where a logical matrix is designed by a special algorithm such that all states in the unreconstructible initial state set can evolve into the reconstructible state set, simultaneously. Third, a sufficient condition for the existence of a free Boolean control sequence is obtained, which guarantees that a locally reconstructible BN can be transformed into a reconstructible one. Besides, an optimization control algorithm is proposed to generate pinning control sequence and further optimize the reconstructibility of BNs. A kind of pinning control-based state estimation method is also developed. Finally, an example is provided to show the feasibility of the proposed methods.

This paper investigates an innovative predefined time output feedback adaptive fuzzy consensus control method for fractional-order nonlinear multi-agent systems(FONMASs). The controlled system includes unmeasurable states and unknown nonlinear functions. The fuzzy state observer is built to evaluate unmeasurable state variables, unknown nonlinear functions are addressed through fuzzy logic system approximation. Combining with fractional-order dynamic surface control (DSC) and the theory of stability of predefined time, the control method is raised. By employing FODSC techniques, the computational explosion problem can be avoided. The stability of the closed-loop system is analyzed using the Lyapunov function, demonstrating that FONMAS achieves semi-global practical predefined time stability (SGPPTS). Eventually, the validity of the prescribed control strategy is verified by a simulation case.

This paper studies a distributed policy gradient in collaborative multi-agent reinforcement learning (MARL), where agents communicating over a network aim to find an optimal policy that maximizes the average of all the agents' local returns. To address the challenges of high variance and bias in stochastic policy gradients for MARL, this paper proposes a distributed policy gradient method with variance reduction, combined with gradient tracking to correct the bias resulting from the difference between local and global gradients. We also utilize importance sampling to solve the distribution shift problem in the sampling process. We then show that the proposed algorithm finds an $\epsilon$-approximate stationary point, where the convergence depends on the number of iterations, the mini-batch size, the epoch size, the problem parameters, and the network topology. We further establish the sample and communication complexity to obtain an $\epsilon$-approximate stationary point. Finally, numerical experiments are performed to validate the effectiveness of the proposed algorithm.

This paper investigates the path-guided distributed formation control of networked autonomous surface vehicles (ASVs) subject to model uncertainties and environmental disturbances. A safety-certified path-guided coordinated control method is proposed for multiple ASVs to achieve a distributed formation in obstacle environments. Specifically, a neural predictor with a high-order tuner is presented to approximate unknown nonlinearities with accelerated learning performance. Subsequently, control Lyapunov functions (CLFs) and control barrier functions (CBFs) are constructed for mapping stability constraints and safety constraints on states to control inputs. A quadratic optimization problem is constructed with the norm of control inputs as the objective function, CLFs and CBFs as constraints. Neurodynamic optimization is used to deal with the quadratic programming problem and generate the optimal kinetic control signals, thereby attaining the desired safe formation. Unlike the high-order CBF, a CBF backstepping method is proposed to establish safety constraints such that repeated time derivatives of system nonlinearities can be avoided. The multi-ASVs system is ensured to be input-to-state safe irrespective of high-order relative degree. Through the Lyapunov theory, the multi-ASVs system is proven to be input-to-state stable. Finally, simulation results are presented to validate the efficacy of the presented safety-certified distributed formation control for networked ASVs.

The distributed optimal output synchronization problem for the leaderless heterogeneous multi-agent system with a general global cost function is investigated for the first time by linear quadratic (LQ) optimal control theory. Conventional algorithms for heterogeneous systems are quite complex, requiring the design of a virtual reference generator and the solving of regulation equations. This paper presents a novel distributed asymptotically optimal controller by incorporating the design of distributed observer and feedforward controller. A general form of the distributed controller is obtained by solving an augmented algebraic Riccati equation, which is parallel to classical optimal control theory. The optimal topology is an arbitrary directed graph containing only a spanning tree. It is shown that the proposed algorithms outperform the traditional consensus methods in the convergence speed by selecting proper observer gain matrices, and eliminate the reliance on the nonzero eigenvalues of Laplacian matrix. Simulation example further demonstrates the effectiveness of the proposed scheme and a faster superlinear convergence speed than the existing algorithm.

This paper is concerned with a mean-field type optimal control problem with terminal state constraint, in which state $X^u$ is partially observed by a stochastic process $Y$. Combining Ekeland's variational principle with backward separation method, a necessary condition for optimal control of this problem is obtained. A linear-quadratic mean-field type optimal control problem with terminal state constraint is analytically solved. A multi-objective mean-field type optimal control problem is also studied.

An algorithm for computing parametric order bases for univariate polynomial matrices with parameters is first presented in this paper. Starting from the non-parametric univariate polynomial matrix, our key idea is to construct a special module and module order. Then based on Gröbasis theory for modules, we present that the order basis can be obtained by computing a minimal Gröbasis for this module under this order. Further, we extend the definition of the order basis to the parametric polynomial matrix, and give the concept of comprehensive order basis systems. More importantly, the method based on Gröbases for modules can be naturally generalized to the parametric case by means of comprehensive Grösystems for modules. As a consequence, we design a new algorithm for computing comprehensive order basis systems. The proposed algorithm has been implemented on the computer algebra system Singular and Maple.

This paper considers the real-time estimation problem of vehicle mass, which has a significant impact on driving comfort and safety. A bilinear parameter identification algorithm is proposed for a type of nonlinear identification problems, which encompass vehicle mass estimation. The feature of this nonlinear model is that two parameters to be estimated are multiplied together, which brings great difficulties to identification compared to linear models. The main idea proposed in the algorithm design is to transform the original nonlinear model into two mutually dependent linear models, which are identified by the recursive algorithms. By constructing a combined Lyapunov function, it is theoretically proved that the algorithm converges under the input excitation condition, and the convergence rate $O(1/t)$ is achieved based on some extra mild conditions. Finally, the algorithm is verified through practical experiments, with the estimated vehicle mass error of $1.06%$ on average, which shows the feasibility of the algorithm.

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.

Rosenblatt and Rosenblatt-Volterra processes are two families of stochastic processes that are described by double Wiener-Itô integrals with singular kernels. The Rosenblatt processes have exponential singular kernels and the Rosenblatt-Volterra processes have singular Volterra kernels for the Wiener-Itô integrals. Empirical evidence shows that for many control systems the assumption of Gaussian noise is not appropriate so Rosenblatt and Rosenblatt-Volterra processes are some generalizations of Gaussian processes that can provide natural alternatives to Gaussian probability laws. Furthermore, the results for Rosenblatt and Rosenblatt-Volterra processes are tractable for some applications. These results can be compared to prediction for Gaussian processes and Gauss-Volterra processes.

In econometric analysis, researchers often encounter vast datasets that greatly reduce model efficiency. In this paper, the authors develop a sequential shrinkage estimation method for use in distributed settings. Within this framework, one dataset is split into several blocks, and each block is regarded as a node. The sequential shrinkage estimation method is implemented on the data in each block until the stopping criteria are satisfied. These sequential procedures are then integrated to produce the final results using a weighted average, which provides approximate regression result estimates for the entire dataset. The proposed method can significantly reduce the required number of samples and perform parameter estimation and variable selection while satisfying the preset accuracy requirements. In addition, the statistical properties of the parameter estimates in the proposed approach are analyzed for use in a linear regression model. Finally, numerical studies on simulated and real datasets show that the proposed method performs well.

In this paper, the authors propose an approach to properly aggregate a reversible discrete-time switched linear system and prove that, for any $n$-dimensional exponentially stabilizable switched system, the authors could design up to $n$ linear gain matrices, such that the extended system is also exponentially stabilizable as a switched autonomous system. By utilizing the pathwise state feedback switching strategy of the switched autonomous system, the original system is aggregated into a piecewise linear system that is step-wise norm contractive and exponentially stable. The authors also develop a robust switching design mechanism that simultaneously achieves exponential stability, structural stability, and input-to-state stability for the closed-loop system. A numerical example is presented to demonstrate the effectiveness of the proposed design scheme.

Building heating, ventilating, and air conditioning (HVAC) systems have one of the largest energy footprint worldwide, which necessitates the design of intelligent control algorithms that improve the energy utilization while still providing thermal comfort. In this work, the authors formulate the HVAC equipment dynamics in the setting of a two-player non-zero-sum cooperative game, which enables two decision variables (mass flow rate and supply air temperature) to perform joint optimization of the control utilization and thermal setpoint tracking by simultaneously exchanging their policies. The HVAC zone serves as a game environment for these two decision variables that act as two players in a game. It is assumed that dynamic models of HVAC equipment are not available. Furthermore, neither the state nor any estimates of HVAC disturbance (heat gains, outside variations, etc.) are accessible, but only the measurement of the zone temperature is available for feedback. Under these constraints, the authors develop a new data-driven Q-learning scheme employing policy iteration and value iteration with a bias compensation mechanism that accounts for unmeasurable disturbances and circumvents the need of full-state measurement. The proposed algorithms are shown to converge to the optimal solution corresponding to the generalized algebraic Riccati equations (GAREs) in dynamic games.

This paper presents a dynamic game framework to analyze the role of large banks in interbank markets. By extending existing models, the authors incorporate a major bank as a dynamic decision-maker interacting with multiple small banks. Using the mean-field game methodology and convex analysis, best-response trading strategies are derived, leading to an approximate equilibrium for the interbank market. The authors investigate the influence of the large bank on the market stability by examining individual default probabilities and systemic risk, through the use of Monte Carlo simulations. The proposed findings reveal that, when the size of the major bank is not excessively large, it can positively contribute to market stability. However, there is also the potential for negative spillover effects in the event of default, leading to an increase in systemic risk. The magnitude of this impact is further influenced by the size and trading rate of the major bank. Overall, this study provides valuable insights into the management of systemic risk in interbank markets.