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We consider an environmentwhere players need to decide whether to buy a certain product (or adopt a technology) or not. The product is either good or bad, but its true value is unknown to the players. Instead, each player has her own private information on its quality. Each player can observe the previous actions of other players and estimate the quality of the product. A classic result in the literature shows that in similar settings, informational cascades occur, where learning stops for the whole network and players repeat the actions of their predecessors. In contrast to this literature, in this paper, players get more than one opportunity to act. In each turn, a player is chosen uniformly at random from all the players and can decide to buy the product and leave the market or wait. Her utility is the total expected discounted reward, and thus, myopic strategies may not constitute equilibria. We provide a characterization of perfect Bayesian equilibria (PBEs) with forward-looking strategies through a fixed-point equation of dimensionality that grows only quadratically with the number of players. Using this tractable fixed-point equation, we show the existence of a PBE and characterize PBEs with threshold strategies. Based on this characterization, we study informational cascades in two regimes. First, we show that for a discount factor $\delta$ strictly smaller than 1, informational cascades happen with high probability as the number of players $N$ increases. Furthermore, only a small portion of the total information in the system is revealed before a cascade occurs. Second, and more surprisingly, we show that for a fixed $N$ , and for a sufficiently large $\delta < 1$ , when the product is bad, there exists an equilibrium where an informational cascade can happen only after at least half of the players revealed their private information, and consequently, the probability for a “bad cascade” where all the players buy the product vanishes exponentially with $N$. Finally, when $\delta =1$ and the product is bad, there exists an equilibrium where informational cascades do not happen at all. [ABSTRACT FROM AUTHOR]

A small correction is made in the example of Section V (A representative application to networked systems) of the paper with the above title. [ABSTRACT FROM AUTHOR]

Model predictive controllers use dynamics models to solve constrained optimal control problems. However, computational requirements for real-time control have limited their use to systems with low-dimensional models. Nevertheless, high-dimensional models arise in many settings, for example, discretization methods for generating finite-dimensional approximations to partial differential equations can result in models with thousands to millions of dimensions. In such cases, reduced-order models (ROMs) can significantly reduce computational requirements, but model approximation error must be considered to guarantee controller performance. In this article, a reduced-order model predictive control (ROMPC) scheme is proposed to solve robust, output feedback, constrained optimal control problems for high-dimensional linear systems. Computational efficiency is obtained by using projection-based ROMs, and guarantees on robust constraint satisfaction and stability are provided. The performance of the approach is demonstrated in simulation for several examples, including an aircraft control problem leveraging an inviscid computational fluid dynamics model with dimension 998 930. [ABSTRACT FROM AUTHOR]

This article investigates the robust cooperative output regulation problem of heterogeneous uncertain linear multiagent systems with switching topologies and infinite distributed communication delays. A novel distributed observer is proposed for each agent to estimate the state of the so-called exosystem by taking consideration of both switching topologies and infinite distributed communication delays. A distributed output feedback controller is then developed based on the internal model principle and the estimated state without using the prior knowledge of communication delays. It is shown via the newly developed Lyapunov-like method that the robust cooperative output regulation problem can be solved under some mild assumptions. Finally, a numerical example is given to demonstrate the effectiveness of the proposed controller. [ABSTRACT FROM AUTHOR]

This article considers the distributed resource allocation problem over a network of n agents with individual optimization functions and coupled resource constraints. The optimization variables are bounded for each agent. We propose an asynchronous distributed gradient descent based method, which is able to tackle time-varying communication networks and communication problems. The main ideas are twofold. First, the degree of freedom of the network is reduced to deal with the global constraint. Second, we utilize delay compensation to counteract the delay of asynchronous communication. We prove that the convergence rate is $O(\frac{1}{k})$ and analyze both the communication complexity and the time complexity. This method is applied into the parallel pump control problem in HVAC system and shows good numerical results. [ABSTRACT FROM AUTHOR]

This article deals with, in the framework of absolute stability, boundary stabilization for a nonlinear axially moving beam under boundary velocity feedback controls. The nonlinear boundary control that satisfies a slope-sector condition covering many types of nonlinear control schemes is a negative feedback of the transverse velocity at the right eyelet of the moving beam. Under the nonlinear control scheme, the well-posedness of the nonlinear partial differential equation, which depends continuously on the initial value is investigated by means of the Faedo–Galerkin approximation and priori estimates. By exploiting the integral-type multiplier method, the exponential stability of the closed-loop system is established, where a novel energy like function is constructed. The numerical simulation examples using the finite element method are presented to illustrate the effectiveness of the established criterion of the controller. [ABSTRACT FROM AUTHOR]

Analytic interpolation problems with rationality and derivative constraints are ubiquitous in systems and control. This article provides a new method for such problems, both in the scalar and matrix case, based on a nonstandard Riccati-type equation. The rank of the solution matrix is the same as the degree of the interpolant, thus providing a natural approach to model reduction. A homotopy continuation method is presented and applied to some problems in modeling and robust control. We also address a question on the positive degree of a covariance sequence originally posed by Kalman. [ABSTRACT FROM AUTHOR]

This article proposes a class of resilient state estimators for linear time-varying discrete-time systems. The dynamic equation of the system is assumed to be affected by a bounded process noise. As to the available measurements, they are potentially corrupted by a noise of both dense and impulsive natures. The latter, in addition to being arbitrary in its form, need not be strictly bounded. In this setting, we construct the estimator as the set-valued map, which associates with the measurements the minimizing set of some appropriate performance functions. We consider a family of such performance functions, each of which yielding a specific instance of the proposed general estimation framework. It is then shown that the proposed class of estimators enjoys the property of resilience, i.e., it induces an estimation error, which, under certain conditions, is independent of the extreme values of the (impulsive) measurement noise. Hence, the estimation error may be bounded, while the measurement noise is virtually unbounded. Moreover, we provide several error bounds (in different configurations), whose expressions depend explicitly on the degree of observability of the system being observed and on the considered performance function. Finally, a few simulation results are provided to illustrate the resilience property. [ABSTRACT FROM AUTHOR]

Optimal control problems are prevalent in model-based control, state and parameter estimation, and experimental design for complex dynamical systems. An approach for obtaining solutions to these problems is based on the notion of parsimonious input parameterization and comprises two tasks: the enumeration of arc sequences followed by the computation of optimal values of a small number of decision variables for each sequence. This article proposes an efficient global solution method for single-input optimal control problems for nonlinear dynamical systems with a potentially large number of states or complex dynamics via sum-of-squares polynomials and parallel computing. The method approximates the problem for a given arc sequence as a polynomial optimization problem that can be efficiently solved to global optimality via semidefinite programming. It is established that the difference between the cost obtained by the proposed method and the globally optimal cost of the original problem is bounded and depends on the polynomial approximation error. The method is illustrated by simulation examples of a reaction system and a rocket. [ABSTRACT FROM AUTHOR]

This article studies the feedback stabilization problem of the motion of a tank that contains an incompressible, Newtonian, viscous liquid. The control input is the force applied on the tank and the overall system consists of two nonlinear partial differential equations and two ordinary differential equations. Moreover, a spill-free condition is required to hold. By applying the control Lyapunov functional methodology, a set of initial conditions (state space) is determined for which spill-free motion of the liquid is possible by applying an appropriate control input. Semi-global stabilization of the liquid and the tank by means of a simple feedback law is achieved, in the sense that for every closed subset of the state space, it is possible to find appropriate controller gains, so that every solution of the closed-loop system initiated from the given closed subset satisfies specific stability estimates. The closed-loop system exhibits an exponential convergence rate to the desired equilibrium point. The proposed stabilizing feedback law does not require measurement of the liquid level and velocity profiles inside the tank and simply requires measurements of 1) the tank position error and tank velocity, 2) the total momentum of the liquid, and 3) the liquid levels at the tank walls. The obtained results allow an algorithmic solution of the problem of the spill-free movement and slosh-free settlement of a liquid in a vessel of limited height (such as water in a glass) by a robot to a prespecified position, no matter how full the vessel is. [ABSTRACT FROM AUTHOR]

This article addresses analysis and control of the SIR model of infectious diseases in the framework of input-to-state stability (ISS) with respect to the net flow of susceptible individuals into a region in both disease-free and epidemic situations. The key development is the construction of a continuously differentiable strict Lyapunov function. First, this article clarifies that a continuously differentiable Lyapunov function whose derivative is nonpositive can deduce asymptotic stability on the whole state space. Second, it is demonstrated that a new idea of rendering the derivative strictly negative allows one to detect a margin proving ISS of the SIR model. The accomplishment is based on the pursuit of a Lyapunov function that is not entirely separable into components. It contrasts with previously studied and popular Lyapunov functions that are proven to be incapable of assessing robustness properties such as ISS. Third, two types of feedback control laws are proposed for mass vaccination of immigrants and inhabitants by making use of the strict Lyapunov functions. One type modifies the other type by focusing on the reduction of peaks of the infected population within the ISS guarantees. [ABSTRACT FROM AUTHOR]

We investigate state estimation of linear systems over channels having a finite state not known by the transmitter or receiver. We show that similar to memoryless channels, zero-error capacity is the right figure of merit for achieving bounded estimation errors. We then consider finite-state, worst-case versions of the common erasure, and additive noise channels models, in which the noise is governed by a finite-state machine without any statistical structure. Upper and lower bounds on their zero-error capacities are derived, revealing a connection with the topological entropy of the channel dynamics. Separate necessary and sufficient conditions for bounded linear state estimation errors via such channels are obtained. These estimation conditions bring together the topological entropies of the linear system and the discrete channel. [ABSTRACT FROM AUTHOR]

We present order reduction results for linear time invariant descriptor systems. Results are given for both forced and unforced systems as well methods for constructing the reduced order systems. Our results establish a precise connection between classical and new results on this topic, and lead to an elementary construction of quasi-Weierstrass forms for a descriptor system. Examples are given to illustrate the usefulness of our results. [ABSTRACT FROM AUTHOR]

In this article, we revisit the concepts and tools of harmonic analysis and control and provide a rigorous mathematical answer to the following question: When does an harmonic control have a representative in the time domain? By representative we mean a control in the time domain that leads by sliding Fourier decomposition to exactly the same harmonic control. Harmonic controls that do not have such representatives lead to erroneous results in practice. The main results of this article are: A one-to-one correspondence between ad hoc functional spaces guaranteeing the existence of a representative, a strict equivalence between the Caratheorody solutions of a differential system and the solutions of the associated harmonic differential model, and as a consequence, a general harmonic framework for linear time periodic systems and bilinear affine systems. The proposed framework allows to design globally stabilizing harmonic control laws. We illustrate the proposed approach on a single-phase rectifier bridge. Through this example, we show how one can design stabilizing control laws that guarantee periodic disturbance rejection and low harmonic content. [ABSTRACT FROM AUTHOR]

A compressed positive quadrature filter (CPQF) is proposed in this technical note. Accuracy, efficiency, and numerical stability are the main concerns for quadrature-based nonlinear Gaussian filtering, but desirable performance in all these three aspects can hardly be simultaneously achieved in previously proposed nonlinear Gaussian filters, such as unscented Kalman filter, Gauss–Hermite quadrature filter (GHQF), and sparse grid quadrature filter. To improve the overall capacity of nonlinear Gaussian filtering techniques, the CPQF is proposed by numerically solving the constrained moment matching equations. By enforcing the positivity of the quadrature weights, the CPQF is numerically as stable as the GHQF. Through exploiting the underlying sparsity while solving the moment matching equations, the CPQF can also achieve the same level of accuracy as the GHQF using far fewer quadrature points. Simulations are conducted to evaluate the effectiveness of the CPQF, and the numerical results demonstrate its superior performance over conventional Gaussian filters. [ABSTRACT FROM AUTHOR]