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The article (Bazanella et al., 2019) presented the first results on generic identifiability of dynamic networks with partial excitation and partial measurements. All previous papers assumed that either all nodes are excited or all nodes are measured. One key contribution of that paper was to establish a set of necessary conditions on the excitation and measurement pattern (EMP) that guarantee generic identifiability: all sources must be excited and all sinks measured, and all other nodes must be either excited or measured. In this article, we show that two other types of nodes, which are defined by the local topology of the network, play an essential rôle in the search for a valid EMP, i.e., one that guarantees generic identifiability. We have called these nodes dources and dinks. We show that a network is generically identifiable only if, in addition to the abovementioned conditions, all dources are excited and all dinks are measured. We also show that sources and dources are the only nodes in a network that always need to be excited, and that sinks and dinks are the only nodes that need to be measured for an EMP to be valid.

This work is concerned with a compositional data-driven approach for formal safety verification of large-scale continuous-time dynamical systems with unknown models. The proposed framework enjoys the interconnection matrix and joint dissipativity-type properties of subsystems, described by the notion of stochastic storage certificates. In the first part of the paper, we cast the required conditions for constructing storage certificates as a robust optimization program (ROP). Since the proposed ROP is not tractable due to the unknown model appearing in one of its constraints, we propose a scenario optimization program (SOP) corresponding to the original ROP by collecting finite numbers of data from trajectories of each subsystem. By establishing a probabilistic relation between the optimal value of SOP and that of ROP, we construct a storage certificate for each unknown subsystem based on the number of data and a required level of confidence. We accordingly propose a compositional technique based on dissipativity reasoning to construct stochastic barrier certificates of interconnected systems based on storage certificates of individual subsystems. By leveraging the acquired barrier certificate, we quantify a lower bound on the probability that an interconnected system never reaches a certain unsafe region in finite-time horizons with an a-priori guaranteed confidence. We also propose an auxiliary compositional approach without requiring any compositionality condition but at the cost of providing a potentially conservative safety guarantee. In the second part of the paper, we propose our approaches for deterministic continuous-time systems with unknown dynamics. We verify our results over an unknown room temperature network containing 100 rooms.

The paper studies the model reduction problem using the notion of least squares moment matching. For linear systems, the main idea is to approximate a transfer function by ensuring that the interpolation conditions imposed by moment matching are satisfied in a least squares sense. The paper revisits this idea using tools from output regulation theory to develop a nonlinear enhancement of the notion of least squares moment matching and a unifying model reduction framework both for linear and nonlinear systems. The proposed framework allows for the direct computation of models through optimization, the use of weights to modulate the quality of approximation, and the possibility of enforcing prescribed properties, such as stability and passivity, via additional constraints. Parameterized families of models achieving least squares moment matching are also determined and shown to admit natural geometric and system-theoretic interpretations. The theory is illustrated by numerical examples.

This paper studies the linear-time temporal logic (LTL) control of a class of fair discrete-event systems (DESs). It is motivated by the curious extent in which the use of LTL can be strengthened and differentiated in control theory development. Over a fair DES model, a marker-progressive supervisory control problem is formulated in LTL. The problem formulation admits a more flexible specification of multiple markers to distinguish different DES tasks, and seeks to find a supervisor—a passive control function by convention for specified temporal safety—such that a fair DES under its control is guaranteed to make constant progress to these markers. The problem is studied in terms of DES marker-controllability—a new controllability concept formulation of temporal safety for constant marker progress. This new formulation sheds light on how event fairness in DESs coachieves such marker progress with supervision that exists. It is shown that a solution supervisor may be found by canonical LTL verification. Three examples are provided for illustration. [ABSTRACT FROM AUTHOR]

This article is concerned with the development and use of duality theory for a nonlinear filtering model with white noise observations. The main contribution of this article is to introduce a stochastic optimal control problem as a dual to the nonlinear filtering problem. The mathematical statement of the dual relationship between the two problems is given in the form of a duality principle. The constraint for the optimal control problem is the backward stochastic differential equation introduced in the companion paper. The optimal control solution is obtained from an application of the maximum principle, and subsequently used to derive the equation of the nonlinear filter. The proposed duality is shown to be an exact extension of the classical Kalman–Bucy duality, and different from other types of optimal control and variational formulations given in literature.

These instructions give guidelines for preparing papers for this publication. Presents information for authors publishing in this journal. [ABSTRACT FROM AUTHOR]

Kernel-based methods have been successfully introduced in system identification to estimate the impulse response of a linear system. Adopting the Bayesian viewpoint, the impulse response is modeled as a zero mean Gaussian process whose covariance function (kernel) is estimated from the data. The most popular kernels used in system identification are the tuned-correlated (TC), the diagonal-correlated (DC) and the stable spline (SS) kernel. TC and DC kernels admit a closed-form factorization of the inverse. The SS kernel induces more smoothness than TC and DC on the estimated impulse response, however, the aforementioned property does not hold in this case. In this paper we propose a second-order extension of the TC and DC kernel, which induces more smoothness than TC and DC, respectively, on the impulse response and a generalized-correlated kernel, which incorporates the TC and DC kernels and their second order extensions. Moreover, these generalizations admit a closed-form factorization of the inverse and thus they allow to design efficient algorithms for the search of the optimal kernel hyperparameters. We also show how to use this idea to develop higher oder extensions. Interestingly, these new kernels belong to the family of the so called exponentially convex local stationary kernels: such a property allows to immediately analyze the frequency properties induced on the estimated impulse response by these kernels.

Reliable quasi-static object manipulation and robotic locomotion require the verification of the stability of equilibria under unilateral contacts and friction. In a recent paper, Posa et al. (2016) demonstrated that sums-of-squares (SOS) programming can be used to verify the Lyapunov stability of planar systems via Lyapunov’s direct method if impacts are inelastic. However, this method appears to be too conservative to verify the stability of some remarkably simple examples. In this article, an extension of Lyapunov’s direct method is proposed, which makes use of a piecewise smooth Lyapunov function and allows a temporary increase of the Lyapunov function along a motion trajectory. In addition, a modified SOS formulation enables the investigation of planar systems with partially elastic contacts. The proposed method remains compatible with SOS programming techniques. The improved stability test is successfully applied to a point mass on a slope and to a rigid body with two contact points. For the latter, several mechanisms of instability have been demonstrated experimentally, but the exact conditions of Lyapunov stability are unknown.

In this article, stabilization of systems by delayed noisy states is investigated. The time delays in the stabilizing noisy states are extended into the general form. To support this novelty, the familiar Doob martingale inequality in the continuous version is improved; the equivalence principle, which says that the exponential stability in moment of an anhysteretic stochastic system infers the same property of the corresponding hysteretic system, is extended to the cases with the newly proposed semi-Lipschitz condition; the implication theorem, which indicates that the exponential stability in moment implies almost sure exponential stability, is generalized to the stochastic systems with time delays of general forms only under the linear growth condition. Technically, variable substitution is applied to time to map the function spaces for the functional differential equation models with unbounded time delays into those with bounded ones. Unified framework for the stability analysis for both bounded and unbounded time delays is built with the mapping, the decay rates, including those for polynomial stability, for estimates of the solutions with time delays of general form are formulated. At the end of the article, typical strategies, including the divided state feedback with unbounded time delays, for the stabilizing noise are presented, a numerical example is proposed to illustrate the method and to show the efficiency of the results of the paper.

This technical note addresses the problem of transforming a single-input–single-output discrete-time system into the extended observer form, which comprise a linear time-invariant observable component, and a nonlinear injection term, which depends on the input, output, and their forward shifts up to a finite order. Intrinsic necessary and sufficient conditions are provided for obtaining the extended observer form via a parametrized state transformation. The conditions are formulated directly in terms of the state equations and do not rely on input–output equations as in the earlier papers. Further, an algorithm for obtaining the required transformation is presented. Unlike the existing results on observer forms, the results are not restricted to reversible systems but to more general submersive systems, i.e., to systems, which are reversible via static state feedback.

This paper investigates the problem of securing exponentially fast consensus (exponential consensus for short) for identical agents with finite dimensional linear system dynamics over dynamic network topology. Our aim is to find the weakest possible conditions that guarantee exponential consensus using a Lyapunov function consisting of a sum of terms of the same functional form. We first investigate necessary conditions, starting by examining the system parameters. It is found that controllability of the linear agents is necessary for achieving consensus. Then, to work out necessary conditions incorporating the network topology, we construct a set of Laplacian matrix-valued functions. The precompactness of this set of functions is shown to be a significant generalization of existing assumptions on network topology. With the aid of such a precompactness assumption and restricting the Lyapunov function to one consisting of a sum of terms of the same functional form, we prove that a joint $(\delta, T)$-connectivity condition on the network topology is necessary for exponential consensus. Finally, we investigate how the above two “necessities” work together to guarantee exponential consensus. To partially address this problem, we define a synchronization index to characterize the interplay between agent parameters and network topology. Based on this notion, it is shown that by designing a proper feedback matrix and under the precompactness assumption, exponential consensus can be reached globally and uniformly if the joint $(\delta,T)$-connectivity and controllability conditions are satisfied, and the synchronization index is not less than one.

This is the first of a two part paper investigating the geometry of the integrator reach sets, and the applications thereof. In this Part I, assuming box-valued input uncertainties, we establish that this compact convex reach set is semialgebraic, translated zonoid, and not a spectrahedron. We derive the parametric as well as the implicit representation of the boundary of this reach set. We also deduce the closed-form formula for the volume and diameter of this set, and discuss their scaling with state dimension and time. We point out that these results may be utilized in benchmarking the performance of the reach set overapproximation algorithms.

In this article, we develop a tracking model predictive control (MPC) scheme for nonlinear systems using the linearized dynamics at the current state as a prediction model. Under reasonable assumptions on the linearized dynamics, we prove that the proposed MPC scheme exponentially stabilizes the optimal reachable equilibrium w.r.t. a desired target setpoint. Our theoretical results rely on the fact that, close to the steady-state manifold, the prediction error of the linearization is small, and hence, we can slide along the steady-state manifold toward the optimal reachable equilibrium. The closed-loop stability properties mainly depend on a cost matrix, which allows us to trade off performance, robustness, and the size of the region of attraction. In an application to a nonlinear continuous stirred tank reactor, we show that the scheme, which only requires solving a convex quadratic program online, has comparable performance to a nonlinear MPC scheme while being computationally significantly more efficient. Furthermore, our results provide the basis for controlling nonlinear systems based on data-dependent linear prediction models, which we explore in our companion paper. [ABSTRACT FROM AUTHOR]

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]

The purposes of this paper are twofold. The first is to derive a convex formulation for optimizing the fictitious dynamics of the extended command governor strategy recently proposed in Gilbert and Ong (2011). The second purpose is to provide an efficient procedure to solve online the optimization problem of the ellipsoidal set-based command governor or the extended command governor. Two numerical examples with comparison to earlier solutions from the literature illustrate the effectiveness of the proposed algorithm.

The identification of local modules in dynamic networks with known topology has recently been addressed by formulating conditions for arriving at consistent estimates of the module dynamics, under the assumption of having disturbances that are uncorrelated over the different nodes. The conditions typically reflect the selection of a set of node signals that are taken as predictor inputs in an multiple-input-single-output (MISO) identification setup. In this paper an extension is made to arrive at an identification setup for the situation that process noises on the different node signals can be correlated with each other. In this situation the local module may need to be embedded in an multiple-input--multiple-output (MIMO) identification setup for arriving at a consistent estimate with maximum likelihood properties. This requires the proper treatment of confounding variables. The result is a set of algorithms that, based on the given network topology and disturbance correlation structure, selects an appropriate set of node signals as predictor inputs and outputs in an MISO or MIMO identification setup. Three algorithms are presented that differ in their approach of selecting measured node signals. Either a maximum or a minimum number of measured node signals can be considered, as well as a preselected set of measured nodes. [ABSTRACT FROM AUTHOR]

Theorem 4.1 in the 2011 paper “A Framework for Control System Design Subject to Average Data-Rate Constraints” allows one to lower bound average operational data rates in feedback loops (including the situation in which encoder and decoder have side information). Unfortunately, its proof is invalid. In this note, we first state the theorem and explain why its proof is flawed, and then provide a correct proof under weaker assumptions. [ABSTRACT FROM AUTHOR]

Presents a listing of the editorial board, board of governors, current staff, committee members, and/or society editors for this issue of the publication. [ABSTRACT FROM AUTHOR]

Presents a listing of the editorial board, board of governors, current staff, committee members, and/or society editors for this issue of the publication. [ABSTRACT FROM AUTHOR]

The article lists the Institute of Electrical and Electronics Engineers Control Systems Society's Board of Governors and presents information for the authors.

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]

In this article, we first show that the main results claimed in the paper by Bikas and Rovithakis (2021) involve some errors as the selection conditions for the design parameters are not sufficient to ensure the boundedness of all the closed-loop signals, then we provide the corresponding corrections under the same controller, so that the underlying quantized control problem can be tackled. [ABSTRACT FROM AUTHOR]

Presents a listing of the editorial board, board of governors, current staff, committee members, and/or society editors for this issue of the publication. [ABSTRACT FROM AUTHOR]

Provides a listing of current committee members and society officers. [ABSTRACT FROM AUTHOR]

Provides a listing of current committee members and society officers. [ABSTRACT FROM AUTHOR]

Provides a listing of current committee members and society officers. [ABSTRACT FROM AUTHOR]

Presents a listing of the editorial board, board of governors, current staff, committee members, and/or society editors for this issue of the publication. [ABSTRACT FROM AUTHOR]

Presents a listing of the editorial board, board of governors, current staff, committee members, and/or society editors for this issue of the publication. [ABSTRACT FROM AUTHOR]

The issue of initial/boundary conditions for a general system of partial difference equations (PDEs)—called a discrete $n$-D system—is resolved through the notion of characteristic sets: the restriction of a solution trajectory to a minimal characteristic set can be considered to be the initial/boundary condition to the corresponding trajectory. In the recent paper (Mukherjee and Pal, 2021), it has been shown that every autonomous $n$-D system admits a minimal characteristic set that is the union of a sublattice (of rank equal to the Krull dimension of the system) and its finitely many parallel translates. Treating the restrictions of every solution trajectories to such a characteristic set as initial/boundary conditions, in this article, we provide a full parametrization of the set of all initial/boundary conditions of a discrete autonomous $n$-D system. The key to this parametrization is that the set of allowable initial/boundary conditions itself can be viewed as a discrete $d$-D system, where $d$ is the Krull dimension of the system: we prove this result here. An upshot of this parametrization is the answer to free assignability of these initial/boundary conditions.

This paper studies optimal motion planning subject to motion and environment uncertainties. By modeling the system as a probabilistic labeled Markov decision process (PL-MDP), the control objective is to synthesize a finite-memory policy, under which the agent satisfies complex high-level tasks expressed as linear temporal logic (LTL) with desired satisfaction probability. In particular, the cost optimization of the trajectory that satisfies infinite horizon tasks is considered, and the trade-off between reducing the expected mean cost and maximizing the probability of task satisfaction is analyzed. The LTL formulas are converted to limit-deterministic Büchi automata (LDBA) with a reachability acceptance condition and a compact graph structure. The novelty of this work lies in considering the cases where LTL specifications can be potentially infeasible and developing a relaxed product MDP between PL- MDP and LDBA. The relaxed product MDP allows the agent to revise its motion plan whenever the task is not fully feasible and quantify the revised plan’s violation measurement. A multi- objective optimization problem is then formulated to jointly consider the probability of task satisfaction, the violation with respect to original task constraints, and the implementation cost of the policy execution. The formulated problem can be solved via coupled linear programs. This work first bridges the gap between probabilistic planning revision of potential infeasible LTL specifications and optimal control synthesis of both plan prefix and plan suffix of the trajectory over the infinite horizons. Experimental results are provided to demonstrate the effectiveness of the proposed framework.

For most networked systems found in the literature, the actuated boundary is usually located at one end. In this article, we first consider the stabilization of a chain of two interconnected subsystems, actuated at the in-between boundary. Each subsystem corresponds to coupled hyperbolic partial differential equations. Such in-domain actuation leads to higher complexity, and represents a significant difference with existing results. Then, starting from a classical controllability condition, we design a state feedback control law for the considered class of systems. The proposed approach is based on the backstepping methodology. However, to deal with the complex structure of the system, we use Fredholm integral transforms instead of classical Volterra transforms. We prove the invertibility of such transforms using an original operator framework. The well posedness of the backstepping kernel equations defining the transformations is also shown with the same arguments. By using a similar procedure, we are then able to design a Luenberger-type observer. Finally, we use the state estimation in the stabilizing controller to obtain an output-feedback law. Some test cases complete the paper.

Presents a listing of the editorial board, board of governors, current staff, committee members, and/or society editors for this issue of the publication. [ABSTRACT FROM AUTHOR]

Presents a listing of the editorial board, board of governors, current staff, committee members, and/or society editors for this issue of the publication. [ABSTRACT FROM AUTHOR]

Presents a listing of the editorial board, board of governors, current staff, committee members, and/or society editors for this issue of the publication. [ABSTRACT FROM AUTHOR]