This paper addresses Lipschitz conditions of infinite dimensional systems. Three types of Lipschitz conditions are discussed, namely, the compact set Lipschitz condition, the local Lipschitz condition and the bounded set Lipschitz condition. These three conditions are equivalent in finite dimensional systems but not necessarily equivalent in infinite dimensional systems on the basis of the Riesz’s

This paper presents a robust learning-based predictive control strategy for nonlinear systems subject to both input and output constraints, under the assumption that the model function is not known a priori and only input–output data are available. The proposed controller is obtained using a nonparametric machine learning technique to estimate a prediction model. Based on this prediction model, a novel

H-infinity optimal control and estimation are addressed for a class of systems governed by partial differential equations with bounded input and output operators. Diffusion equations are an important example in this class. Explicit formulas for the optimal state feedback controller as well as the optimal state estimator are given. Unlike traditional methods for H-infinity synthesis, no iteration is

In this paper, the stability of linear systems with sawtooth input delay widely existing in networked systems and predictor-based controller is considered. Under the assumption that there exists an instant where the input delay is zero, a necessary and sufficient condition is obtained to guarantee the exponential stability of the closed-loop system, that is, the closed-loop system is stable if and

This paper investigates the existence of non-impulsive unique solution and stochastic stability problems for the continuous-time linear rectangular descriptor Markov jump systems (DMJSs) at two cases. For every case, the sufficient and necessary conditions, in terms of strict linear matrix inequalities (LMIs), are eventually proposed to guarantee that the continuous-time linear DMJSs are column (row)

This paper discusses the boundary feedback stabilization of a reaction–diffusion equation with Robin boundary conditions and in the presence of a time-varying state-delay. The proposed control design strategy is based on a finite-dimensional truncated model obtained via a spectral decomposition. By an adequate selection of the number of modes of the original infinite-dimensional system, we show that

In unconstrained maximum a posteriori (MAP) and maximum likelihood estimation, the inverse of minus the merit-function Hessian matrix is an approximation of the estimate covariance matrix. In the Bayesian context of MAP estimation, it is the covariance of a normal approximation of the posterior around the mode; while in maximum likelihood estimation, it is an approximation of the inverse Fisher information

The asynchronously switched multi-agent systems comprising switched agents of different dynamics and switching signals are considered under arbitrarily switching communication topologies. The practical output synchronization problem is studied for such a kind of systems due to the heterogeneity brought by both the dynamics and the switchings of agents. A switching-dependent controller with an embedded

This paper introduces a new discrete-time filter proportional–integral–derivative (FPID) controller framework for linear time-invariant (LTI) systems. The discrete-time FPID controller plays an important role in both determining the dynamic response of the system and further improving the performance of the controller in itself. However, the introduction of the filter parameter brings more challenge

Considering a retarded nonlinear system, this note proposes several modifications of the Lyapunov–Razumikhin approach guaranteeing the existence of an upper estimate on convergence rate of the system solutions. The cases of exponential, finite-time and fixed-time (with respect to a ball) convergences are studied. The proposed approach is illustrated by simulation of academic examples.

The super-twisting algorithm is a robust sliding-mode control law, which in the case of a saturated control input suffers from a windup effect. This contribution proposes a modified control law that is obtained by mitigating windup by means of the conditioning technique. Closed-loop stability is analyzed for bounded and Lipschitz continuous perturbations acting on a first-order linear time-invariant

The paper is devoted to reachable sets of linear time-varying continuous or discrete systems under uncertain initial states and disturbances with a bounded uncertainty measure. The uncertainty measure is the sum of a quadratic form of the initial state and the integral/sum over the finite-time interval from a quadratic form of the disturbance. It is shown that the reachable set of the system under

In this paper, the design of all possible switching signal-dependent state feedback and output feedback stabilizers for switched Boolean control networks (SBCNs) under arbitrary switching signal is investigated. By making use of the algebraic state-space approach to SBCNs, necessary and sufficient conditions for the stabilization at a given equilibrium point are presented. A new algorithm is proposed

This article studies consensus of linear multi-agent systems (MASs) on undirected graphs. An adaptive event-triggering protocol is constructed for consensus control by using relative information between agents. Sufficient conditions are established for consensus of linear MASs without and with external disturbances, respectively. Zeno behavior is proved to be excluded. Moreover, a self-triggered realization

This paper proposes a coordinate-free controller to drive a mobile robot to encircle a target at unknown position only using range-based measurements. Different from the existing works, a backstepping based controller is proposed to encircle the target with zero steady-state error for any desired smooth pattern. Moreover, we show its asymptotic exponential stability under a fixed set of parameters

An increasing concern in power systems is how to elicit flexibilities in demand, which leads to nontraditional electricity products for accommodating loads of different flexibility levels. We have proposed Multiple-Arrival Multiple-Deadline (MAMD) differentiated energy services for the flexible loads which require constant power for specified durations. Such loads are indifferent to the actual power

This paper studies stabilization of discrete-time switched linear systems (SLSs) using the notion of graph control Lyapunov functions (GCLFs). A GCLF is a set of Lyapunov functions defined on a weighted digraph, where each Lyapunov function is represented by a node in the digraph and there is a Lyapunov inequality associated with each subgraph consisting of a node and its out-neighbors. The weight

This paper deals with second-order continuous-time linear time-invariant systems by means of a pulse-width modulation (PWM)-type input. In general, it is difficult to analyze and design a PWM system because of its nonlinearity in terms of the duty ratio. In this paper, it is shown that the nonlinearity appearing in the discrete-time model at the sampling instants can be eliminated by varying the location

This paper focuses on stabilization of second-order oscillatory systems using both feedback control and intentionally introduced time delay. The argument principle is employed as a key technique to divide the parameter space of time delay and controller gain into several regions. Every admissible value in these regions moves the poles of the closed-loop system towards the left of the complex plane

We extend previous results regarding infinite-dimensional backstepping-based controller design for linear hyperbolic partial (integro-)differential equations (P(I)DEs), and derive a state-feedback controller for a PIDE system with time-varying system parameters. The system state converges to zero in the ∞-norm, in a finite time corresponding to the propagation time between the boundaries. Secondly

In this paper, we consider performance output tracking for a one dimensional Euler–Bernoulli beam equation with boundary moment control and unmatched internal uncertainty and external disturbance. For such system, the reference Feng and Guo (2017) firstly studied the active disturbance rejection control (ADRC) problem. We design an infinite-dimensional disturbance estimator to estimate the total disturbance

In this paper, the efficient hinging hyperplanes (EHH) neural network is proposed, which is basically a single hidden layer neural network. Different from the dominant single hidden layer neural networks, the hidden layer in the EHH neural network can be seen as a directed acyclic graph (DAG) and all the nodes in the DAG contribute to the output. It is proved that for every EHH neural network, there

In this paper, we first address adverse effects of attacks on distributed synchronization of multi-agent systems, by providing conditions under which an attacker can destabilize the underlying network, as well as another set of conditions under which local neighborhood tracking errors of intact agents converge to zero. Based on this analysis, we propose a Kullback–Libeler divergence based criterion

Although homography estimation from correspondences of mixed-type features, namely points and lines, has been relatively well studied with algebraic approaches by the computer vision community, this problem has never been addressed with nonlinear observer paradigms. In this paper, a novel nonlinear observer on the Special Linear group SL(3) applied to homography estimation is developed. The key advance

In this paper, the filtering problem for systems with fading measurements is considered. Taking advantage of the cascaded structure of the system, the original filtering problem is decomposed into two subproblems: 1) recovery of the original measurements from the faded ones, and 2) state estimation based on the recovered signals. A two-stage particle filtering (PF) algorithm is proposed to achieve

We propose an offline algorithm that simultaneously estimates discrete and continuous components of a hybrid system’s state. We formulate state estimation as a continuous optimization problem by relaxing the discrete component and using a robust loss function to accommodate large changes in the continuous component during switching events. Subsequently, we develop a novel nonsmooth variable projection

In this paper, and inspired by the recent discrete-time model in Parsegov et al. (2017) and Friedkin et al. (2016), we study two continuous-time opinion dynamics models (Model 1 and Model 2) where the individuals discuss opinions on multiple logically interdependent topics. The logical interdependence between the different topics is captured by a “logic” matrix, which is distinct from the Laplacian

This paper considers dynamic (multi-stage) signaling games involving an encoder and a decoder who have subjective models on the cost functions. We consider both Nash (simultaneous-move) and Stackelberg (leader–follower) equilibria of dynamic signaling games under quadratic criteria. For the multi-stage scalar cheap talk, we show that the final stage equilibrium is always quantized and under further

Within a differential–algebraic framework, this paper studies the leader-following consensus problem for networks of a class of strictly different nonlinear systems. In this case, by allowing any type of interplay between followers and assuming a directed spanning tree in the network, a dynamic consensus protocol with diffusive coupling terms is designed to achieve the leader-following consensus. In

We solve in this article the problem of robust output feedback regulation for a system composed of two hyperbolic equations with collocated input and output in presence of a general class of disturbances and noise. Importantly, the robustness of the controller is considered with respect to delays in the actuation and in the measurements but also with respect to uncertainties on parameters, most importantly

A PDE-based control concept is developed to deploy a multi-agent system into desired formation profiles. The dynamic model is based on a coupled linear, time-variant parabolic distributed parameter system. By means of a particular coupling structure parameter information can be distributed within the agent continuum. Flatness-based motion planning and feedforward control are combined with a backstepping-based

In this paper, the design problem of recursive state estimator is discussed for a class of coupled nonlinear dynamical networks with randomly switching topologies and multiple missing measurements under the event-triggered mechanism. A sequence of random variables obeying the Bernoulli distribution with certain occurrence probabilities is adopted to model the multiple missing measurements and the random

In this paper we consider the problem of constructing non-asymptotic confidence regions for the parameters of Errors-In-Variables (EIV) systems where both inputs and outputs are observed in noise. The Leave-out Sign-dominant Correlation Regions (LSCR) and Sign-Perturbed Sums (SPS) approaches which are two methods for constructing confidence regions from a finite number of data points, are extended

Difference equations, such as a Ricker map, for an increased value of the parameter, experience instability of the positive equilibrium and transition to deterministic chaos. To achieve stabilization, various methods can be applied. Proportional Feedback control suggests a proportional reduction of the state variable at every kth step. First, if k≠1, a cycle is stabilized rather than an equilibrium

This paper addresses the design of finite-dimensional feedback control laws for linear discrete-time fractional-order systems with additive state disturbance. A set of sufficient conditions are provided to guarantee convergence of the state trajectories to an ultimate bound around the origin with size increasing with the magnitude of the disturbances. Performing a suitable change of coordinates, the

Hill’s equations describe the linearized relative motion of deputy spacecraft with respect to the chief spacecraft which moves around the Earth in a circular orbit. The reachable set is defined as the set of all possible final positions of the deputy spacecraft that can be reached by a control force under certain constraints. The computation of the reachable set has been a focus of recent study, and

This article treats global uniform exponential stability (GUES) of discrete-time switched linear systems under restricted switching. Given admissible minimum and maximum dwell times, we provide sufficient conditions on the subsystems under which they admit a set of switching signals that obeys the given restrictions on dwell times and preserves stability of the resulting switched system. Our analysis

This paper focuses on the problem of estimating bearing vectors between the agents in a two dimensional multi-agent network based on subtended angle measurements. We propose an edge localization graph to investigate the solvability of this problem and a distributed estimation method via orientation estimation of virtual agents to solve the problem. Under the proposed method, the estimated bearing vector

We consider tracking control for uncertain linear systems with known relative degree which are possibly non-minimum phase, i.e., their zero dynamics may have an unstable part. For a given sufficiently smooth reference signal we design a low-complexity controller which achieves that the tracking error evolves within a prescribed performance funnel. We present a novel approach where a new output is constructed

Herdability is a variant of controllability, and is an indicator of the ability to drive system states to a specific subset of the state space. This paper characterizes the controllable subspace and herdability of signed weighted networks. Specifically, a dynamic signed leader–follower network is considered, in which a small subset of the network nodes (i.e., the leaders) is endowed with exogenous

In this paper, the notions of pseudo Gramians are introduced for linear time-invariant semistable systems, which allow multiple semisimple poles at the origin. The proposed Gramians are the generalizations of standard Gramian matrices defined for asymptotically stable systems, and they can be computed by a set of Lyapunov equations. Furthermore, it is shown that the controllability and observability

Pairs trading is about simultaneously trading a pair of stocks. A pairs trade is triggered when their prices diverge and consists of a short position of the strong stock and a long position of the weak one. Pairs trading bets on the reversal of their price strengths. In this paper, we study the optimal pairs-trading problem under general geometric Brownian motions and focus on trading with cutting

This paper proposes a novel block-wise observer structure for Linear Parameter-Varying (LPV) systems in the presence of non-uniform measurements. The proposed observer is robust to parametric variations and measurement noise. Structural detectability and stability of the proposed observer are guaranteed. Numerical simulations of a real case study allowed the validation of the effectiveness of the Robust

A major gap in the proof of the central Theorem 7 (Kim, 2010) is pointed out. Accordingly, the claim of robustness made in the theorem statement (and in the paper title) is not established, and indeed is questionable. This also invalidates the numerical results in Kim (2010).

Due to the inherent periodic nature of cycling tasks, iterative and repetitive learning controllers are well motivated for rehabilitative cycling. Motorized functional electrical stimulation induced cycling is a rehabilitation treatment where multiple lower-limb muscle groups are activated jointly with an electric motor to achieve cycling objectives such as speed (cadence) and torque tracking. This

The term stealthy has come to encompass a variety of techniques that attackers can employ to avoid being detected. In this manuscript, for a class of perturbed linear time-invariant systems, we propose two security metrics to quantify the potential impact that stealthy attacks could have on the system dynamics by tampering with sensor measurements. We provide analysis tools to quantify these metrics

Distributed data sharing in dynamic networks is ubiquitous. It raises the concern that the private information of dynamic networks could be leaked when data receivers are malicious or communication channels are insecure. In this paper, we propose to intentionally perturb the inputs and outputs of a linear dynamic system to protect the privacy of target initial states and inputs from released outputs

This paper considers a class of interconnected nonlinear systems where each subsystem, in the absence of coupling, is individually exponentially stable. The cyclic-small-gain theorem is significantly extended in such a way that the interconnected system is proved to be globally exponentially stable, an exponential converging upper bound of state norm is obtained which fully reveals the relations between

This paper is concerned with the distributed filtering problem for a class of two-dimensional shift-varying systems over sensor networks subject to stochastic communication protocol (SCP) over a finite horizon. The communication between the sensor nodes and the filters is implemented through shared channels of limited capacity. To avoid data collisions, the SCP is applied to determine the transmission

An optimal state and fault estimation scheme is proposed for two-dimensional discrete systems subject to either deterministic disturbances or stochastic disturbances (noises). A direct solution to the deterministic estimation problem is obtained first, based on a well-designed regularized least squares problem with a dynamic constraint of a two-dimensional singular system, augmented from the original

“Prescribed-time” stabilization addresses the problem of regulating the state to the origin in a fixed (prescribed) time irrespective of the initial state. While prior results on prescribed-time stabilization considered specific classes of systems such as a chain of integrators with uncertainties matched with the control input (i.e., normal form), we address here a general class of nonlinear systems

This paper addresses the problem of distributed learning of average belief with sequential observations, in which a network of n>1 agents aim to reach a consensus on the average value of their beliefs, by exchanging information only with their neighbors. Each agent has sequentially arriving samples of its belief in an online manner. The neighbor relationships among the n agents are described by a graph

The goal of this paper is to obtain online abstractions for coupled multi-agent systems in a decentralized manner. A discrete model which captures the motion capabilities of each agent is derived over a bounded time-horizon, by discretizing a corresponding overapproximation of the agent’s reachable states. The individual abstractions’ composition provides a correct representation of the coupled continuous

We consider a linear system affected by an additive stochastic disturbance and address the design of a finite horizon control policy that is optimal according to some cost criterion and accounts also for probabilistic constraints on both the input and state variables. The resulting policy can be implemented over a receding horizon according to the model predictive control strategy. Such a possibility

The k-winners-take-all (kWTA) problem is to find the k largest inputs from N inputs. In this paper, we design and propose a novel distributed kWTA model, for which no central unit is needed to realize the computation of the k winners. As a result, the proposed model has the general advantages of distributed models over centralized ones, such as better robustness to faults of agents. The global asymptotic

This paper considers the problem of set-membership estimation for discrete-time linear time-varying descriptor systems subject to unknown but bounded disturbance and noise. We propose a set-membership estimation method based on a descriptor system observer and a zonotopic estimator of the observer error bounds. The observer parameters are optimized in order to minimize the sizes of the zonotopes enclosing

The paper presents a novel strategy to control the instantaneous rotational velocity of a planar slider subject to a soft contact with friction and to external loads, including gravity. The approach is based on a novel model that combines the LuGre dynamic friction model with the limit surface concept for two main reasons. First, the limit surface allows considering both translational and rotational

This paper describes a new approach for identifying FIR models from a finite number of measurements, in the presence of additive and uncorrelated white noise. In particular, two different frequency domain algorithms are proposed. The first algorithm is based on some theoretical results concerning the dynamic Frisch scheme. The second algorithm maps the FIR identification problem into a quadratic eigenvalue

In this paper, the synchronization problem for networks over finite fields is investigated, which is a generalization of consensus and provides a new perspective for networks of agents with limited capacities of memory and communication. It is assumed that the states and communication weights can only attain values from a finite alphabet equipped with a prime number of integers, termed finite fields

This paper studies the cooperative source seeking problem via a networked multi-vehicle system. In contrast to existing literature, the multi-vehicle system is controlled to the source position that maximizes aggregated multiple unknown scalar fields and each sensor-enabled vehicle only samples measurements of one scalar field. Thus, a single vehicle is unable to localize the source and has to cooperate