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In this paper, the coordination control problem of multi-agent systems (MASs) subjected to stealthy attacks and uncertainties is considered, where the uncertainties refer to unknown external disturbances and initial states. We consider a scenario in which the sensors are maliciously attacked, rendering the traditional interval observer's bounds ineffective for estimating the system states. By solving the linear programming problem, the maximum destructive attack sequences are generated. A distributed resilient interval observer composed of a resilient framer and a control protocol is designed, in which the construction of control protocol for each agent depends on the framer information of its own and its neighbors. It is demonstrated by the cooperativity theory and the Lyapunov stability theory that the distributed resilient interval observer can not only realize interval-valued state estimation for each agent but also drive the cooperative behavior of MASs. In addition, the observer gain matrix is selected and optimized by solving a semi-definite programming problem to provide tighter bounds for each agent. Meanwhile, the bounds of stealthy attacks are calculated. Finally, through a simulation example, the superiority of the distributed resilient interval observer and the effectiveness of the resilient interval observer-based consensus control algorithms are validated. [ABSTRACT FROM AUTHOR]

This paper presents a novel backstepping formation control strategy for multiple Euler–Lagrange (EL) systems. To enhance parallel communication capability, the communication channels for systems' position vectors and filters' states are independent. Subsequently, the corresponding dynamic event-triggered mechanisms are designed specifically for them to reduce the frequency of interactive communication networks, and a distributed filter is devised to eliminate the non-differentiability problem of event-triggered signals, respectively. Furthermore, we introduce a new barrier Lyapunov function (BLF) to indirectly restrict the velocity vector. The key novelty of this BLF is that the controller gain matrix caused by the designed BLF can be approximated as an identity matrix, when the distance between the velocity component and the designed boundary is substantial. To prevent the designed dynamic event-triggered mechanisms from being triggered infinitely for a period of time, Zeno behavior is excluded. By leveraging Lyapunov stability theory and Barbalat lemma, we demonstrate that all signals of the closed-loop system are bounded and the formation error asymptotically converges to the origin. Finally, simulation results are provided to demonstrate the efficacy of the proposed control schemes. [ABSTRACT FROM AUTHOR]

This paper is concerned with designing two-dimensional event generators and sliding mode controllers for discrete-time two-dimensional systems described by the celebrated Roesser model with external mismatched disturbance. First of all, aimed at the characteristics of the Roesser model, the horizontal and vertical disturbance observers and sliding surface functions are established for the addressed two-dimensional systems, respectively. Then based on the disturbance estimation and rejection technique, a modified reaching law and its corresponding sliding mode controller are designed to achieve the system robustness and disturbance attenuation. To reduce the resource usage, the event-triggered strategy is further incorporated in the design of sliding mode control law. Moreover, the stability of the sliding-mode dynamics is analyzed by resorting to the Lyapunov stability theory. Finally, a simulation example is presented to verify the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

In this paper, we consider a constrained distributed optimization problem for multi-integrator agent systems with mixed neighbor interactions, where the neighbors of the agents can be classified as cooperative or noncooperative by introducing a cooperation-competition network into the modeling of the communication graph. The agent's goal is to optimize the total objective function of the cooperators. Since agents can only communicate with their neighbors, they are unable to obtain complete information about cooperators. The distributed optimization algorithm is proposed to classify cooperative subnetworks by introducing additional auxiliary variables, and the outputs of all agents exponentially converge to the optimal solution of the optimization problem under the condition of satisfying the global equality constraint of the subnetwork. The Lyapunov stability theory is used to analyze the algorithm's convergence. Simulation results show the effectiveness of the proposed algorithm in two examples of economic dispatch in smart grids and optimal area coverage in multi-sensor networks. [ABSTRACT FROM AUTHOR]

Reduction theorems provide a framework for stability analysis that consists in breaking down a complex problem into a hierarchical list of subproblems that are simpler to address. This paper investigates the following reduction problem for time-varying ordinary differential equations on R n. Let Γ 1 be a compact set and Γ 2 be a closed set, both positively invariant and such that Γ 1 ⊂ Γ 2 ⊂ R n . Suppose that Γ 1 is uniformly asymptotically stable relative to Γ 2. Find conditions under which Γ 1 is uniformly asymptotically stable. We present a reduction theorem for uniform asymptotic stability that completely addresses the local and global version of this problem, as well as two reduction theorems for uniform stability and either local or global uniform attractivity. These theorems generalize well-known equilibrium stability results for cascade-connected systems as well as previous reduction theorems for time-invariant systems. We also present Lyapunov characterizations of the stability properties required in the reduction theorems that to date have not been investigated in the stability theory literature. [ABSTRACT FROM AUTHOR]

This paper studies distributed resource allocation problems of multi-agent systems, where the decisions of agents are subject to inequality network resource constraints and local inequality constraints. Compared with well-known resource allocation problems, our problem considers the high-order dynamics of agents. Without involving the control of high-order dynamics, existing distributed resource allocation algorithms cannot deal with our problem. Meanwhile, the high-order dynamics together with the inequality constraints makes it difficult to design and analyze distributed resource allocation algorithms, because the outputs of agents cannot be decided by their inputs directly and the optimal decisions of agents must satisfy the inequality constraints. In order to control the high-order agents to accomplish the resource allocation tasks autonomously, a distributed algorithm is designed by state feedback, gradient descent and primal–dual methods. Moreover, the convergence of the algorithm is analyzed by convex analysis and Lyapunov stability theory. With the algorithm, the high-order agents converge to the optimal allocation. Finally, numerical simulations verify the effectiveness of the algorithm. [ABSTRACT FROM AUTHOR]

In this paper, we study the noncooperative games of multi-agent systems. Different from the well-known noncooperative games, our problem involves not only the coupling inequality constraints and the local inequality constraints of decisions, but also the second-order dynamics of players. Due to the second-order dynamics and the inequality constraints, existing generalized Nash equilibrium seeking algorithms for noncooperative games cannot solve our problem. Besides, the second-order dynamics together with the inequality constraints give rise to the difficulties in distributed algorithm design and analysis. In order to seek the variational generalized Nash equilibrium of the games, we design a distributed algorithm based on gradient descent, state feedback and projection operations. Moreover, we analyze the asymptotic convergence of the algorithm via variational analysis and Lyapunov stability theory. Finally, two examples verify the effectiveness of the algorithm. [ABSTRACT FROM AUTHOR]

This paper presents an on-line parametric estimation method for robot manipulators. The identification algorithm estimates the parameters by using the input error between the robot and a parallel estimated model. Both, the robot and the estimated model are controlled by two Proportional–Derivative (PD) controller tuned with the same gain values, and a persistent excitation (PE) signal for ensuring parameters convergence is included. The exact model matching and the estimation error cases are analysed. Noisy state measurements and filters are avoided in the model parameterization by using only the states of the estimated model. A second parameter identification algorithm, which is based on a composite update law, is also proposed. It improves parameters convergence and robustness of the update rule in presence of estimation errors. The stability of the closed-loop dynamics related to the estimated model is assessed via Lyapunov stability theory. Simulations are carried out to validate the proposed approaches. [ABSTRACT FROM AUTHOR]

This paper studies the problem of generalized Nash equilibrium seeking in population games under general affine equality and convex inequality constraints. In particular, we design a novel payoff dynamics model to steer the decision-making agents to a generalized Nash equilibrium of the underlying game, i.e., to a self-enforceable state where the constraints are satisfied and no agent has incentives to unilaterally deviate from her selected strategy. Moreover, using Lyapunov stability theory, we provide sufficient conditions to guarantee the asymptotic stability of the corresponding equilibria set in stable population games. Auxiliary results characterizing the properties of the equilibria set are also provided for general continuous population games. Furthermore, our theoretical developments are numerically validated on a Cournot game considering various market-related and production-related constraints. [ABSTRACT FROM AUTHOR]

The event-triggered fault detection problem for nonlinear semi-Markov jump systems constructed by Takagi–Sugeno fuzzy approach is studied in this paper. Owing to that the premise variables and the modes are usually mismatched for both the filter and the plant in actual network environment, i.e., the double asynchronous phenomenon, a novel double asynchronous fault detection filter is designed to take the place of the traditional filter and tackle the fault detection problem for fuzzy semi-Markov jump systems. Particularly, the event-triggered scheme is considered to reduce the waste of communication resources, which gives rise to the premise variables asynchronous phenomenon for the plant and the filter. The modes information of the fuzzy semi-Markov jump systems is not always instantaneously accessible, which leads to the mode asynchronous phenomenon for the plant and the filter. This mode asynchronous phenomenon is described by a hidden semi-Markov model. Based on Lyapunov stability theory, the sufficient conditions are developed to ensure that the system not only is stochastically stable and meets an H ∞ performance, but also can make sure that the filter gains could be captured. Finally, an illustrative tunnel diode circuit example is provided to show the effectiveness of proposed approach. [ABSTRACT FROM AUTHOR]

Abstract: This paper addresses stability analysis of closed-loop sampled-data piecewise affine (PWA) slab systems. In particular, we study the case in which a PWA plant is in feedback with a discrete-time emulation of a PWA controller. We consider the sampled-data system as a continuous-time system with a variable time delay. The contributions of this work are threefold. First, we present a modified Lyapunov–Krasovskii functional (LKF) for studying PWA systems with time delays that is less conservative when compared to previously suggested alternatives. Second, based on the new LKF, sufficient conditions are provided for asymptotic stability of sampled-data PWA slab systems to the origin. These conditions become Linear Matrix Inequalities (LMIs) in the case of a piecewise linear (PWL) controller. Finally, we present an algorithm for finding a lower bound on the maximum delay that preserves asymptotic stability. Therefore, the output of the algorithm provides an upper bound on the minimum sampling frequency that guarantees asymptotic stability of the sampled data system. The new results are successfully applied to a unicycle example. [Copyright &y& Elsevier]

Abstract: In this paper we derive necessary and sufficient conditions for the existence of a common linear co-positive Lyapunov function for a finite set of linear positive systems. Both the state dependent and arbitrary switching cases are considered. Our results reveal an interesting characterisation of “linear” stability for the arbitrary switching case; namely, the existence of such a linear Lyapunov function can be related to the requirement that a number of extreme systems are Metzler and Hurwitz stable. Examples are given to illustrate the implications of our results. [Copyright &y& Elsevier]

This paper deals with sliding mode control for networked Markovian jump systems with partially-known transition probabilities via an event-triggered scheme to reduce network bandwidth usage and save network resources. First, based on the analysis of event-triggered scheme and sliding mode control, a corresponding time-delay system model is constructed by investigating the effect of the network transmission delay. Then, the less-conservative mean-square asymptotic stability of the overall closed-loop system is established. Sufficient conditions are obtained to co-design both the switching function and trigger parameters. Simultaneously, a novel control scheme is used to handle the Markovian jump parameters. Cases of completely known or unknown probabilities transition probabilities are also presented. Furthermore, the reachability of the sliding surface under the event-triggered sliding mode controller is analyzed using the Lyapunov stability theory. Finally, simulation results are provided to verify the effectiveness of the proposed design schemes. [ABSTRACT FROM AUTHOR]

This paper presents two distributed event-triggered algorithms under directed communication networks to solve a class of convex optimization problems such as the economic dispatch problem (EDP) with equality constraint, while the objective of optimization is the sum of all locally convex functions. One is distributed continuous-time event-triggered optimization algorithm, and the other is discrete-time algorithm based on iteration scheme. Continuous communication is not required by adopting event-triggered communication strategy. It means that the communication cost can be reduced and unnecessary waste of network resources can be avoided. Moreover, the convergence for the proposed algorithms are rigorously proved with the aid of Lyapunov stability theory under the strongly connected and weight-balanced network topology. Finally, four numerical simulations show the effectiveness and advantages of the two novel distributed event-triggered optimization algorithms. [ABSTRACT FROM AUTHOR]

This paper addresses the stability problem for systems with state-dependent state delay (delay which involves the state of the system). Different from the time-dependent delay, the state dependence of the delay makes the value of delay dependent on the state change, which indicates that it is impossible to exactly know a priori how far in the history the state-information is needed. We apply the Lyapunov stability theory to obtain sufficient conditions for exponential stability of the zero equilibrium. Then we apply those results to some specific examples to illustrate the effectiveness of the approach and our general results. A class of stabilizing memoryless controllers for a second-order system with state-dependent state delay is also proposed. [ABSTRACT FROM AUTHOR]