Designing a reasonable M/G/1 retrial queue system that enhances service efficiency and reduces energy consumption is a challenging issue in Information and Communication Technology systems. This paper presents an M/G/1 retrial queue system incorporating random working vacation (RWV) and improved service efficiency during vacation (ISEV) policies, and examines its optimal queuing strategies. The RWV policy suggests that the server takes random working vacations during reserved idle periods, effectively reducing energy consumption. In contrast, the ISEV policy strives to augment service efficiency during regular working periods by updating, inspecting or maintaining the server on vacations. The system is transformed into a Cauchy problem to investigate its well-posedness and stability, employing operator semigroup theory. Based on the system’s stability, steady-state performance measures, such as service efficiency, energy consumption and expected costs, are quantified using the steady-state solution. The paper subsequently demonstrates the existence of optimal queuing strategies that achieve maximum efficiency and minimum expected costs. Finally, two numerical experiments are provided to illustrate the effectiveness of the system.

Multidimensional linear hyperbolic systems with constraints and delay are considered. The existence and uniqueness of solutions for rough data are established using Friedrichs method. With additional regularity and compatibility on the initial data and initial history, the stability of such systems are discussed. Under suitable assumptions on the coefficient matrices, we establish standard or regularity-loss type decay estimates. For data that are integrable, better decay rates are provided. The results are applied to the wave, Timoshenko, and linearized Euler–Maxwell systems with delay.

In this paper, we are interested in investigating notions of stability for generalized linear differential equations (GLDEs). Initially, we propose and revisit several definitions of stability and provide a complete characterization of them in terms of upper bounds and asymptotic behaviour of the transition matrix. In addition, we illustrate our stability results for GLDEs to linear periodic systems and linear impulsive differential equations. Finally, we prove that the well-known definitions of uniform asymptotic stability and variational asymptotic stability are equivalent to the global uniform exponential stability introduced in this article.

In this study, we are concerned with the asymptotic stability towards a rarefaction wave of the solution to an outflow problem for the Navier-Stokes Korteweg equations of a compressible fluid in the half space. We assume that the space-asymptotic states and the boundary data satisfy some conditions so that the time-asymptotic state of this solution is a rarefaction wave. Then we show that the rarefaction wave is non-linearly stable, as time goes to infinity, provided that the strength of the wave is weak and the initial perturbation is small. The proof is mainly based on $L^{2}$-energy method and some time-decay estimates in $L^{p}$-norm for the smoothed rarefaction wave.

This paper addresses robust stability and position tracking problems in teleoperation systems subject to varying delay in the communication medium, uncertainties in the models of manipulators, and non-passive interaction forces in the terminations. Fixed-structure nonlinear control law is developed based on the notion of Interconnection and Damping Assignment Passivity-Based Control (IDA-PBC) scheme. Then, utilizing the Lyapunov–Krasovskii theorem, sufficient conditions are derived in terms of Linear Matrix Inequalities (LMIs) to tune the controller parameters. Differently from literature, the objectives are achieved without requirement for any passive parts in the model of interaction forces. Comparative simulations and experimental results demonstrate the applicability and superiority of the proposed method.

We prove by the Hilbert–Mumford criterion that a slope stable polarized weighted pointed nodal curve is Chow asymptotic stable. This generalizes the result of Caporaso on stability of polarized nodal curves and of Hassett on weighted pointed stable curves polarized by the weighted dualizing sheaves. It also solves a question raised by Mumford and Gieseker, to prove the Chow asymptotic stability of stable nodal curves by the Hilbert–Mumford criterion.

This paper formulates a new scalable algorithm for motion planning and control of multiple point-mass robots. These autonomous robots are designated to move safely to their goals in a priori known workspace cluttered with fixed and moving obstacles of arbitrary positions and sizes. The control laws proposed for obstacle and collision avoidance and target convergence ensure that the equilibrium point of the given system is asymptotically stable. Computer simulations with the proposed technique and applications to a team of two planar (RP) manipulators working together in a common workspace are presented. Also, the robustness of the system in the presence of noise is verified through simulations.

This paper concerns the numerical stability of an eikonal transformation based splitting method which is highly effective and efficient for the numerical solution of paraxial Helmholtz equation with a large wave number. Rigorous matrix analysis is conducted in investigations and the oscillation-free computational procedure is proven to be stable in an asymptotic sense. Simulated examples are given to illustrate the conclusion.

We investigate the stability properties of Muth's model of price movements when agents choose a production level using replicator dynamic learning. It turns out that when there is a discrete set of possible production levels, possible stable states and stability conditions differ between adaptive learning and replicator dynamic learning.

In this paper a new sliding mode controller for set-point control of robot manipulators is proposed. The controller does not use any part of the robot dynamics in the control law. Thus, it is structurally simpler than other sliding mode controllers where the control law uses a nominal model of the robot dynamics. The controller uses a new nonlinear Proportional-Integral-Derivative (PID) sliding surface. The stability of the controlled robot dynamics is proved. On applying the boundary-layer approach to remove chattering, a nonlinear PID controller exists inside the boundary layer. This PID controller ensures that the error tend to zero asymptotically if there is no disturbances applied to the robot dynamics.

In this paper, we introduce a new method for feedback controller design for the complex distributed parameter networks governed by wave equations, which ensures the stability of the closed loop system. This method is based on the uniqueness theory of ordinary differential equations and cutting-edge approach in the graph theory, but it is not a simple extension. As a realization of this idea, we investigate a bush-type wave network. The well-posedness of the closed loop system is obtained via Lax-Milgram’s lemma and semigroup theory. The validity of cutting-edge method is proved by spectral analysis approach. In particular, we give a detailed procedure of cutting-edge for the bush-type wave networks. The results show that if we impose feedback controllers, consisting of velocity and position terms, at all the boundary vertices and at most three velocity feedback controllers on the cycle, the system is asymptotically stabilized. Finally, some examples are given.

Being a unique phenomenon in hybrid systems, mode switchis of fundamental importance in dynamic and control analysis. Inthis paper, we focus on global long-time switching and stabilityproperties of conewise linear systems (CLSs), which are a class oflinear hybrid systems subject to state-triggered switchingsrecently introduced for modeling piecewise linear systems. Byexploiting the conic subdivision structure, the “simple switchingbehavior” of the CLSs is proved. The infinite-time mode switchingbehavior of the CLSs is shown to be critically dependent on twoattracting cones associated with each mode; fundamental propertiesof such cones are investigated. Verifiable necessary andsufficient conditions are derived for the CLSs with infinite modeswitches. Switch-free CLSs are also characterized by exploringthe polyhedral structure and the global dynamical properties. Theequivalence of asymptotic and exponential stability of the CLSs isestablished via the uniform asymptotic stability of the CLSs thatin turn is proved by the continuous solution dependence on initialconditions. Finally, necessary and sufficient stability conditionsare obtained for switch-free CLSs.

For the trajectory following problem of a robot manipulator, a robust estimation and control scheme which requires only position measurements is proposed to guarantee uniform ultimate bounded stability under significant uncertainties and disturbances in the robot dynamics. The scheme combines a class of robust control laws with a robust estimator where the robust control law can be chosen to be either a modification of the standard computed torque control law or simply a linear and decentralized “PD” control law. The proposed robust estimator is also linear and decentralized for easy implementation. Constructive choices of the gains in the control law and estimator are proposed which depend only on the coefficients of a polynomial bounding function of the unknown dynamics. The asymptotic stability of the tracking errors and the estimation error is also investigated. Experimentation results verify the theoretical analysis.

The fundamentals of an approach to solving the control task of robots interaction with a dynamic environment based on the stability of a closed-loop control system are given in this paper. The task is set and solved in its general form. The traditional control concept of compliant robot motion—the hybrid position/force control is discussed. In the paper the proposed control laws ensure simultaneous stabilization of both the desired robot motion and the desired interaction force, as well as their required quality of transient responses. In order to emphasize the fundamental point of this approach in controlling the contact tasks in robotics, the authors have assumed ideal parameters of interacting dynamic systems. The proposed control procedure is demonstrated by one simple example.

We investigated and identified the conditions necessary for stable dynamic gait generation in biped robots from the mechanical energy balance point of view. The equilibrium point at impact in a dynamic gait is uniquely determined by two conditions; keeping the restored mechanical energy constant and settling the relative hip-joint angle to the desired value before impact. The generated gait then becomes asymptotically stable around the equilibrium point determined by these conditions. This is shown by a simple recurrence formula of the kinetic energy immediately before impact. We verified this stability theorem using numerical simulation of virtual passive dynamic walking. The results were compared with those for a rimless wheel and an inherent stability principle was derived. Finally, we derived a robust control law using a reference mechanical energy trajectory and demonstrated its effectiveness numerically.

A k-out-of-N:G reparable system with an arbitrarily distributed repair time is studied in this paper. We translate the system into an Abstract Cauchy Problem (ACP). Analysing the spectrum of the system operator helps us to prove the well-posedness and the asymptotic stability of the system.

A direct construction of a stabilizing hybrid feedback that is robust togeneral measurement error is given for a general nonlinear control system that is asymptotically controllable to a compact set.

This paper proposes a stable control structure for the bilateral teleoperation of mobile robots. The proposed control structure includes a time-delay compensation placed on both the local and remote sites of the teleoperation system. To illustrate the performance and stability of the proposed control structure, experiences on a Pioneer 2DX mobile robot teleoperated through a commercial joystick with visual feedback, are shown.

In this paper we study linear conservative systems of finitedimensioncoupled with an infinite dimensional system of diffusive type. Computing the time-derivative of anappropriate energy functional along the solutions helps us toprove the well-posedness of the systemand a stability property.But in order to prove asymptotic stability we need to applya sufficient spectral condition. We also illustrate the sharpness of thiscondition by exhibiting some systems for which we do not have the asymptoticproperty.