Operational space consensus of multiple heterogeneous robots without velocity measurements

This paper proposes a control algorithm for networks of multiple heterogeneous robot manipulators, which solves the leader–follower and the leaderless consensus problems in the operational space. In the leader–follower scenario, the controller ensures that all the robots in the network asymptotically reach a given leader pose (position and orientation), provided that, at least, one follower robot has access to the leader pose. Without a leader pose, in the leaderless problem, the robots asymptotically reach a pose of consensus. The controller is a simple distributed proportional plus damping injection (P+d) scheme which does not require velocity measurements. A singularity-free representation, unit quaternions, is used to describe the orientation of each manipulator. The paper presents some simulations, with a network of six 6-Degrees-of-Freedom (DoF) manipulators, and experiments, with a network of three 6-DoF manipulators, to show the effectiveness of the proposed controller.     

Dynamic output feedback sliding mode control for spacecraft hovering without velocity measurements

In consideration of target angular velocity uncertainty and external disturbance, a modified dynamic output feedback sliding mode control (DOFSMC) method is proposed for spacecraft autonomous hovering system without velocity measurements. As a stepping-stone, an additional dynamic compensator is introduced into the design of sliding surface, then an augmented system is reconstructed with the system uncertainty and external disturbance. Based on the linear matrix inequality (LMI), a sufficient condition is given, which guarantees the disturbance attenuation performance of sliding mode dynamics. By introducing an auxiliary variable, a modified version of adaptive sliding mode control (ASMC) law is designed, and the finite-time stability of sliding variable is established by the Lyapunov stability theory. Compared with other results, the proposed method is less conservative and can decrease the generated control input force significantly. Finally, two simulation examples are performed to validate the effectiveness of the proposed method.     

Explicit condition for consensus of third-order discrete-time multi-agent systems without accelerated velocity measurements

This paper investigates the consensus problem for third-order discrete-time multi-agent systems in directed networks. For the case when each agent can only receive the information of position and velocity from its neighbors, necessary and sufficient conditions for consensus have been proposed. In contrast to the preceding work, we not only present the exact consensus value, but also illustrate the influence of scaling parameters and nonzero eigenvalues of the involved Laplacian matrix on consensus. Two numerical examples are given to demonstrate the effectiveness of the obtained results.     

Cooperative pointing control of collinear double-integrators without angular velocity

We deal with the cooperative pointing control problem of collinear double-integrators with unknown rotational inertia in this paper. In particular, we consider the case that the rotational angular velocity information is not available for this coordination task. First, we propose a cooperative pointing control protocol without using the rotational angular velocity measurements. By means of the passivity tool, a distributed estimation scheme is devised to access the relative rotational angular velocity information at each agent via the relative rotational angle information of the agent and its left and respectively right neighbors. Subsequently, we redesign the cooperative pointing control protocol as well as the distributed estimation scheme in the presence of saturated relative rotational angle information. It turns out that, here the unknown rotational inertia does not prevent the coordination task because of the bidirectional interactions. Meanwhile, two local estimation schemes are also presented respectively for the above two control protocols. Besides the rigorous convergence analysis, the effectiveness of our obtained theoretical results is illustrated through numerical simulations.     

Stability analysis of nonlinear Hadamard fractional differential system

The stability of the zero solution of a class of nonlinear Hadamard type fractional differential system is investigated by utilizing a new fractional comparison principle. The novelty of this paper is based on some new fractional differential inequalities along the given nonlinear Hadamard fractional differential system. A comparison principle employing the new fractional differential inequality for scalar Hadamard fractional differential system is presented. Based on the new comparison principle, some sufficient conditions for the (generalized) stability and the (generalized) Mittag-Leffler stability are given.     

Design of digital controllers for uncertain chaotic systems using fuzzy logic

A new and systematic method to design digital controllers for uncertain chaotic systems with structured uncertainties is presented in this paper. Takagi-Sugeno (TS) fuzzy model is used to model the chaotic dynamic system, while the uncertainties are decomposed such that the uncertain chaotic system can be rewritten as a set of local linear models with an additional disturbed input. Conventional control techniques are utilized to develop the continuous-time controllers first. Then, the digital controllers are obtained as the digital redesign of the continuous-time controllers using the state-matching approach. The performance of the proposed controller design is illustrated through numerical examples.     

Stability criteria for certain classes of nonlinear difference equations

The general mth order difference equation X(n+m)+a₁X(n+m?1)+…+a_mX(n) = F[n,X(n),…,X(n+m?1)] is considered. The stability properties of its solutions are studied using the discrete form of Liapunov's direct method. A quadratic form is selected as a possible Liapunov function V(n,X) and a scheme is developed for determining appropriate conditions on this function to insure that its total difference ΔV(n,X) is negative semi-definite or negative definite with respect to the difference equation. The approach is applied to the fourth-order difference equation in full detail to illustrate the method for determining the conditions which imply either uniform stability or uniform asymptotic stability and specific results are obtained. Several comments on, and extensions of, the work done by Puri and Drake for the cases m = 2 and m = 3 are presented.The results of the present approach in the homogeneous case where F[n,X(n),…,X(n+m?1)] = 0 are compared with the usual Schur-Cohn criteria and are shown to be at least as good.     

Stability analysis of nonlinear control systems with characteristics equations having complex coefficients

In this paper, the stability equation method is applied to the analysis of nonlinear systems with characteristics equations having complex coefficients. Three types of systems are studied: those with unstable open-loop poles, unstable characteristics roots or an equal number of open-loop poles and zeros.     

Stability criteria of a class of nonlinear impulsive switching systems with time-varying delays

This paper investigates stability problems of a class of nonlinear impulsive switching systems with time-varying delays. Based on the common Lyapunov function method and Razumikhin technique, several stability criteria are established for nonlinear impulsive switching systems with time-varying delays. Our results show that switching systems can be stabilized by impulsive switching signals even if the system matrices are all unstable. In the absence of impulses, some of our results reduce to similar stability criteria for nonimpulsive switching systems in some recent research articles. Several examples with simulations are given to illustrate the efficiency of our results.     

Stability analysis of a class of stochastic differential delay equations with nonlinear impulsive effects

In this paper, we study stability of a class of stochastic differential delay equations with nonlinear impulsive effects. First, we establish the equivalent relation between the stability of this class of stochastic differential delay equations with impulsive effects and that of a corresponding stochastic differential delay equations without impulses. Then, some sufficient conditions ensuring various stabilities of the stochastic differential delay equations with impulsive effects are obtained. Finally, two examples are also discussed to illustrate the efficiency of the obtained results.     

Design of optimal strictly positive real controllers using numerical optimization for the control of flexible robotic systems

The design of optimal strictly positive real (SPR) controllers using numerical optimization is considered. We focus on how to parameterize the SPR controllers being optimized and the effect of parameterization. Minimization of the closed-loop H₂-norm is the optimization objective function. Various single-input single-output and multi-input multi-output controller parameterizations using transfer functions/matrices and state–space equations are considered. Depending on the controller form, constraints are enforced (i) using simple inequalities guaranteeing SPRness, (ii) in the frequency domain or, (iii) by implementing the Kalman–Yakubovich–Popov Lemma. None of the parameterizations we consider foster an observer-based controller structure. Simulated control of a single-link and a two-link flexible manipulators demonstrates the effectiveness of our proposed controller optimization formulations.     

A reset observer with discrete/continuous measurements for a class of fuzzy nonlinear systems

This paper proposes the design of a reset fuzzy observer for the class of nonlinear systems able to be described by a Takagi–Sugeno fuzzy model. The observer uses both continuous and discrete measurements and in contrast with the observers based on the First Order Reset Element (FORE), it updates its states resetting the initial condition of the integrator at each instant when the discrete measurements are available. The proposed fuzzy observer is applied to estimate the substrate and biomass concentration of an anaerobic wastewater treatment process and the effectiveness of the proposed method is tested by simulations comparing the results of a reset fuzzy observer with two fuzzy observers using continuous measurements only. Finally, the estimation scheme is validated using experimental data from an actual anaerobic digestion process, suggesting that the proposed reset fuzzy observer is a practical and encouraging approach to the state estimation of the class nonlinear processes under study.     

Stability of a forced system with a single nonlinear element in the feedback path

This paper presents a numerical technique to determine the stability of a nonlinear feedback control system with a single nonlinear element in the feedback path. By expressing the output explicitly in terms of the input the bounded inputand bounded output stability criterion of the nonlinear system is investigated.     

一个无单向Hash函数的签名方案的安全性分析

2004年,Chang等提出了一种不使用单向Hash函数和消息冗余度的数字签名方案。但是Zhang指出他们的方案存在伪造攻击。为了克服Zhang的攻击,Zhang等基于Chang的签名方案提出了一个改进方案,并且对改进的签名方案进行了安全性分析。然而,通过给出一种简单的攻击,指出Zhang等的方案仍是不安全的。为了抵抗这种攻击,Hash函数和消息冗余度可能仍旧需要作用。     

Fixed-time bipartite consensus of nonlinear multi-agent systems using event-triggered control design

This paper focuses on designing a leader-following event-triggered control scheme for a category of multi-agent systems with nonlinear dynamics and signed graph topology. First, an event-triggered controller is proposed for each agent to achieve fixed-time bipartite consensus. Then, it is shown that the Zeno-behavior is rejected in the proposed algorithm. To avoid intensive chattering due to the discontinuous controller, the control protocol is improved by estimating the sign function. Moreover, a triggering function is proposed which avoids continuous communication in the event-based strategy. Finally, numerical simulations are given to show the accuracy of the theoretical results.     

Velocity field control of robot manipulators by using only position measurements

In the velocity field control approach the robot motions are specified through a vectorial function that assigns the desired velocity to each point of the configuration space. In other words, a velocity field defines the robot desired velocity in the operational space as a function of its current position. In this paper is introduced a new algorithm to solve the velocity field control formulation in the robot operational space. The proposed approach assumes only joint position measurements and is based on a hierarchical structure that results of using the kinematic control concept and a joint velocity controller. To estimate the joint velocity, nonlinear filtering of the joint position is used.