Ahmed Rahmani

Bond graph aided design of controlled systems

Abstract An active or controlled system is generally composed of two parts: a passive basis and a control architecture containing actuators and sensors. When dealing with such a system, the first point usually considered is the study of the system without control. To do this, we need a model in order to get simulation-based results on the frequency domain and dynamical behaviour for dimensioning purpose. The second step is then to design a control architecture, with its actuators and sensors, specified in a way allowing the objectives to be reached as accurately and cheaply as possible. Since many years, the bond graph methodology has shown its qualities for modelling and generation of physical insight, specially when applied to multidisciplinary systems. The aim of this paper is to show how a bond graph model may be used for analysis of structural properties, i.e., properties depending only on the model structure and on the type of elements composing it, but not on the numerical values of the parameters. The properties pointed out in this way are generic, and can be used for “integrated design”, i.e., the simultaneous design of the passive system model, its control architecture and control laws for specific aims. The proposed methodology depends on causal manipulations on the bond graph model (assignment of integral and derivative causality, causal path and loops); its application may necessitate a return to the model in order to check and sometimes modify the modelling hypotheses. The proposed procedure is implemented on an example, which will be the guideline of the presentation.

Leader-follower formation control of nonholonomic mobile robots based on a bioinspired neurodynamic based approach

This paper investigates the leader-follower formation control problem for nonholonomic mobile robots based on a bioinspired neurodynamics based approach. The trajectory tracking control for a single nonholonomic mobile robot is extended to the formation control for multiple nonholonomic mobile robots based on the backstepping technique, in which the follower can track its real-time leader by the proposed kinematic controller. An auxiliary angular velocity control law is proposed to guarantee the global asymptotic stability of the followers and to further guarantee the local asymptotic stability of the entire formation. Also a bioinspired neurodynamics based approach is further developed to solve the impractical velocity jumps problem. The rigorous proofs are given by using Lyapunov theory. Simulations are also given to verify the effectiveness of the theoretical results.

Distributed leader-following consensus for second-order multi-agent systems with nonlinear inherent dynamics

In this paper, the leader-following consensus problem for second-order multi-agent systems with nonlinear inherent dynamics is investigated. Two distributed control protocols are proposed under fixed undirected communication topology and fixed directed communication topology. Some sufficient conditions are obtained for the states of followers converging to the state of virtual leader globally exponentially. Rigorous proofs are given by using graph theory, matrix theory and Lyapunov theory. Simulations are also given to verify the effectiveness of the theoretical results.

Distributed consensus-based formation control for multiple nonholonomic mobile robots with a specified reference trajectory

In this paper, the distributed formation control problem for multiple nonholonomic mobile robots using consensus-based approach is considered. A transformation is given to convert the formation control problem for multiple nonholonomic mobile robots into a state consensus problem. Distributed control laws are developed for achieving the formation control objectives: a group of nonholonomic mobile robots at least exponentially converge to a desired geometric pattern with its centroid moving along the specified reference trajectory. Rigorous proofs are provided by using graph, matrix , and Lyapunov theories. Simulations are also given to verify the effectiveness of the theoretical results.

Asynchronous decentralised event-triggered control of multi-agent systems

In this paper, the consensus problem of first-order multi-agent systems under linear asynchronous decentralised event-triggered control is investigated. Both undirected and directed topologies are considered. In the analysis, the closed-loop multi-agent systems with the event-triggered control are modelled as switched systems. After proposing the decentralised event-triggered consensus protocols, decentralised state-dependent event conditions are derived, which act as switching signals. The consensus analyses are performed based on graph theory and stability results of switched systems. Under the event-triggered control schemes presented, consensus is reached with enlarged sampling periods and no Zeno behaviour. Simulation examples are given to illustrate the effectiveness of the proposed theoretical results.

Adaptive distributed formation control for multiple nonholonomic wheeled mobile robots

This paper investigates the adaptive distributed formation control problem for multiple nonholonomic wheeled mobile robots. First, the formation control problem is converted into a state consensus problem by the aid of a variable transformation. Then, distributed kinematic controllers and adaptive dynamic controllers are developed for each robot such that a group of nonholonomic mobile robots asymptotically converge to a desired geometric pattern with its centroid moving along the specified reference trajectory. The specified reference trajectory is assumed to be the trajectory of a virtual leader whose information is available to only a subset of the followers. Also the followers are assumed to have only local interaction. Some sufficient conditions are derived for accomplishing the asymptotically stability of the systems based on algebraic graph theory, matrix theory, and Lyapunov control approach. Finally, simulation examples illustrate the effectiveness of the proposed controllers. HighlightsAdaptive distributed formation control for multiple nonholonomic wheeled mobile robots is investigated.Formation control problem is converted to a state consensus problem via a variable transformation.The specified reference trajectory is assumed to be the trajectory of a virtual leader whose information is available to only a subset of the followers.Distributed kinematic controllers are designed for guaranteeing to reach desired formation.Adaptive dynamic controllers are proposed for guaranteeing mobile robots to track theirs desired kinematic inputs.

Consensus with a reference state for fractional-order multi-agent systems

This paper investigates consensus of fractional-order multi-agent systems (MASs) with a reference state. First, a consensus control law with a constant reference state is given using graph theory and stability analysis of fractional-order. Then, a general control law and a particular one for consensus of fractional-order MASs with a time-varying reference state are proposed. Next, the above control laws are extended to solve formation tracking problem. Finally, several simulations are presented to verify the effectiveness of the obtained results.

Distributed formation control of fractional-order multi-agent systems with absolute damping and communication delay

The distributed formation control of fractional-order multi-agent systems is mainly studied under directed interaction topology in this paper. First, the control algorithm with absolute damping and communication delay is proposed to achieve the formation control. Then, some sufficient conditions are derived by using the matrix theory, graph theory and the frequency-domain analysis method. Finally, based on the numerical method of predictor–corrector, several simulations are presented to illustrate the effectiveness of the obtained results.

Comparison of multipath algorithms for load balancing in a MPLS network

Traffic Engineering aims to optimize the operational performance of a network. This paper focuses on multipath routing for traffic engineering that routes the demand on multiple paths simultaneously for balancing the load in the network. According to the schematic approach of multipath routing that we propose in this paper, a multipath routing algorithm selects candidate paths using multicriteria simultaneously and then distributes the traffic demand among selected paths. Among multipath routing algorithms, we select four algorithms which fit our expectations in terms of architecture: WDP, MATE, multipath-AIMD and LDM. We focused exclusively on technologies designed for MPLS networks. Each algorithm is compared with respect to complexity and stability of two stages: the computation of multiple paths and the traffic splitting among multiple paths.

Pole assignment for systems modelled by bond graph

Abstract In this paper, the pole assignment problem is considered for linear systems modelled by bond graphs. A procedure for the formal determination of the controllability matrix is proposed. This matrix is used to transform the state and control matrices into a controllability form. It allows us to formally assign the poles of the system.