Sid Ahmed Attia

Max-consensus in a max-plus algebraic setting: The case of fixed communication topologies

Consensus algorithms have been studied in the field of distributed computing for decades. Recently consensus algorithms have attracted renewed attention because they can be exploited for distributed cooperative control. The purpose of this paper is the analysis of a specific class of consensus algorithms called max-consensus. This class of algorithms is needed for applications such as minimum time rendezvous and leader election. A new approach using max-plus algebra is proposed to analyze convergence of max-consensus algorithm. In this paper we focus on the problem of achieving max-consensus in time-invariant communication topologies. Conditions to achieve max-consensus are discussed and the convergence rate of the algorithm for different communication topologies is studied.

On the Maximum Principle for Impulsive Hybrid Systems

In this contribution, we consider a class of hybrid systems with continuous dynamics and jumps in the continuous state (impulsive hybrid systems). By using a newly elaborated version of the Pontryagin-type Maximum Principle (MP) for optimal control processes governed by hybrid dynamics with autonomous location transitions, we extend the necessary optimality conditions to a class of Impulsive Hybrid Optimal Control Problems (IHOCPs). For these problems, we obtain a concise characterization of the Impulsive Hybrid MP (IHMP), namely, the corresponding boundary-value problem and some additional relations. As in the classical case, the proposed IHMP provides a basis for diverse computational algorithms for the treatment of IHOCPs.

SUB OPTIMAL CONTROL OF SWITCHED NONLINEAR SYSTEMS UNDER LOCATION AND SWITCHING CONSTRAINTS

Abstract This paper considers an optimal control problem for switched nonlinear systems. The objective is to minimize an associated cost functional, by finding an appropriate continuous control input and location switching strategy. We propose an extension of an algorithm based on strong variations to handle constraints on both locations and switching instants. Numerical experiments testify the viability and the tractability of such a scheme.

On an Optimization Problem for a Class of Impulsive Hybrid Systems

This contribution addresses the problem of optimal control for a class of hybrid systems, where discrete transitions are accompanied by instantaneous changes in the continuous state variables, and where these changes can be considered as control variables. Based on a variational approach, necessary conditions of optimality are first established. The problem is then cast as a parametric optimization problem for which gradient information is derived. Finally, we discuss assumptions that guarantee convergence of a conceptual algorithm to a stationary solution. A brief discussion on the main implementation issues is also included.

Intelligent Control of an Induction Motor

Induction motors are characterized by complex, highly nonlinear, and time-varying dynamics and inaccessibility of some states and outputs for measurements, and hence may be considered as a challenging engineering problem. The advent of vector control techniques has partially solved induction motor control problems because they are sensitive to drive parameter variations and performance may deteriorate if fixed parameter controller are used. Fuzzy logic-based controllers are considered as potential candidates for such application. This paper presents some design approaches of intelligent control systems combining conventional control techniques with fuzzy logic and neural networks. Such a hybrid implementation leads to a more effective control design with improved system performance and robustness. While conventional control allows different design objectives, such as steady state and transient characteristics of the closed-loop system to be specified, fuzzy logic techniques are integrated to overcome the problems with uncertainties in the plant parameters and structure encountered with classical model-based design. Two control approaches are developed and applied to adjust the speed of the drive system. The first control design combines the variable structure theory with fuzzy logic concept. In the second approach, a fuzzy state feedback controller is developed based on pole placement technique. A simulation study of these methods is presented. The effectiveness of these controllers is demonstrated for different operating conditions of the drive system.

Consensus for double integrator dynamics in heterogeneous networks

In this paper we study topological properties of consensus algorithms for agents with double integrator dynamics communicating over networks modeled by undirected graphs. Unlike existing work we drop the assumption that the positions and the velocities of the agents are shared along homogeneous communication networks. In fact, our main result is that consensus can be achieved even though the networks along which position and velocity information is shared are different, and not even connected. We further provide insights on consensus rate based only on the topological properties of the network and show that unlike in homogeneous networks, consensus type cannot be changed by introducing gains.

Necessary optimality conditions for a class of hybrid optimal control problems

In this paper we study a class of Mayer-type hybrid optimal control problems. Using Lagrange techniques, we formulate a version of the Hybrid Maximum Principle for optimal control problems governed by hybrid systems with autonomous location transitions in the presence of additional target constraints.

State Jump Optimization for a Class of Hybrid Autonomous Systems

In this contribution, optimization of state jumps for a class of hybrid systems is considered. Basically, the control variables to be determined are the amounts of jump in the continuous states such that a corresponding cost functional is minimized. Based on a variational approach, necessary conditions of optimality are first established. The problem is then cast as a parametric optimization problem where the gradient information is derived. Finally and under some assumptions, convergence to the optimal solution of a conceptual algorithm is established. A brief discussion on the main implementation issues is also included.

VOLTAGE COLLAPSE AVOIDANCE IN POWER SYSTEMS: A RECEDING HORIZON APPROACH

In this paper, a receding horizon control approach is developed for voltage stabilization in power systems. The primary focus is on a benchmark system proposed in the context of a European project. The system is termed hybrid due to the finite set of control inputs, state automata description of the voltage primary controller and their interactions with the load nonlinear continuous dynamics. Moreover, the network topology imposes hard constraints on the states. All these make the control problem quite challenging. For different realistic scenarios, the proposed control algorithm is shown to stabilize the bus voltages at acceptable levels. The computational demand fits the real time allowed slot, making the scheme attractive for large scale applications as an area central controller.

On leader election in multi-agent control systems

In this contribution, we discuss the election of an optimal leader out of a network of agents described by first integrator dynamics and running a consensus algorithm. The network of agents may be a group of autonomous robots or more generally communicating vehicles, and the target is, for instance, to move the formation to a new location. A leader is said to be optimal if it leads to a controllable network, and minimizes a quadratic cost of reaching a target for all the other agents of the network. In the first part, controllability conditions and a decentralized way of checking them are discussed. We then study the correlation between the value of a quadratic cost function measuring the leader performance and the network properties. Strong correlation is found between closeness and degree centrality indices of the agents and the cost of achieving the assigned tasks. This allows us to run the optimal leader election process without a central authority and without the nodes having full knowledge of the network topology.