Formation reconfiguration using model predictive control techniques for multi-Agent dynamical systems.

International audienceThe classical objective for multiple agents evolving in the same environment is the preservation of a predefined formation because it reinforces the safety of the global system and further lightens the supervision task. One of the major issues for this objective is the task assignment problem, which can be formulated in terms of an optimization problem by employing set-theoretic methods. In real time the agents will be steered into the defined formation via task (re)allocation and classical feedback mechanisms. The task assignment calculation is often performed in an offline design stage, without considering the possible variation of the number of agents in the global system. These changes (i.e., including/excluding an agent from a formation) can be regarded as a typical fault, due to some serious damages on the components or due to the operator decision. In this context, the present chapter proposes a new algorithm for the dynamical task assignment formulation of multi-agent systems in view of real-time optimization by including fault detection and isolation capabilities. This algorithm allows to detect whether there is a fault in the global multi-agent system, to isolate the faulty agent and to integrate a recovered/healthy agent. The proposed methods will be illustrated by means of a numerical example with connections to multi-vehicle systems

Positive invariant sets for fault tolerant multisensor control schemes

This article deals with fault tolerant multisensor control schemes for systems with linear dynamics. Positive invariance is a common analysis and control design tool for systems affected by bounded constraints and disturbances. This article revisits the construction of ε-approximations of minimal robust positive invariant sets for linear systems upon contractive set-iterations. The cases of switching between different sets of disturbances and the inclusion of a predefined region of the state space are treated in detail. All these results are used in multisensor control schemes which have to deal with specific problems originated by the switching between different estimators and by the presence of faults in some of the sensors. The construction of positive invariant sets for different operating regimes provides, in this context, effective fault detection information. Within the same framework, global stability of the switching strategies can be assured if the invariant sets topology allows the exclusive selection of estimates obtained from healthy sensors

A fault tolerant control scheme based on sensor-actuation channel switching and dwell time

The present paper deals with a switching control scheme for a plant with multiple estimator-controller-actuator pairs. The scheme has to deal with specific problems originated by the switching between the different feedback loops and accommodate to faults in the observation channels (sensors outputs). The main contribution is a fault tolerant switching scheme with stability guarantees assured by a pre-imposed dwell-time. The detection and the fault tolerance capabilities are assured through set separation for the residual signals corresponding to healthy and faulty functioning. Another contribution of the paper resides in a recovery technique for faulty sensors which makes use of a virtual sensor whose estimation, based on an optimization procedure, minimizes recovery time

On the structure of polyhedral positive invariant sets with respect to delay difference equations

International audienceThis chapter is dedicated to the study of the positive invariance of poly-hedral sets with respect to dynamical systems described by discrete-time delay difference equations DDE. Set invariance in the original state space, also referred to as D-invariance, leads to conservative definitions due to its delay independent property. This limitation makes the D-invariant sets only applicable to a limited class of systems. However, there exists a degree of freedom in the state-space transformations which can enable the positive invariant set-characterizations. In this work we revisit the set factorizations and extend their use in order to establish flexible set-theoretic analysis tools. With linear algebra structural results, it is shown that similarity transformations are a key element in the characterization of low complexity invariant sets within the class of convex polyhedral candidates. In short, it is shown that we can construct, in a low dimensional state-space, an invariant set for a dynamical system governed by a delay difference equation. The basic idea which enables the construction is a simple change of coordinates for the DDE. The obtained D-invariant set exists in the new coordinates even if its existence necessary conditions are not fulfilled in the original state space. This proves that the D-invariance notion is dependent on the state-space representation of the dynamics. It is worth to recall as a term of comparison that the positive invariance for delay-free dynamics is independent of the state-space realization