P. Bertrand

On the identifiability of linear state systems

Abstract The conditions are investigated that ensure the uniqueness of a linear state model with constant coefficients consistent with experimental data which correspond to some terms of the transition matrix. A simple study procedure is deduced from some properties of this matrix. It enables one to decide on the model identifiability, knowing only the order of the system and the place in the transition matrix of the known elements. The application of these results to compartmental models used in biology and chemistry is finally discussed.

A new operating method for the kinetic study of open systems by means of tracer elements

Abstract A new method for studying non-linear kinetics in an open reactor is described, including experimental, mathematical and numerical treatments. It is based on using a radioactive tracer for one of the reactants with the same kinetic properties. The tracer reactant is then included in the input flow in such a way that the sum of reactant and tracer reactant remains constant throughout the experiment. Thus no perturbation occurs when the tracer is added. It is shown that the non-linear initial system is reduced to a linear one for the tracer. The parameters of this tracer system are easily identified from experimental data, and then the parameters of the non-linear kinetics can be deduced.

Comments on "Identifiability of linear and nonlinear dynamical systems"

In this correspondence it is shown how one of the given procedures can be extended to check the global identifiability of linear state systems.

Approximate Aggregation of Interconnected Systems

Abstract In this communication, an approximate reduction method is proposed which leads to a reduced order model having essentially the same natural decomposition into interconnected sub-systems as the original one. The approach consists in first simplifying each subsystem and then reconstituting a global but reduced model of the system. It allows, whatever the real system topology, to keep the same structural information on the simplified model, and thus would yield simplified but meaningful control structures. As on illustration, the reduction of a nuclear reactor model is presented.

Reliable Flight Control Systems: Components Placement and Feedback Synthesis

Abstract For modern spacecraft and aircraft, reliable Flight Control Systems must be designed to provide some fault tolerance. The mission has to be carried out in the presence of failures. Jump Linear Quadratic systems are proposed as a suitable mathematical model and it is shown how control laws can be built with automatic reconfiguration and failure anticipation. A global approach to the design of reliable Flight Control Systems is outlined. It incorporates into a single analytical framework the three basic steps of the design, components selection, components location and control law synthesis, and provides a cost index that is sensitive to both reliability and performance issues.

A New Approach for Real-Time Control of Urban Traffic Networks

Abstract Using a new decomposition-coordination approach, an efficient design method for traffic regulation in congested network is presented. A simplified network model is chosen here for testing the proposed two-level structure which alleviates some of the difficulties encountered with classical methods. A local feedback control law is determined which is based on the length of the vehicles queues at each intersection. This law is modified by a coordination term, calculated at the upper level, which takes into consideration the state of the traffic at other intersections. Due to the inherent flexibility of the method, state constraints are treated at the upper level. Only simple calculations are required to determine the control law, leading to short computation time and thus allowing real time control of over saturated networks. The results obtained on various examples confirm the advantages of the proposed technique.

On the Choice of Aggregated Models for Analysis and Control

Abstract This communication is concerned with the analysis and control of large scale systems by linear aggregation. A method for the selection of the modes to be retained in the aggregated model is presented. Based on this method, a new approach is developped to tackle the control problem for large systems.

Reconstitution of the transition matrix from experimental data

The identification of a linear compartment model, which may describe a chemical or biological process, is a difficult task, since the available data is generally limited. In this paper we propose a method for determining the state transition matrix by minimizing a given quadratic criterion. To solve the resulting matrix equation, an assumption has to be made which constitutes a necessary condition for the identifiability of the model. Moreover when this assumption is satisfied, it is shown that the knowledge of one line or one column of the transition matrix is sufficient to define it completely.

On a Practical Approach to Real-time Control

Abstract Real-time process control using a new decomposition-coordination method is presented. By a proper decomposition of the global criterion : centralized, decentralized or hierarchical control structures may be designed. The obtained control law is formed of two parts : a closed loop part which guarantees a fast reaction when perturbations occur, and an open loop part which corresponds to a coordination vector computed at the upper level. Due to disturbances, the coordination parameters must be reestimated on-line, this may be done rapidly using the proposed method. The control design procedure is described and the on-line tasks of each controller are defined.

Reduced-Order Modelling by Aggregation for Control and Suboptimality Evaluation

Abstract A methodology based on the aggregation technique is presented to design control laws for large systems. In order to evaluate the stability and the sub-optimality of the system under such control laws, a small parameter is introduced in the modelling. Then using perturbation theory, various results are presented.