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In this note, a robust model predictive control scheme for constrained discrete-time nonlinear systems affected by bounded disturbances and state-dependent uncertainties is presented. In order to guarantee the robust satisfaction of the state constraints, restricted constraint sets are introduced in the optimization problem, by exploiting the state-dependent nature of the considered class of uncertainties. Moreover, unlike the nominal model predictive control algorithm, a stabilizing state constraint is imposed at the end of the control horizon in place of the usual terminal constraint posed at the end of the prediction horizon. The regional input-to-state stability of the closed-loop system is analyzed. A simulation example shows the effectiveness of the proposed approach. Index Terms--Constrained systems, input-to-state stability, model predictive control, nonlinear discrete-time systems, robust control.

This technical note deals with the problem of designing a distributed fault detection methodology for distributed (and possibly large-scale) nonlinear dynamical systems that are modelled as the interconnection of several subsystems. The subsystems are allowed to overlap, thus sharing some state components. For each subsystem, a Local Fault Detector is designed, based on the measured local state of the subsystem as well as the transmitted variables of neighboring states that define the subsystem interconnections. The local detection decision is made on the basis of the knowledge of the local subsystem dynamic model and of an adaptive approximation of the interconnection with neighboring subsystems. The use of a specially-designed consensus-based estimator is proposed in order to improve the detectability of faults affecting variables shared among different subsystems. Simulation results provide an evidence of the effectiveness of the proposed distributed fault detection scheme. Index Terms--Adaptive estimation, distributed detection, fault diagnosis, large-scale systems, nonlinear systems.

This paper addresses the problem of cooperative control of a team of distributed agents with decoupled nonlinear discrete-time dynamics, which operate in a common environment and exchange-delayed information between them. Each agent is assumed to evolve in discrete-time, based on locally computed control laws, which are computed by exchanging delayed state information with a subset of neighboring agents. The cooperative control problem is formulated in a receding-horizon framework, where the control laws depend on the local state variables (feedback action) and on delayed information gathered from cooperating neighboring agents (feedforward action). A rigorous stability analysis exploiting the input-to-state stability properties of the receding-horizon local control laws is carried out. The stability of the team of agents is then proved by utilizing small-gain theorem results. Index Terms--Constrained systems, cooperative control, model predictive control, nonlinear systems, receding-horizon control.

In this paper, we consider the problem of actively providing an estimate of the state of a stochastic dynamic system over a (possibly long) finite time horizon. The active estimation problem (AEP) is formulated as a stochastic optimal control one, in which the minimization of a suitable uncertainty measure is carried out. Toward this end, the use of the Renyi entropy as an information measure is proposed and motivated. A neural control scheme, based on the application of the extended Ritz method (ERIM) and on the use of a Ganssian sum filter (GSF), is then presented. Simulation results show the effectiveness of the proposed approach. Index Terms--Active estimation, entropy, neural networks (NNs).

In this paper, the problem of fault detection in mechanical systems performing linear motion, under the action of friction phenomena is addressed. The friction effects are modeled through the dynamic LuGre model. The proposed architecture is built upon an online neural network (NN) approximator, which requires only system's position and velocity. The friction internal state is not assumed to be available for measurement. The neural fault detection methodology is analyzed with respect to its robustness and sensitivity properties. Rigorous fault detectability conditions and upper bounds for the detection time are also derived. Extensive simulation results showing the effectiveness of the proposed methodology are provided, including a real case study on an industrial actuator. Index Terms--Actuator fault detection, friction, online neural approximations.

This note presents a robust fault isolation scheme for a class of nonlinear systems with sensor bias type of faults. The proposed fault diagnosis architecture consists of a fault detection estimator and a bank of isolation estimators, each corresponding to a particular output sensor. Based on the class of nonlinear systems and sensor bias faults under consideration, the stability and learning properties of the fault isolation estimators are obtained, adaptive thresholds are derived for the isolation estimators, and fault isolability conditions are rigorously investigated, characterizing the class of nonlinear faults that are isolable by the proposed scheme. A simulation example is used to illustrate the effectiveness of the sensor bias fault isolation methodology. Index Terms--Fault detection and approximation, fault isolation, non-linear adaptive estimator, nonlinear uncertain systems, sensor bias.

This paper presents a unified methodology for detecting, isolating and accommodating faults in a class of nonlinear dynamic systems. A fault diagnosis component is used for fault detection and isolation. On the basis of the fault information obtained by the fault-diagnosis procedure, a fault-tolerant control component is designed to compensate for the effects of faults. In the presence of a fault, a nominal controller guarantees the boundedness of all the system signals until the fault is detected. Then the controller is reconfigured after fault detection and also after fault isolation, to improve the control performance by using the fault information generated by the diagnosis module. Under certain assumptions, the stability of the closed-loop system is rigorously investigated. It is shown that the system signals remain bounded and the output tracking error converges to a neighborhood of zero. Index Terms--Fault detection and isolation, fault-tolerant control, neural networks, nonlinear systems.

This paper presents a robust fault diagnosis scheme for abrupt and incipient faults in nonlinear uncertain dynamic systems. A detection and approximation estimator is used for online health monitoring. Once a fault is detected, a bank of isolation estimators is activated for the purpose of fault isolation. A key design issue of the proposed fault isolation scheme is the adaptive residual threshold associated with each isolation estimator. A fault that has occurred can be isolated if the residual associated with the matched isolation estimator remains below its corresponding adaptive threshold, whereas at least one of the components of the residuals associated with all the other estimators exceeds its threshold at some finite time. Based on the class of nonlinear uncertain systems under consideration, an isolation decision scheme is devised and fault isolability conditions are given, characterizing the class of nonlinear faults that are isolable by the robust fault isolation scheme. The nonconservativeness of the fault isolability conditions is illustrated by deriving a subclass of nonlinear systems and of faults for which these conditions are also necessary for fault isolability. Moreover, the analysis of the proposed fault isolation scheme provides rigorous analytical results concerning the fault isolation time. Two simulation examples are given to show the effectiveness of the fault diagnosis methodology. Index Terms--Fault detection and approximation, fault isolation, nonlinear adaptive estimator, nonlinear uncertain systems.

In an access node to a hybrid - switching network (e.g., a base station handling the downlink in a cellular wireless network), the output link bandwidth is dynamically shared between isochronous (guaranteed bandwidth) and asynchronous traffic types. The bandwidth allocation is effected by an admission controller, whose goal is to minimize the refusal rate of connection requests as well as the loss probability of packets queued in a finite buffer. Optimal admission control strategies are approximated by means of backpropagation feedforward neural networks, acting on the embedded Markov chain of the connection dynamics. The case of unknown, slowly varying, input rates is explicitly considered. Numerical results are presented, comparing the approximation with the optimal solution obtained by dynamic programming. Index Terms - Backpropagation, broadband communication, communication system control, feedforward neural networks, neural network applications, time decision multiplexing.

Approximate solutions to the Witsenhausen counterexample are derived by constraining the unknown control functions to take on fixed structures containing "free" parameters to be optimized. Such structures are given by "nonlinear approximating networks," i.e., linear combinations of parametrized basis functions that benefit by density properties in normed linear spaces. This reduces the original functional problem to a nonlinear programming one which is solved via stochastic approximation. The method yields lower values of the costs than the ones achieved so far in the literature, and, most of all, provides rather a complete overview of the shapes of the optimal control functions when the two parameters that characterize the Witsenhausen counterexample vary. One-hidden-layer neural networks are chosen as approximating networks. Index Terms--Approximating networks, extended Ritz method, functional optimization, neural networks, Witsenhausen counterexample.

Large-scale traffic networks (e.g., computer and communication networks, freeway systems, etc.) can be modeled as graphs in which a set of nodes (with storing capacities) are connected through a set of links (where traffic delays and transport costs may be incurred) that cannot be loaded above their traffic capacities. Traffic flows may vary over time. Then the nodes (i.e., the decision makers acting at the nodes) may be requested to modify the traffic flows to be sent to their neighboring nodes. In this case, a dynamic routing problem arises. The decision makers are realistically assumed 1) to generate their routing decisions on the basis of local information and possibly of some data received from other nodes, typically, the neighboring ones and 2) to cooperate on the accomplishment of a common goal, that is, the minimization of the total traffic cost. Therefore, they can be regarded as the cooperating members of informationally distributed organizations, which, in control engineering and economics, are called team organizations. Team optimal control problems cannot be solved analytically unless special assumptions on the team model are verified. In general, this is not the case with traffic networks. An approximate resolutive method is then proposed, in which each decision maker is assigned a fixed-structure routing function where some parameters have to be optimized. Among the various possible fixed-structure functions, feedforward neural networks have been chosen for their powerful approximation capabilities. The routing functions can also be computed (or adapted) locally at each node. Concerning traffic networks, we focus attention on store-and-forward packet switching networks, which exhibit the essential peculiarities and difficulties of other traffic networks. Simulations performed on complex communication networks point out the effectiveness of the proposed method. Index Terms--Distributed-information organizations, neural control, optimal routing, team optimal control, traffic and communication networks.

The problem of clearing congestion situations in freeway traffic is addressed for both an N-stage and an infinite-stage control horizon (in the latter case, a receding-horizon control mechanism is used). Traffic is controlled by regulating the vehicle access to the freeway and by limiting the vehicle speed by means of variable message signs. To describe the traffic behavior, a 'classical' macroscopic model, first proposed by Payne, is adopted. Even though the problem is stated within a deterministic context, an optimal control law in feedback form is sought to react to unpredictable events. The resulting functional optimization problem is reduced to a nonlinear programming problem by constraining the control law to take on a fixed structure in which free parameters have to be optimized. For such a structure, a multilayer feedforward neural mapping is chosen. Simulation results show the effectiveness of the proposed method in two different case studies. For the simulation of the second case study, real traffic data are used, which allows one to very well represent critical traffic conditions on freeways. Index Terms--Neural networks, optimal control, traffic control.

A neural state estimator is described, acting on discrete-time nonlinear systems with noisy measurement channels. A sliding-window quadratic estimation cost function is considered and the measurement noise is assumed to be additive. No probabilistic assumptions are made on the measurement noise nor on the initial state. Novel theoretical convergence results are developed for the error bounds of both the optimal and the neural approximate estimators. To ensure the convergence properties of the neural estimator, a minimax tuning technique is used. The approximate estimator can be designed off line in such a way as to enable it to process on line any possible measure pattern almost instantly. Index Terms--Bounded error state estimation, discrete-time nonlinear systems, neural networks.

A feedback control law is proposed that drives the controlled vector [v.sub.t] of a discrete-time dynamic system (in general, nonlinear) to track a reference [Mathematical Expression Omitted] over an infinite time horizon, while minimizing a given cost function (in general, nonquadratic). The behavior of [Mathematical Expression Omitted] over time is completely unpredictable. Random noises act on the dynamic system and the state observation channel, which may be nonlinear, too. The random noises and the initial state are, in general, non-Gaussian; it is assumed that all such random vectors are mutually independent, and that their probability density functions are known. As is well known, so general a non-LQG (linear quadratic Gaussian) optimal control problem is very difficult to solve. The proposed solution is based on three main approximating assumptions: 1) the optimal control problem is stated in a receding-horizon framework where [Mathematical Expression Omitted] is assumed to remain constant within a shifting-time window; 2) the control law is assigned a given structure (the one of a multilayer feedforward neural network) in which a finite number of parameters have to be determined in order to minimize the cost function (this makes it possible to approximate the original functional optimization problem by a nonlinear programming one); and 3) the control law is given a 'limited memory,' which prevents the amount of data to be stored from increasing over time. The errors resulting from the second and third assumptions are discussed. Due to the very general assumptions under which the approximate optimal control law is derived, we are not able to report stability results. However, simulation results show that the proposed method may constitute an effective tool for solving, to a sufficient degree of accuracy, a wide class of control problems traditionally regarded as difficult ones (an example of freeway traffic optimal control is given that may be of practical importance). Index Terms - Limited-memory regulators, neural control, receding-horizon regulators, stochastic optimal control.