Thomas Parisini

A robust detection and isolation scheme for abrupt and incipient faults in 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.

Adaptive fault-tolerant control of nonlinear uncertain systems: an information-based diagnostic approach

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.

Fault diagnosis of a class of nonlinear uncertain systems with Lipschitz nonlinearities using adaptive estimation

This paper presents a fault detection and isolation (FDI) scheme for a class of Lipschitz nonlinear systems with nonlinear and unstructured modeling uncertainty. This significantly extends previous results by considering a more general class of system nonlinearities which are modeled as functions of the system input and partially measurable state variables. A new FDI method is developed using adaptive estimation techniques. The FDI architecture consists of a fault detection estimator and a bank of fault isolation estimators. The fault detectability and isolability conditions, characterizing the class of faults that are detectable and isolable by the proposed scheme, are rigorously established. The fault isolability condition is derived via the so-called fault mismatch functions, which are defined to characterize the mutual difference between pairs of possible faults. A simulation example of a single-link flexible joint robot is used to illustrate the effectiveness of the proposed scheme.

A receding-horizon regulator for nonlinear systems and a neural approximation

A receding-horizon (RH) optimal control scheme for a discrete-time nonlinear dynamic system is presented. A nonquadratic cost function is considered, and constraints are imposed on both the state and control vectors. Two main contributions are reported. The first consists in deriving a stabilizing regulator by adding a proper terminal penalty function to the process cost. The control vector is generated by means of a feedback control law computed off line instead of computing it on line, as is done for existing RH regulators. The off-line computation is performed by approximating the RH regulator by means of a multilayer feedforward neural network (this is the second contribution of the paper). Bounds to this approximation are established. Simulation results show the effectiveness of the proposed approach.

Cooperative Constrained Control of Distributed Agents With Nonlinear Dynamics and Delayed Information Exchange: A Stabilizing Receding-Horizon Approach

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.

Approximating networks and extended Ritz method for the solution of functional optimization problems

Functional optimization problems can be solved analytically only if special assumptions are verified; otherwise, approximations are needed. The approximate method that we propose is based on two steps. First, the decision functions are constrained to take on the structure of linear combinations of basis functions containing free parameters to be optimized (hence, this step can be considered as an extension to the Ritz method, for which fixed basis functions are used). Then, the functional optimization problem can be approximated by nonlinear programming problems. Linear combinations of basis functions are called approximating networks when they benefit from suitable density properties. We term such networks nonlinear (linear) approximating networks if their basis functions contain (do not contain) free parameters. For certain classes of d-variable functions to be approximated, nonlinear approximating networks may require a number of parameters increasing moderately with d, whereas linear approximating networks may be ruled out by the curse of dimensionality. Since the cost functions of the resulting nonlinear programming problems include complex averaging operations, we minimize such functions by stochastic approximation algorithms. As important special cases, we consider stochastic optimal control and estimation problems. Numerical examples show the effectiveness of the method in solving optimization problems stated in high-dimensional settings, involving for instance several tens of state variables.

Sensor bias fault isolation in a class of nonlinear systems

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.

Distributed Fault Detection and Isolation of Large-Scale Discrete-Time Nonlinear Systems: An Adaptive Approximation Approach

This paper deals with the problem of designing a distributed fault detection and isolation methodology for nonlinear uncertain large-scale discrete-time dynamical systems. As a divide et impera approach is used to overcome the scalability issues of a centralized implementation, the large scale system being monitored is modelled as the interconnection of several subsystems. The subsystems are allowed to overlap, thus sharing some state components. For each subsystem, a Local Fault Diagnoser 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 diagnostic 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 and isolability of faults affecting variables shared among overlapping subsystems. Theoretical results are provided to characterize the detection and isolation capabilities of the proposed distributed scheme. Finally, simulation results are reported showing the effectiveness of the proposed methodology.

Networked Predictive Control of Uncertain Constrained Nonlinear Systems: Recursive Feasibility and Input-to-State Stability Analysis

In this paper, the robust state feedback stabilization of uncertain discrete-time constrained nonlinear systems in which the loop is closed through a packet-based communication network is addressed. In order to cope with model uncertainty, time-varying transmission delays, and packet dropouts (typically affecting the performances of networked control systems), a robust control scheme combining model predictive control with a network delay compensation strategy is proposed in the context of non-acknowledged UDP-like networks. The contribution of the paper is twofold. First, the issue of guaranteeing the recursive feasibility of the optimization problem associated to the receding horizon control law has been addressed, such that the invariance of the feasible region under the networked closed-loop dynamics can be guaranteed. Secondly, by exploiting a novel characterization of regional Input-to-State Stability in terms of time-varying Lyapunov functions, the networked closed-loop system has been proven to be Input-to-State Stable with respect to bounded perturbations.

A neural state estimator with bounded errors for nonlinear systems

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 offline in such a way as to enable it to process on line any possible measure pattern almost instantly.