A neighboring extremal solution for an optimal switched impulsive control problem

This paper presents a neighboring extremal solution for a class of optimal switched impulsive control problems with perturbations in the initial state, terminal condition and system's parameters. The sequence of mode's switching is pre-specified, and the decision variables, i.e. the switching times and parameters of the system involved, have inequality constraints. It is assumed that the active status of these constraints is unchanged with the perturbations. We derive this solution by expanding the necessary conditions for optimality to first-order and then solving the resulting multiple-point boundary-value problem by the backward sweep technique. Numerical simulations are presented to illustrate this solution method

Robust fault detection and isolation for uncertain linear retarded systems

A robust fault detection and isolation scheme is proposed for uncertain continuous linear systems with discrete state delays for both additive and multiplicative faults. Model uncertainties, disturbances and noises are represented as unstructured unknown inputs. The proposed scheme consists of a Luenberger observer for fault detection and a group of adaptive observers, one for each class of faults, for fault isolation. The threshold determination and fault isolation are based on a multi-observer strategy. Robustness to model uncertainties and disturbances can be guaranteed for the scheme by selecting proper thresholds. All the signals, i.e., the fault estimate and the state and output estimation errors of each isolation observer can be shown to be uniformly bounded, and the estimate of the fault by the matched observer is shown to be satisfactory in the sense of extended L-2 norm. Furthermore, the sensitivity to fault and the fault isolability condition are analyzed also in the paper. Simulations of a heating process for detecting and isolating an actuator gain fault and an additive fault show the proposed scheme is effective

Variable structure control for a class of nonlinear systems with mismatched uncertainties

A scheme to stabilize nonlinear time-varying systems with both matched and mismatched uncertainties is proposed in this paper by switching between two control laws: a first-order sliding-mode control and a second-order sliding-mode control. Based on this idea, a variable structure control algorithm is designed for a class of second-order systems. The closed-loop system is globally or locally asymptotically stable. It has been proven that the stability region has relation with the order of the boundary function and the region can be obtained by solving an inequality. The uncertainty considered in this work is also more general than those in the existing works. (C) 2007 Elsevier Inc. All rights reserved

Discrete Component Prognosis for Hybrid Systems Under Intermittent Faults

Prognosis of discrete component with intermittent fault in hybrid systems is challenging since the component has only two states (i.e., ON and OFF) and no associated physical parameter in the model can quantify the degradation. This article aims to solve the discrete component prognosis problem under the model-based paradigm. First, the fault detection and isolation module help find the possible faulty discrete components. Based on the isolated possible faulty discrete components, Levy flight biogeography-based optimization is proposed to identify the faulty discrete component states, as well as the fault appearing and fault disappearing instants. Second, a Weibull function-based degradation model which can capture the duration evolution of intermittent fault of discrete component in observation window (OW) is developed using coordinate reconstruction approach, and the degradation model coefficients can be calculated from the fault identification results. After that, the concept of failure threshold for faulty discrete component is defined based on the ratio of fault duration to OW, which enables the prognosis of intermittent fault in discrete component. Finally, the proposed methodologies are validated by experiment results. Note to Practitioners —This article is motivated by the intermittent fault prognosis problem of discrete components (e.g., relays and hydraulic valves) in hybrid systems. Existing fault prognosis researches do not consider discrete component which is an important part of hybrid systems. For the intermittent fault prognosis of discrete component, the observation window (OW) concept and coordinate reconstruction (CR) method are proposed to establish the degradation model, and the ratio of fault duration to OW is used to define the failure threshold of discrete component. To show the effectiveness of the proposed methods, an application on a hybrid circuit system is considered. It is noted that the degradation pattern (e.g., increase of frequency or duration of intermittent fault) of discrete components may vary in different systems, while the degradation process can be quantified by the OW and CR methods developed in this article, which enables the prognosis of intermittent fault in discrete component for various hybrid industrial systems. The proposed approach can be applied to industrial hybrid systems if the following conditions are satisfied: 1) the hybrid bond graph model of the monitored system can be established, based on which the fault detection and isolation can be implemented and 2) the monitored system contains multiple discrete components suffering from intermittent faults whose appearing and disappearing instants can be identified by certain method

An exact penalty method for free terminal time optimal control problem with continuous inequality constraints

In this paper, we consider a class of optimal control problems with free terminal time and continuous inequality constraints. First, the problem is approximated by representing the control function as a piecewise-constant function. Then the continuous inequality constraints are transformed into terminal equality constraints for an auxiliary differential system. After these two steps, we transform the constrained optimization problem into a penalized problem with only box constraints on the decision variables using a novel exact penalty function. This penalized problem is then solved by a gradient-based optimization technique. Theoretical analysis proves that this penalty function has continuous derivatives, and for a sufficiently large and finite penalty parameter, its local minimizer is feasible in the sense that the continuous inequality constraints are satisfied. Furthermore, this local minimizer is also the local minimizer of the constrained problem. Numerical simulations on the range maximization for a hypersonic vehicle reentering the atmosphere subject to a heating constraint demonstrate the effectiveness of our method