An optimal feedback regulation of nonlinear singularly perturbed systems via slow manifold approach

A concept of exact slow optimal control is defined for a general class of nonlinear singularly perturbed systems utilizing the slow manifold theory. Under a set of conditions an exact optimal feedback regulation restricted to the slow manifold is obtained. The result is applied to a class of nonlinear systems with nonlinear fast actuators. It is shown that by adding an extra compensating slow control to the near optimal control an exact optimal feedback regulation is achieved on the manifold. An upper bound on the perturbation parameter is obtained under which the result is valid.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/27477/1/0000520.pd

A Geometric Approach to Fault Detection and Isolation of Continuous-Time Markovian Jump Linear Systems

This paper is concerned with development of novel fault detection and isolation (FDI) strategies for the Markovian jump linear systems (MJLS's) and the MJLS's with time-delays (MJLSD's). First a geometric property that is related to the unobservable subspace of MJLS's is presented. The notion of a finite unobservable subspace is then introduced for the MJLSD's. The concept of unobservability subspace is introduced for both the MJLS's and the MJLSD's and an algorithm for its construction is described. The necessary and sufficient conditions for solvability of the fundamental problem of residual generation (FPRG) for the MJLS's are developed by utilizing our introduced unobservability subspace. Furthermore, sufficient solvability conditions of the FPRG for the MJLSD's are also derived. Finally, sufficient conditions for designing an H∞-based FDI algorithm for the MJLS's with an unknown transition matrix that are also subject to input and output disturbances are developed

Optimal hybrid fault recovery in a team of unmanned aerial vehicles

This paper introduces and develops an optimal hybrid fault recovery methodology for a team of unmanned vehicles by taking advantage of the cooperative nature of the team to accomplish the desired mission requirements in presence of faults/failures. The proposed methodology is developed in a hybrid framework that consists of a low-level (an agent level and a team level) and a high-level (discrete-event system level) fault diagnosis and recovery modules. A high-level fault recovery scheme is proposed within the discrete-event system (DES) supervisory control framework, whereas it is assumed that a low-level fault recovery designed based on classical control techniques is already available. The low-level recovery module employs information on the detected and estimated fault and modifies the controller parameters to recover the team from the faulty condition. By taking advantage of combinatorial optimization techniques, a novel reconfiguration strategy is proposed and developed at the high-level so that the faulty vehicles are recovered with minimum cost to the team. A case study is provided to illustrate and demonstrate the effectiveness of our proposed approach for the icing problem in unmanned aerial vehicles, which is a well-known structural problem in the aircraft industry

Hierarchical Fault Diagnosis and Health Monitoring in Satellites Formation Flight

Current spacecraft health monitoring and fault-diagnosis practices involve around-the-clock limit-checking and trend analysis on large amount of telemetry data. They do not scale well for future multiplatform space missions due the size of the telemetry data and an increasing need to make the long-duration missions cost-effective by limiting the operations team personnel. The need for efficient utilization of telemetry data achieved by employing machine learning and reasoning algorithms has been pointed out in the literature for enhancing diagnostic performance and assisting the less-experienced personnel in performing monitoring and diagnosis tasks. In this paper, we develop a systematic and transparent fault-diagnosis methodology within a hierarchical fault-diagnosis framework for a satellites formation flight. We present our proposed hierarchical decomposition framework through a novel Bayesian network, whose structure is developed from the knowledge of component health-state dependencies. We have developed a methodology for specifying the network parameters that utilizes both node fault-diagnosis performance data and domain experts' beliefs. Our proposed model development procedure reduces the demand for expert's time in eliciting probabilities significantly. Our proposed approach provides the ground personnel with an ability to perform diagnostic reasoning across a number of subsystems and components coherently. Due to the unavailability of real formation flight data, we demonstrate the effectiveness of our proposed methodology by using synthetic data of a leader-follower formation flight architecture. Although our proposed approach is developed from the satellite fault-diagnosis perspective, it is generic and is targeted toward other types of cooperative fleet vehicle diagnosis problems