Fault detection in a mixed H/sub 2//H/sub /spl infin// setting

In this note, we study the problem of fault detection in linear time-invariant (LTI) systems which are simultaneously effected by two classes of unknown inputs: Noises having fixed spectral densities and unknown finite energy disturbances. This problem is formulated as a mixed H/sub 2//H/sub /spl infin// filtering problem. Necessary and sufficient conditions for local optimality are presented. Moreover, it is shown that suboptimal solutions can be computed by solving a convex minimization problem with a set of linear matrix inequality (LMI) constrains. A numerical example is given to illustrate the advantage of the mixed H/sub 2//H/sub /spl infin// approach as compared to existing techniques which are based on optimization of H/sub 2/ and H/sub /spl infin// criteria.     

A new H∞ design methodology for the control of flexible structures: Application to a sight system

We present an Hscr;^∞ controller design methodology for flexible systems. We illustrate our approach using an example drawn from an industrial application. The proposed method avoids undesirable (lightly damped) pole-zero cancellations and yields a low-order controller, using a new formulation of the standard problem.     

Robust least-squares estimation with a relative entropy constraint

Given a nominal statistical model, we consider the minimax estimation problem consisting of finding the best least-squares estimator for the least favorable statistical model within a neighborhood of the nominal model. The neighborhood is formed by placing a bound on the Kullback-Leibler (KL) divergence between the actual and nominal models. For a Gaussian nominal model and a finite observations interval, or for a stationary Gaussian process over an infinite interval, the usual noncausal Wiener filter remains optimal. However, the worst case performance of the filter is affected by the size of the neighborhood representing the model uncertainty. On the other hand, standard causal least-squares estimators are not optimal, and a characterization is provided for the causal estimator and the corresponding least favorable model. The causal estimator takes the form of a risk-sensitive estimator with an appropriately selected risk sensitivity coefficient.     

Innovations generation in the presence of unknown inputs: Application to robust failure detection

The first step in innovations-based failure detection is the construction of an innovations generator, i.e. a filter which, in the absence of failures from the inputs and the outputs of the system, generates a zero-mean white process with known covariance called innovations. A decision on whether a failure has occurred is then made by monitoring and applying statistical tests to this innovations process. In this paper, a method for constructing innovations in the case where the model contains unknown inputs and disturbances is presented. The solution is complete in the sense that it covers ‘singular’ cases.     

Auxiliary signal design for robust active fault detection of linear discrete-time systems

In this paper, algorithms are proposed to design auxiliary signals for active fault detection based on a multi-model formulation of discrete-time systems. Two different scenarios are considered for this problem; the first one assumes there is no a priori information on initial conditions and no exogenous input signal, while the second allows for having a priori information and the possibility of having a known input in addition to the test signal. Approaches are proposed for solving these two types of problems which are capable of solving the problems efficiently. This is achieved by using a recursive approach based on the use of special Riccati equations. These algorithms can be used for systems of higher dimension and on longer time horizons than the existing methods.     

Auxiliary signal design for robust multimodel identification

Under the assumption that one of two given linear models is the real underlying model of the system, a proper auxiliary signal is defined as an input signal that allows the selection of the correct model. Under the assumption that model noises have bounded energy, the separability index is defined as the inverse of the energy of the proper auxiliary signal of least energy. A method for the computation of this index and the construction of the auxiliary signal is presented. Finally, an efficient procedure for online identification, called the "hyperplane test", is developed     

Effects of feedback on active fault detection

In recent years there has been increased interest in the use of active approaches for fault detection. In one of these approaches an auxiliary signal is designed such that over a short period it will reveal a fault not otherwise detectable and do so with as little perturbation of system performance as possible. This method is robust in the sense of guaranteeing the detection of the fault for a whole set of bounded uncertainties. Feedback plays an important role in control but its role in active fault detection based on auxiliary signals has not been explored, yet. This paper begins that investigation.