Optimization Design Of LMI-based Robust Filtering And Memory Scheduling Fault Detection

The optimization designs of robust filtering and fault detection have been the research focuses of automation and signal processing fields.In general,robust filtering can help us to extract the objective system state information from measurement signals,and fault detection can help us to decide the system operation situation from measurement signals.Both of them will benefit us to understand the system condition in order to facilitate the subsequent system optimization.From the perspective of model-based methods,the major target of filtering is to estimate the regulated output signal,and the primary task of fault detection is to generate the residu-al signal.Hence how to construct the robust filter becomes the key precondition to achieve the desired regulated output estimation and residual signal generation.Motivated by these observations,this dissertation aims at solving some key tech-nique questions encountered in designing robust estimation filter and robust fault detection filter.First,in terms of current LMI-based robust filter design methods,there are several aspects needed to be improved:(1)insufficiency of slack matrix variables introduced by extended LMI technique;(2)unsatisfied relaxation effect of one bounded scalar parameter methods;(3)no results to improve the filter robustness from the point of view of recovering the missed solution space information of filtering analysis condition.In addition,there are also some deficiencies about existing memory scheduling fault detection filter design methods:(1)the dynamic mathematical models of monitored systems are assumed to be precise and the statistical magnitudes of external disturbances are assumed to be known in advance,which are difficult to be satisfied in practical modeling;(2)the memory window horizons of fault detection filter/observer are set to be constant and time-invariant,which weakens ten effective utilization of historical data.For the aforementioned several problems of LMI-based robust filtering and memory scheduling fault detection,this dissertation explores related solutions and extended applications.The main work is summarized as below:(1)The secondary relaxation method,diagonal matrix scalar parameter method,and two-stage strategy are proposed to solve above three conservatism problems encountered in LMI-based robust filter design,respectively.First of all,the secondary relaxation method utilizes the mutual representation charac-teristic between Finsler theorem and Projection theorem(or the internal equivalence relation of Finsler theorem),to twice introduce extra slack matrix variables.By doing so,the degree of freedom of solution space has been increased significantly.Second,the diagonal matrix scalar parameter method utilizes optimized diagonal matrix scalar multiplier coefficients to relax struc-tural constraints of auxiliary matrix variable during linearization of filter anal-ysis condition.Depending on these scalar parameters,the solution space of filter design condition is enlarged,and robust filtering performance is thus im-proved.Third,the two-stage strategy is formulated by virtue of the combined matrix inequality with a prefixed binary choice signal,which is composed of linear matrix inequality in stage one and nonlinear matrix inequality in stage two.Then,by optimizing these two stages interactively,the missed solution space information during linearization of filter analysis condition can be re-covered and employed gradually.Finally,the conservatism of filter design condition is reduced significantly.(2)A robust reduced-order partially mode-dependent filter design problem is extendedly studied for a class of particular polytopic systems(Markov jump systems).The considered Markov jump systems suffers from partially unknown transition probabilities,random quantizer faults,external disturbance and state-dependent noises.These restriction factors affect the estimation effet of filter seriously.In order to improve robust filtering performance,this dissertation utilizes stochastic analysis method,scalar parameter method,and mode-dependent technique to establish LMI-based less conservative filter de-sign conditions.Numerical simulation verifies the effectiveness of the proposed partially mode-dependent robust filter.(3)A fixed horizon finite memory scheduling fault detection filter is constructed to generate residual signal for the purpose of monitoring networked polytopic uncertain systems through wireless fading channel.Rigorous theoretical proof and simulation test are shown to verify that the proposed memory scheduling fault detection method has high robustness against model uncertainty,unreliable transmission channel and external disturbance.In addition,a robust periodically time varying horizon finite memory fault detection filter is further constructed.Compared with fixed horizon finite memory manner,the period-ically time varying horizon finite memory scheduling can provide more design degrees of freedom.Hence,the historical data can be further utilized effectively,and the reliability of fault detection results is thus enhanced significantly.