| Discrete-time 2-D systems have received a lot of attention and research due to their profound theoretical significance and wide practical application value.On the other hand,with the rapid development of computer technology and network communication technol-ogy,networked systems have been widely used in various practical engineering fields due to their flexibility,simple installation,and low cost,and networked 2-D systems have also received increasing attention from researchers.As an effective means to alleviate network communication pressure,event-triggered mechanisms have been widely studied.At the same time,as a popular topic in the field of control research,the filtering problem of 2-D systems has also made significant progress.Due to the influence of uncertain factors such as disturbances and noise in actual systems,how to deal with the impact of uncertain factors on the state estimation problem is an important research direction.As one of the main methods for dealing with uncertain factors,set-membership estimation method only assumes that uncertain factors such as noise and disturbance are unknown and bounded,which is more suitable for practical situations compared with the energy-bounded as-sumption.Moreover,unlike traditional estimation methods that can only obtain point estimates,set-membership estimation methods can obtain a set containing all states,pro-viding richer state information.On the other hand,with the largescale and complexity of control systems,failure of system components may cause the collapse of the entire networked control system,leading to serious personal injury and huge economic losses.Therefore,timely detection and alarm of the impending faults are crucial to improving the safety and reliability of the system.It can be seen that the research and development of networked 2-D systems and the guarantee of their safety and reliability have important practical significance and application value.The purpose of this dissertation is to investigate the set-membership estimation of networked discrete-time 2-D systems and its application in fault detection.First,an effec-tive set-membership estimation method based on zonotope is performed for discrete-time2-D systems by constructing a suitable radius function.Considering the widespread use of networked systems,an event-triggered mechanism is introduced to save limited net-work communication resources,and the problem of event-triggered discrete-time 2-D systems for set-membership estimation is analyzed.In view of the relationship between two common models describing discrete 2-D systems,the FMLSS model and the Roesser model,we further study the problem of set-membership estimation for discrete-time 2-D systems described by different models under the dynamic event-triggered mechanism.Then,the results of set set-membership estimation are extended to the fault detection of2-D systems,and a residual dynamic threshold design method is proposed to overcome the drawback that the conventional fault detection constant thresholds are difficult to be selected.Finally,considering some shortcomings of zonotope in describing sets,a new ellipsoid bundle-based set-membership estimation method is proposed and applied to the fault detection of 2-D systems.The main work of this dissertation are as follows:The set-membership estimation of networked 2-D systems based on the event-trigge-red mechanism is studied.Considering that the assumption that the disturbance and noise energy are bounded has a small application range in practical engineering,this dissertation assumes that the disturbance and noise are unknown-but-bounded.In order to obtain the estimation interval of system state affected by uncertain factors,the set-membership esti-mation method based on zonotopes is adopted in this dissertation.In order to save limited network resources and reduce the burden of network data transmission,this dissertation determines whether the current data needs to be transmitted through the communication network by designing event-triggered conditions.Firstly,according to the characteris-tics of Fornasini–Marchesini local state-space model,we define the radius and weighted radius of the zonotopes in 2-D system.We analyze the L_∞performance of the 2-D sys-tem by constructing an appropriate radius functional.In order to avoid that the designed event-triggered mechanism causes too little data to be transmitted in the network and damages the observation performance of the system,this dissertation comprehensively considers the design of event-triggered parameters and observer gain to ensure that the system can effectively reduce the number of data packets transmitted through the net-work,while meeting the expected performance indicators of the system.Then,according to the designed transformation algorithm,we can calculate the estimation interval of the networked 2-D system state with the designed event-triggered mechanism.Based on the dynamic event-triggered mechanism,we study the interval estimation problems of 2-D system under Fornasini–Marchesini local state model and Roesser model,respectively.As two models commonly used to represent and study 2-D systems,Fornasini–Marchesini local state-space model and Roesser model have different struc-tural characteristics.Therefore,this dissertation designs corresponding dynamic event-triggered mechanisms for 2-D systems under different models.Different from the pre-vious two parts,another method to measure the size of the zonotopes in 2-D system is proposed:F-radius.Then,based on three different optimization criteria(minimum vol-ume of zonotope,minimum segment of zonotope and robust observer design technology),we propose the optimal observer design methods for the 2-D systems with different mod-els according to the established F-radius functional and Lyapunov functional.In addition,considering that there is a certain conversion relationship between Fornasini–Marchesini local state-space model and Roesser model,this dissertation discusses the relationship be-tween the results obtained based on the application of the robust observer design method to different system models.Based on the adaptive event-triggered mechanism,the application of set-membership estimation method based on zonotope in fault detection is investigated for 2-D systems.First,in order to save limited network communication resources and detect the system faults in time,we design an adaptive event-triggered mechanism under the Fornasini–Marchesini local state-space model,so that the system can send the appropriate number of data packets to ensure the system performance when no faults occur.When faults occur,the number of data packets sent is reduced to ease the network communication burden.Then,by designing the L_∞/H_∞fault detection observer and the set-membership analysis of the residual signal in the case of fault-free,it is ensured that the generated residual signal is robust to external disturbance and measurement noise and sensitive to the fault signal.Furthermore,we can provide the residual signal estimation interval for the system fault detection.Compared with the traditional residual evaluation methods that need to select a constant residual evaluation threshold in advance,the method proposed in this dissertation can generate a dynamic threshold for residual evaluation,which is relatively more flexible.Considering a class of 2-D Roesser systems with dynamic event-triggered mecha-nism,we study the problem of fault detection based on the ellipsoid bundle-based set-membership estimation method.As a new set description tool,ellipsoid bundle combines the characteristics of zonotope and ellipsoid:it can describe complex polyhedron and smooth boundary sets.Therefore,the application range of the set-membership estimation method based on ellipsoid bundle is wider than that based on zonotope and ellipsoid.In this dissertation,considering the structural characteristics of Roesser model,we design a suitable dynamic event-triggered mechanism.Based on the designed event-triggered mechanism,we introduce an optimization method of L_∞/H_∞fault detection observer.The L_∞performance ensures the robustness of the residual signal to disturbance and noise,and the H_∞performance guarantees the sensitivity of the residual signal to the fault sig-nal.Then,based on the ellipsoid bundle-based set-membership estimation approach,we present a dynamic threshold residual evaluation algorithm for 2-D Roesser system under dynamic event-triggered mechanism. |
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