Research On Estimation Methods For Complex Network Systems Based On Insufficient Information

In the areas of process control of petroleum and petrochemical industry,for a series of complex engineering problems such as operation state estimation and fault signal estimation of petroleum and petrochemical equipments,they can be modeled as the investigation of the problems of performance analysis and design of estimators for complex network systems under practical measurement signals.In the engineering practice of petroleum and petrochemical industry,the states of complex network systems can often not be acquired directly,and need to be estimated on the basis of the measurement signals.The insufficient information refers to the phenomena of incomplete measurements during the signal transmission process which are caused by reasons such as physical device limitations of the network or limited communication bandwidth.Cyber-attacks,sensor saturations,channel fadings,measurement quantization,data packet dropouts,sensor nonlinearities,delays and disturbances are included in the phenomena of insufficient information.Then,it becomes a challenging problem of how to estimate the complex network systems via such insufficient information.In this paper,models of complex network systems and measurements are considered with many network-induced phenomena and system complexities,and several estimator structures are constructed.The estimator design problems which satisfy different performance requirements are investigated by employing Lyapunov stability theory,stochastic analysis method and techniques such as matrix inequality or Riccati difference equation.To be specific,according to the differences of research objects,the work of this paper can be divided into the following several parts:Firstly,based on the insufficient information from partial network nodes and characterizing the phenomenon of randomly occurring deception attacks,the design problem of security-guaranteed estimators is solved for a class of uncertain complex networks subject to finite-distributed delays and stochastic disturbances.Norm-bounded uncertainties are considered in the network parameters and the inner couplings.Randomly occurring deception attacks are taken into account in the information from partial nodes to reflect the likely unavailability of the output signals from certain nodes in harsh environments and the phenomenon of insecure data transmission in the network.The proposed partial-nodes-based estimation method guarantees that the overall estimation error dynamics satisfies the specified security performance constraint,the estimator gain parameters are acquired by solving certain matrix inequalities with nonlinear constraints.Secondly,based on the insufficient information from partial network nodes and containing the phenomenon of sensor saturations,the design of the finite-horizon robust H_∞state estimators is carried out for a class of time-varying complex networks with randomly occurring parameter uncertainties and multiple stochastic time-varying communication delays under the random access protocol.According to the mode evolution of the Markov chain,one node is randomly selected by the random access protocol to transmit data at each time step,while other nodes are not allowed to transmit data.Sensor saturations are introduced in the measureable information from partial nodes to reflect the size limit of transmission signals existing in the practical situation.The designed time-varying partial-nodes-based state estimators ensure that the estimation error dynamics achieves the prescribed H_∞performance requirement,and the unknown parameters are obtained by solving recursive matrix inequalities.Thirdly,based on the insufficient information involving channel fadings,the problems of synchronization and finite-horizon H_∞state estimation are solved for a class of complex networks with randomly varying inner and outer couplings,time-varying parameters as well as multiplicative noises.The random variations of the topology and the inner coupling matrix of complex networks are determined by the transition probability matrix of the Markov chain.Multiplicative noises are denoted by the random variables which conform to the standard Normal distribution.The testing criterion for synchronization of complex networks is established which guarantees that the synchronization error satisfies the specified H_∞performance constraint,and an estimation method is developed which ensures that the estimation error dynamics achieves the H_∞disturbance attenuation level.The determination of time-varying estimator gains is on the basis of the solutions to recursive matrix inequalities.Fourthly,based on the insufficient information containing measurement quantization,the variance-constrained H_∞state estimation approach is proposed for a class of time-varying complex networks with randomly varying topologies and stochastic inner coupling and nonlinearities.A Kroneckerδfunction and Markovian jumping parameters are utilized to describe the random changes of network topologies.Stochastic inner coupling and nonlinearities are depicted respectively by a Gaussian random variable and nonlinear functions with known statistical characteristics.Measurement quantization is adopted to reflect the phenomenon of signal distortion in the transmission process.The state estimation method is developed which satisfies the prescribed variance constraints on the estimation error and the desired H_∞performance requirements over a finite horizon.The estimator gain parameters for each instant are calculated out by using the solutions to a series of recursive matrix inequalities.Finally,based on the insufficient information containing data packet dropouts,the H_∞fault estimator design method is presented for a class of complex networks with randomly varying topologies,stochastic inner couplings and randomly occurring faults.The random occurrences of the faults,the data packet dropouts,topology variations and inner-coupling matrix variations in the complex networks are described by mutually independent Bernoulli distributed white sequences.The Gaussian white noise sequences are utilized to account for possible stochastic disturbances in the inner-coupling matrices.Different from the sufficient conditions acquired in the aforementioned estimation methods,necessary and sufficient conditions are established here to guarantee that estimation error dynamics satisfies the prescribed H_∞performance constraint.With the help of the completing squares method,the time-varying fault estimator parameters are acquired by recursively solving a set of coupled backward Riccati difference equations.The fault estimation algorithm is summarized which realizes that the influence from the disturbance inputs to the error dynamics of the fault estimation is attenuated at a required level.Furthermore,it is used to solve the fault estimation problem for motors of several parallel pumping units in the well pattern of pumped wells.In the simulation examples,the effectiveness is verified respectively of the proposed estimation methods mentioned above,i.e.,the partial-nodes-based security estimation method for uncertain complex networks under deception attacks,the partial-nodes-based finite-horizon state estimation method for complex networks under random access protocol,synchronization and state estimation method for complex networks with channel fadings and randomly varying couplings,variance-constrained finite-horizon state estimation method for complex networks with randomly varying topologies,and finite-horizon H_∞fault estimation method for complex networks with randomly varying topologies and stochastic inner couplings.It is revealed in the simulation results that the designed estimators all satisfy their given performance constraints such as security,finite-horizon H∞and covariance respectively,and have good estimation effects.