Research On Interval State Estimation For Singular Systems

State estimation algorithms are generally recognized as a way of conceptualizing ”software” sensors that provide a more reliable and optimized service to the overall control system by using the minimum measurement information available to obtain internal states that are inaccessible to physical sensors.With the increasing demand for high performance in industrial processes,state estimation is faced with more complex and precise tasks.A class of interval state estimation(ISE)methods with allowability and static geometric boundary information as the design objective and condition is proposed.This unique and novel estimation strategy greatly reduces the design conservatism and difficulty in state estimation for complex systems,and guarantees the simple feasibility and continuous reliability of state estimation for complex systems perturbed by multiple uncertainties,such as process perturbations and noise.Besides,it also provides far more available information than point estimation.The ISE offers a rationalized improvement and a powerful complement to fundamental design tasks.This paper separately takes the singular dynamic description of complex industrial processes on multiple-time scales and non-causal,two kinds of novel Luenberger-type dynamics,the parametric solutions to rank explicit and Sylvester matrix equations as the research objects,the design core and the theoretical basis,thus realizing the relaxation and supplement of the limitations and theoretical results for the current ISE algorithms.The research contents are concluded as follows:(1)Based on canonical transformation,the differential-algebraic(Di A)full-order and reduced-order interval dynamic estimation(IDE)design methods for continuous-time singular systems are studied.Firstly,an interval observer(IO)framework with the canonical transformation and a Di A Luenberger-type structure is given,which relaxes the detectable rank condition and solves the regular characteristic and the measurement noise derivatives.Further,the block diagonal transformation is introduced to relax the non-negative constraint,and the posterior existence condition is derived as the rank equality about transformation matrices and an observer gain.Meanwhile,under the elementary transformation,the equivalent explicit matrix equation condition of rank equality is obtained.In addition,a novel reduced-order input-coupled IO structure and its existence condition in the form of a Sylvester matrix equation are proposed by using the canonical and coordinate transformations,and its solvability is guaranteed under the submatrix constraint and the less conservative detectable condition.Finally,the observer gain solution sets of the full-and reduced-order estimation methods and the comprehensive optimization strategies are obtained by solving the rank explicit and Sylvester matrix equations.(2)Based on canonical transformation,the difference-algebraic(Dc A)interval dynamics and set-valued iterative ISE methods for discrete-time singular systems are studied.Firstly,given the canonical realization of the discrete-time singular system and its non-negativity criteria,the discrete-time extension of the DIA structure is established.Furthermore,the structure is extended to the set-valued iterative estimation(SIE)framework based on error gain integration(EGI)and Zonotope representation.It inherits the relevant advantages of the Dc A structure and further solves the non-negative construction problem without any coordinate transformation operation,reduces design conservatism,and verifies the advantages of the SIE framework in estimation accuracy compared to the interval dynamics method.Finally,under the solution to the Sylvester matrix equation,the parametric solution and an explicit optimization function of the EGI-SIE method based on the Dc A structure are given.(3)Based on shift transformation,the auxiliary-normal(AN)full-order and reduced-order IDE design methods for continuous-time singular systems are studied.Firstly,by applying shift and coordinate transformations,a novel AN full-order IO structure with rich design degrees of freedom is constructed to relax the constraints about regular characteristics and the measurement noise derivatives and to solve the non-negative construction problem.By utilizing the normal error dynamic analysis and the generalized inverse condition,the existence condition in the form of a Sylvester matrix equation and its rank explicit form are obtained.Besides,under the decoupling transformation,the structure is further applied to the realization of the reduced-order strategy.A output-coupled AN reduced-order IO(R-IO)design method is proposed.Meanwhile,under the prior detectable condition,the solvability of the proposed design methods is guaranteed.Finally,the parametric design methods and the comprehensive optimization indexes for the AN full-and reduced-order IDE are built by applying the matrix equation solution and the matrix eigenstructure decomposition.(4)Based on shift transformation,the AN interval dynamic and set-valued iterative ISE methods for discrete-time singular systems are studied.By means of the above novel Luenberger-type continuous-time IO structure,the auxiliary coupled component is introduced to further obtain the discrete-time extension for both the structure with more design degrees of freedom and its related work.Moreover,the above-mentioned Luenberger-type full-order structure is reasonably simplified on the premise of ensuring method feasibility and improving computational efficiency,and by inheriting the relevant structural advantages,it is successfully applied to the SIE method,and the advantage in its estimation accuracy is verified.Finally,by virtue of the parametric design method of the rank explicit matrix equation,the parametric solution and an explicit optimization index of the EGI-SIE method based on the AN structure are given.