Design Of Interval/Set-Membership State Estimators And Its Application

In the past few decades,one of the most important,fundamental and challenging problems in the control system theory is to estimate the unknown states of the system in the presence of the exogenous disturbances and noises for designing control laws,fault detection,isolation and so on.Therefore the state estimation problem for linear,nonlinear and hybrid dynamical systems has been studied and applied widely in the literature.To solve this problem,a new technique is recently developed to deal with the large uncertainties and disturbances by determining certain upper and lower estimates for the system states at each time instant,which is known as interval/set-membership state estimators.The mean of the interval can be considered as the pointwise estimate whereas the interval width provides the admissible deviation from that value.Thus,an error bound is provided at any time instant and the norm of the interval estimation error converges to zero in the absence of exogenous signals.In addition to the structure importance,the interval estimator design process give certain information about the uncertainties that makes the interval estimators further significant and simple to design for the state disturbance.They are successfully applied to many real-time life problems having large uncertainties such as mechanical,biological or chemical processes.The interval observer design methods mainly rely on the strong assumption of the existence of an observer gain such that the cooperativity and stability conditions for the error dynamics matrix are satisfied simultaneously.Unfortunately,this is a restrictive assumption and verified rarely in practice.Therefore,much work still need to be done in order to avoid or relax such restrictions for designing interval state estimators.Based on the theoretical as well as practical applications,we will further discuss and study the design of the interval/set-membership estimators in this dissertation.The core contribution and innovation of this dissertation are summarized in the following manner:1)For a specific class of Linear Time-Varying(LTV)discrete-time systems subject to component faults and uncertainties,a Luenberger type interval observer is designed based on Monotone System Theory(MST).The component faults and uncertainties are assumed to be unknown but bounded without giving any other information,whose effect can be approximated using these estimated bounds.The result is then extended to find an interval state estimator for non-cooperative systems by similarity transformation of coordinates to make this approach appropriate for a huge class of LTV processes.The observer convergence is also ensured.This kind of interval observer is very useful in handling the effects of component faults in systems.2)In order to avoid the strict assumption for the existence of observer gain such that both the stability and cooperativity conditions for the estimation error dynamics are satisfied simultaneously,a novel interval state estimator is designed that will generate a tight interval vector for the real state vector in a guaranteed way by employing interval analysis and consistency techniques for the Single-Input-Single-Output(SISO)systems and Multi-InputMulti-Output(MIMO)systems.The estimation error dynamics bounds are computed a-priori to measurements and the convergence of the width of the interval state vector towards a known value within finite time is provided to prove the boundedness of the interval state vector and estimation error without the observer gain.The proposed method is then successfully applied to Linear Parameter Varying(LPV)systems as well.3)One of the most important classes of hybrid dynamical systems is SLS that plays a vital role both in theoretical as well as practical research that can be used in several fields such as electrical devices,flight control systems,congestion modeling.Therefore,the problem of setmembership interval state estimator design for the uncertain discrete-time SLS with an application to the DC-DC Converters is considered.The observability matrix and the setinversion of the available system outputs are used to solve the interval-based state estimation problem under arbitrary switching sequence.Unlike the existing methods,no observer gain is required to show the boundedness of the estimation error dynamics.To summarize,this work concludes that first,an interval observer is designed for uncertain LTV discrete-time system under the assumption that there exists an observer gain such that the error dynamics matrix is nonnegative and stable at the same time,which is not always possible.Therefore,in order to avoid this restrictive assumption,a novel method to design interval state estimators for LTV,LPV and Switched Linear Systems(SLS)using the observability matrix and interval analysis are developed.