Study On Moving Horizon Estimation For Time-domain Constrained System

For many real systems the state can not be measured explicitly. Thereforestate estimators giving an estimate of the actual state, based on measurements,are required to implement state feedback control strategies.In reality, the states are known to lie in certain regions, namely, the systemsatisfy constraints. More general constraints include physics constraints and pro-cess constraints. Physics constraints can be called time-domain hard constraints,such as the liquid leak is not negative, the concentration of matter is not negative;process constraints are the information of system process, such as the states lie incertain regions, the disturbance can be approximated in di?erent regions by dif-ferent Gaussian distributions.So we must take this condition as a constraint whiledesigning the estimator, otherwise, some very useful information may be neglectedor even lost.The standard state estimation method used for linear systems is the Kalmanfilter. One reason for the popularity of the Kalman filter is that it possesses manyimportant theoretical properties such as stability. But, Kalman filter can not han-dle the disturbance of model, So robust filtering developed. At present, the es-timation methods contain H∞estimation, set-valued estimation, guaranteed-costestimation and Min-Max estimation. The methods above can not consider theconstraints of the systems. So state estimation problem for uncertain constrainedsystems is important in practice.The main object of this dissertation is to study how to design a moving horizonestimator for nominal constrained linear system and uncertain constrained linearsystem.Based on'Bayes'theory, we present a mathematic description about the con-strained state estimation problem, on condition that the system noise and measure noise are both white noise. This description converts the estimation issue to aquadratic optimization problem, making the calculating of the optimization andthe dealing with of the constraints in a moving horizon way possible. All of theseideas construct the general algorithm of MHE. We discuss the MHE algorithmbased on probability theory, and an explanation of MHE is given in the view ofprobability. We analyse the relationship between constrained holographic estimatorand moving horizon estimator, and the stability issue is studied in detail.We propose a robust MHE method for constrained system with uncertainmeasurement output. For systems with uncertain variance of metrical noise andsystems with lost metrical output values, we give a particular analysis and basedon which the corresponding robust MHE algorithm is respectively deduced. Whenlooking for robust estimation algorithm for systems with uncertain variance, wefirst recall the estimator designing algorithm for unconstrained uncertain systems,and translate the algorithm in the form of LMIs, so that the design parametersof the estimator and the arrival cost function in the moving horizon optimizationcan be obtained by solving those LMIs. And then we take the constraints intoconsideration, the current state estimation can then be calculated by solving theconstrained optimization problem. While searching the algorithm for systems withlost metrical output values, we first design estimator for unconstrained systems,and then the cost function in the moving horizon estimation is described accordingto the previously obtained estimator and estimation error variance matrix. Andfinally the initial state of the system and disturbances can be estimated in a movinghorizon fashion, thus the current state can also be reached.We also discuss the optimal estimation algorithm for constrained systems withunknown input. First, we express the recursive estimator based on the non-biasof the minimum variance estimation, and counteract the in?uence from unknowninputs to the system, by choosing parameters of the estimator. Since it is necessaryto adjust the relationship between the designed parameters of the estimator andthe system parameters in order to counteract the in?uence from unknown input,the conservation of the estimator is inevitable. We adopt given technique here andbased on which the constraints are also taken into the consideration when solvingthe optimization problem. All of these construct the general idea of the robustmoving horizon estimation algorithm.We have also deduced the robust MHE algorithm based on the discussion on the robust optimal estimation issue for systems with Polytopic uncertainties in thestate matrix and norm-bounded parameter uncertainties in the output matrix. Thededuction can be described as two steps. Firstly, we translate the state estimationissue of systems with uncertainties in the output matrix into a Min-Max problem,and obtain the corresponding algorithm. Then based on the obtained algorithm inthe fist step, we take uncertainties in the state matrix into consideration and find akind of robust optimal state estimation method on the worst case, by solving fixedsize Min-Max moving horizon estimation problem.We apply the proposed algorithm in the estimation of sideslip angle of centerof the mass and yaw rate. We first construct the model of the vehicle estimationsystem, reduce the order of the 8 degree of freedom (DOF) model to a nonlinearreduced model. For the convenience of stability analysis, we adopt the 2DOFvehicle model under some assumptions, and the disturbance brought by wind isalso considered. The 2DOF model is somehow simple in the view of configuration,since the model parameters only involve the common parameters in vehicle stabilitycontrol and ABS control, but it is so applicable that the realizing becomes veryeasy.The formulation processes and the proof of mentioned approaches are pre-sented in detail in this thesis. Moreover, in order to validate the e?ciencies ofthe proposed approaches, we give simulation results for each approach,which isdiscussed in detail from constrained modelling,estimator parameter choosing, dis-turbance testing. The simulation results indicate that the estimate e?ects with theproposed approaches are satisfactory.Deeper research work needs to be done since some problems are still remainto be solved, for example, for uncertain system, we need to discuss the stability ofmoving horizon estimation algorithm in detail. Moreover, it is a valuable investi-gation for nonlinear constrained system, time delayed systems and hybrid systemsand bounded energy system.