Constrained Linear Moving Horizon Estimation And Applications

In reality, the system states often cannot be measured directly. So estimates ofthe actual state based on output measurements must be used instead. This methodcan be regarded as 'estimate'. It is well known that, the standard state estimation method used for linearstochastic system is the Kalman filter. The importance of Kalman approach followsfrom the fact that it provides a recursive and probabilistic "optimal" solution fordynamical systems. The other reason for the popularity of the Kalman filter is thatit possesses many important theoretical properties such as stability. Oftenadditional insight about the process is available in the form of inequality constrains.However, with the addition of inequality constrains, that could improve theestimates, general recursive solution such as Kalman filtering are unavailable. Inorder to incorporate constrains, we employs on-line optimization. This article considers moving horizon strategies for constrained linear stateestimation. Model predictive control (MPC), also referred to moving horizon control orreceding horizon control, has become an attractive feedback strategy, especially for linear ornonlinear systems subject to input and state constraints. In general, the model predictive controlproblem is formulated as solving on-line a finite horizon open-loop optimal control problemsubject to system dynamics and constrains involving states and controls. During the last decade,many MPC schemes have been developed and successfully applied in various industries.Additional information for estimating state variables from output measurements isoften available in the form of equality constraints on states, noise, and othervariables. Formulating a linear state estimation problem estimation problem growswith time as more measurements are available. To bound the problem size, weexplore moving horizon strategies for constrained linear state estimation. The success of model predictive control has motivated many researchers to 61吉林大学硕士学位论文investigate online optimization strategies for constrained and nonlinear stateestimation. The basic strategy of MHE is to reformulate the estimation problem asa quadratic program using a moving estimation window. When all of the availablemeasurements are considered, we refer to this problem as the full informationestimator. Efficient strategies exist for solving the quadratic program. However, theproblem size grows with time as the estimator processes more data. As a result, theproblem complexity scales at least linearly with time. To make the estimationproblem tractable, we need to bound the problem size. One strategy to reduce theproblem to a fixed dimension quadratic program is to employ a moving horizonapproximation. The basic strategy of the moving horizon approximation is toconsider explicitly a fixed amount of data, the key to preserving stability andperformance is the construction of the initial penalty using arrival cost thatapproximately summarizes the past data. Arrival cost is fundamental in estimation,because, by providing a means to transform the unbounded mathematical probleminto an equivalent fixed-dimension mathematical program. Using the arrival cost,the MHE accounts for the data not included in the estimation window. The pastdata are indirectly accounted for through the initial penalty by penalizing deviationaway from the past estimate in accordance with our confidence in the estimate.Consider the unconstrained estimation problem, we are able to construct analyticexpression for the cost, it is possible to develop recursive estimators. One exampleis Kalman filtering. Unfortunately, for the constrained problem, we are unable togenerate its analytic expression. One reasonable solution then is to approximate thearrival cost for the constrained problem with the arrival cost for the unconstrainedproblem. We approximate arrival cost by using Kalman filtering. T...