Robust stability of moving horizon estimation for non‐linear systems with bounded disturbances using adaptive arrival cost (original) (raw)

Advances in moving horizon estimation for nonlinear systems

2010

In the past decade, moving horizon estimation (MHE) has emerged as a powerful technique for estimating the state of a dynamical system in the presence of nonlinearities and disturbances. MHE is based on the idea of minimizing an estimation cost function defined on a sliding window composed of a finite number of time stages. The cost function usually comprises two contributions: a prediction error computed on a recent batch of inputs and outputs and an arrival cost that serves the purpose of summarizing the past data. The diffusion of such techniques has been hampered by the difficulty in choosing the arrival cost so as to ensure stability of the overall estimation scheme and by the need for an adequate computational time.

Enhancement of the Moving Horizon Estimation Performance Based on an Adaptive Estimation Algorithm

Journal of Control Science and Engineering

Although moving horizon estimation (MHE) is a very efficient technique for estimating parameters and states of constrained dynamical systems, however, the approximation of the arrival cost remains a major challenge and therefore a popular research topic. The importance of the arrival cost is such that it allows information from past measurements to be introduced into current estimates. In this paper, using an adaptive estimation algorithm, we approximate and update the parameters of the arrival cost of the moving horizon estimator. The proposed method is based on the least-squares algorithm but includes a variable forgetting factor which is based on the constant information principle and a dead zone which ensures robustness. We show by this method that a fairly good approximation of the arrival cost guarantees the convergence and stability of estimates. Some simulations are made to show and demonstrate the effectiveness of the proposed method and to compare it with the classical MHE.

Remarks on Moving Horizon State Estimation with Guaranteed Convergence

Lecture Notes in Control and Information Science, 2005

In this paper, a moving horizon state estimation scheme is proposed. The scheme is inspired by combining the system-theoretic concept of observability maps with optimization-based estimators. As a result, a simple moving horizon state estimator scheme for nonlinear discrete time control systems is established which guarantees global convergence under certain observability conditions.

A real-time algorithm for moving horizon state and parameter estimation

Computers & Chemical Engineering, 2011

A moving horizon estimation (MHE) approach to simultaneously estimate states and parameters is revisited. Two different noise models are considered, one with measurement noise and one with additional state noise. The contribution of this article is twofold. First, we transfer the real-time iteration approach, developed in for nonlinear model predictive control, to the MHE approach to render it real-time feasible. The scheme reduces the computational burden to one iteration per measurement sample and separates each iteration into a preparation and an estimation phase. This drastically reduces the time between measurements and computed estimates. Secondly, we derive a numerically efficient arrival cost update scheme based on one single QR-factorization. The MHE algorithm is demonstrated on two chemical engineering problems, a thermally coupled distillation column and the Tennessee Eastman benchmark problem, and compared against an Extended Kalman Filter. The CPU times demonstrate the real-time applicability of the suggested approach. (P. Kühl). 1 We refer to the growing number of measurements in full-information estimators. The curse of dimensionality associated with the number of states to be estimated is yet another issue.

Moving horizon estimation for linear singular systems

In this paper, the moving horizon recursive state estimator for linear singular systems is derived from the minimum variance estimation problem. The proposed estimate of the state using the measured outputs samples on the recent finite time horizon is unbiased and independent of any a priori information of the state on the horizon. The convergence and stability of the filter are evoked. A numerical example is presented to prove the performance of the proposed filter

Simple and efficient moving horizon estimation based on the fast gradient method

IFAC-PapersOnLine, 2015

By now many results with respect to the fast and efficient implementation of model predictive control exist. However, for moving horizon estimation, only a few results are available. We present a simple solution algorithm tailored to moving horizon estimation of linear, discrete-time systems. In a first step the problem is reformulated such that only the states remain as optimization variables, i.e. process and measurement noise are eliminated from the optimization problem. This reformulation enables the use of the fast gradient method, which has recently received a lot of attention for the solution of model predictive control problems. In contrast to the model predictive control case, the Hessian matrix is timevarying in moving horizon estimation, due to the time-varying nature of the arrival cost. Therefore, we outline a tailored method to compute online the lower and upper eigenvalues of the Hessian matrix required by the here considered fast gradient method. In addition, we discuss stopping criteria and various implementation details. An example illustrates the efficiency of the proposed algorithm.

Moving Horizon State Estimation for Linear System with Application to Autonomous Vehicle

InPrime: Indonesian Journal of Pure and Applied Mathematics

This paper proposes moving horizon estimation (MHE) to estimate the state variables of autonomous vehicle linear systems under measurement noises. To solve the MHE optimization problem, quadratic programming is employed. The steering angle, yaw angle, and global position constraints of an autonomous vehicle are considered in the estimation design. According to the simulation results, it can be observed that although the longer MHE step can give better results compared to the shorter MHE step, the difference in the MHE step only slightly affects the estimated results. However, the longer MHE step can increase the computational time. Additionally, the proposed MHE scheme is compared to the Kalman filter (KF) estimator. Based on the obtained results, the KF gives a better estimation than the MHE, but this notion must be verified for other case studies.Keywords: autonomous vehicle; Kalman filter; linear system; MHE; quadratic programming. AbstrakPaper ini mengusulkan moving horizon esti...

Moving horizon estimators for large-scale systems

In this report, a review on state estimation schemes applied to large-scale systems is made. The attention is focused on Moving Horizon Estimation (MHE) schemes due to the addressing of the estimation problem in an optimal way, and it inherent capability to handle the process constraints. Moreover, the cost function can be proposed unlike other optimal estimation schemes like those based on Kalman Filters. Therefore, contributions on state estimation schemes applied to large-scale systems are described, in order to outline its merits and limitations. Finally, open problems are listed with the aim to prepare a basis for future contributions.

Double Moving Horizon Estimation: Linearization by a Nonlinear Transformation

2018 European Control Conference (ECC), 2018

Moving horizon estimation (MHE) is a constrained non-convex optimization problem in principle, which needs to be solved online. One approach to avoid dealing with several local minima is to linearize the nonlinear dynamics. This type of convex approximation usually utilizes the estimated state as a linearization trajectory, providing no guarantees of stability and optimality in general. In this paper, we study the cascade of a linear and linearized observer, which is called double MHE. The first stage makes use of a model transformation, that in the nominal case is globally equivalent to the nonlinear dynamics. Since this approach does not consider the input and output disturbances optimally, the second stage uses the first stage estimates as an external signal for linearizing the nonlinear dynamics to improve the quality of estimation. The overall configuration can be transformed into two quadratic programs. This approach not only avoids solving a non-convex optimization problem, but also reduces the computational complexity significantly compared to the one needed for solving a nonconvex problem. This estimation method has been validated in a simulation study, where our approach converged to the global minimum without the need to explicitly solve a nonconvex optimization problem.