Simultaneous state and input estimation with applications in vehicle problems
type: CreativeWork
description: Engineering is about design of materials, structures, systems and interconnections to obtain a desired behaviour. In control engineering the focus is often on systems equipped with sensors whose output is used to provide feedback control and achieve the desired behaviour. A central paradigm in control is the separation principle, that is the optimal control action is achieved by applying the control law that is optimal under an assumption of full information to an “optimal estimate” of the system state. While in the context of linear-quadratic problems there is a well developed theory of optimal estimation and control, research on systems with inputs that are not measured directly is still ongoing. Motivated by automotive applications where it is not always feasible or practical to have sensors that measure all vehicle inputs, we aim to advance the theory on simultaneous state and input estimation and apply it to commercially important automotive examples. In particular, we formulate a deterministic estimation problem to find the input and state of a linear continuous time dynamical system which minimises a weighted integral squared error between the resulting output and the measured output. A completion of squares approach is used to find the unique optimum in terms of the solution of a Riccati differential equation. The optimal estimate is obtained from a two-stage procedure that is reminiscent of the Kalman filter. The first stage is an end-of-interval estimator for the finite horizon which may be solved in real time as the horizon length increases. The second stage computes the unique optimum over a fixed horizon by a backwards integration over the horizon. A related tracking problem is solved in an analogous manner. Making use of the solution to both the estimation and tracking problems a constrained estimation problem is solved which shows that the Riccati equation solution has a least squares interpretation that is analogous to the meaning of the covariance m…
abstract: Engineering is about design of materials, structures, systems and interconnections to obtain a desired behaviour. In control engineering the focus is often on systems equipped with sensors whose output is used to provide feedback control and achieve the desired behaviour. A central paradigm in control is the separation principle, that is the optimal control action is achieved by applying the control law that is optimal under an assumption of full information to an “optimal estimate” of the system state. While in the context of linear-quadratic problems there is a well developed theory of optimal estimation and control, research on systems with inputs that are not measured directly is still ongoing. Motivated by automotive applications where it is not always feasible or practical to have sensors that measure all vehicle inputs, we aim to advance the theory on simultaneous state and input estimation and apply it to commercially important automotive examples. In particular, we formulate a deterministic estimation problem to find the input and state of a linear continuous time dynamical system which minimises a weighted integral squared error between the resulting output and the measured output. A completion of squares approach is used to find the unique optimum in terms of the solution of a Riccati differential equation. The optimal estimate is obtained from a two-stage procedure that is reminiscent of the Kalman filter. The first stage is an end-of-interval estimator for the finite horizon which may be solved in real time as the horizon length increases. The second stage computes the unique optimum over a fixed horizon by a backwards integration over the horizon. A related tracking problem is solved in an analogous manner. Making use of the solution to both the estimation and tracking problems a constrained estimation problem is solved which shows that the Riccati equation solution has a least squares interpretation that is analogous to the meaning of the covariance m…
author: Gakis, Grigorios
language: eng
keywords: estimation, least squares optimisation, optimal control
license: https://www.rioxx.net/licenses/all-rights-reserved/
date published: 2021-09-09
date modified: 2026-07-22T22:24:00Z
provider: Cambridge University
publisher: Networked Digital Library of Theses and Dissertations
type: WebPage
source organization: University of Cambridge

PropertyValue
property ID: DOI
value: 10.17863/CAM.87520