Simultaneous input and parameter estimation with input observers and set‐membership parameter bounding: theory and an automotive application

Abstract

The paper addresses an on-line, simultaneous input and parameter estimation problem for a first-order system affected by measurement noise. This problem is motivated by practical applications in the area of engine control. Our approach combines an input observer for the unknown input with a set-membership algorithm to estimate the parameter. The set-membership algorithm takes advantage of a priori available information such as (i) known bounds on the unknown input, measurement noise and time rate of change of the unknown input; (ii) the form of the input observer in which the unknown parameter affects only the observer output; and (iii) the input observer error bounds for the case when the parameter is known exactly. The asymptotic properties of the algorithm as the observer gain increases are delineated. It is shown that for accurate estimation the unknown input needs to approach the known bounds a sufficient number of times (these time instants need not be known). Powertrain control applications are discussed and a simulation example based on application to engine control is reported. A generalization of the basic ideas to higher order systems is also elaborated.

Adaptive Control for Flow and Volume Regulation in Multi-Producer District Heating Systems

“…In this work we have addressed the flow and storage volume regulation of a multi-producer DH system via a novel adaptive decentralized control scheme which offers closed-loop (local) stability guarantees and overcomes the nonlinear, networked and uncertain characteristics of the considered system model, notably stemming from our consideration of frictional effects in pipes. Part of our ongoing research is related to the following: (i) the establishment of estimates of the closed-loop system's domain of attraction; (ii) the identification of gain tuning rules to improve performance, e.g., the speed of convergence of x b ; and (iii) the compatibility of our control design procedure with other, more general, parameter and disturbance estimation schemes (see [21]), to formally study and address the effects of measurement noise, which were not considered in the present work.…”

Adaptive input and parameter estimation with application to engine torque estimation

“…Remark 5: As shown in Lemma 2, the classical PE condition is required to prove the estimation convergence, and can be numerically online validated by calculating the minimum eigenvalue of P and testing for min 2 ( ) 0 P λ σ > > in this paper. In this respect, the nontrivial validation of the uniquely identifiable property [7] is avoided.…”

“…gradient and least squares method) may fail to obtain satisfactory performance, because of the fast time-varying parameters in the torque generation dynamics [10]. Nevertheless, the set-membership estimation algorithm for time-varying parameters [7] depends on the knowledge for precise bounds on the unknown parameters. This assumption may be stringent in practical applications.…”

“…Only one tuning parameter needs to be selected. Comparisons to two other input observers in [7] are studied with respect to their performance and robustness. In the second part, the unknown input is parameterized in a quasilinear form with some time-varying parameters (this is particularly true for the engine torque [4]).…”

Set‐theoretic localization for mobile robots with infrastructure‐based sensing

“…Given ̂li,𝜃 (k + 1) ∈ L i,𝜃 (k + 1|k) and equation above, we can show ̂li,𝜃 (k + 1) ∈ L i,𝜃 (k + 1) as in (19).…”