Asad A. Ali

Retrospective-cost-based model refinement for system emulation and subsystem identification

We consider the problem of data-based model refinement, where we assume the availability of an initial model, which may incorporate both physical laws and empirical observations. With this initial model as a starting point, our goal is to use additional measurements to refine the model. In particular, components of the model that are poorly modeled can be updated, thereby resulting in a higher fidelity model. We consider two special cases, namely, system emulation and subsystem identification. In the former case, the main system is assumed to be uncertain and we seek an estimate of the unknown subsystem that allows the overall model to approximate the true system. In this case, there is no expectation that the constructed subsystem model approximates the unknown subsystem. In the latter case, we assume that the main system is accurately modeled and we seek an estimate of the unknown subsystem that approximates the unknown subsystem.

Noninvasive Battery-Health Diagnostics Using Retrospective-Cost Identification of Inaccessible Subsystems

Health management of Li-ion batteries depends on knowledge of certain battery internal dynamics (e.g., lithium consumption and film growth at the solid-electrolyte interface) whose inputs and outputs are not directly measurable with noninvasive methods. This presents a problem of identification of inaccessible subsystems. To address this problem, we apply the retrospective-cost subsystem identification (RCSI) method. As a first step, this paper presents a simulation-based study that assumes as the truth model of the battery an electrochemistrybased battery charge/discharge model of Doyle, Fuller, and Newman, and later augmented with a battery-health model by Ramadass. First, this truth model is used to generate the data needed for the identification study. Next, the film-growth component of the battery-health model is assumed to be unknown, and the identification of this inaccessible subsystem is performed using RCSI. The results show that the subsystem identification method can identify the film growth quite accurately when the chemical reactions leading to film growth are consequential.

Adaptive State Estimation for Nonminimum-Phase Systems with Uncertain Harmonic Inputs

We develop a method for obtaining state estimates for a possibly nonminimum-phase system in the presence of an unknown harmonic input. We construct a state estimator based on the system model, and then introduce an estimator input provided by an adaptive feedback model whose goal is to drive the estimated output to the measured output despite the presence of the unknown harmonic input. Using input reconstruction based on a retrospective surrogate cost, we reconstruct the unknown harmonic input. Using the reconstructed input we update the parameters of the adaptive model using recursive least squares identification. We then extend the method to nonlinear systems. The performance of this method is compared with the Kalman filter for linear examples, as well as with the extended and unscented Kalman filters for nonlinear examples.

Growing window recursive quadratic optimization with variable regularization

We present a growing-window variableregularization recursive least squares (GW-VR-RLS) algorithm. Standard recursive least squares (RLS) uses a time-invariant regularization. More specifically, the inverse of the initial covariance matrix in classical RLS can be viewed as a regularization term, which weights the difference between the next state estimate and the initial state estimate. The present paper allows for time-varying in the weighting as well as what is being weighted. This extension can be used to modulate the speed of convergence of the estimates versus the magnitude of transient estimation errors. Furthermore, the regularization term can weight the difference between the next state estimate and a time-varying vector of parameters rather than the initial state estimate as is required in standard RLS.

Retrospective-cost-based adaptive state estimation and input reconstruction for a maneuvering aircraft with unknown acceleration

A method is presented to obtain state estimates for a possibly nonminimum-phase system in the presence of unknown harmonic inputs. The method estimates the states and reconstructs the unknown harmonic input. An adaptive feedback model injects an input into the estimator such that the error between the estimator output and the actual output converges to zero despite the presence of the unknown harmonic input. Using input reconstruction based on a retrospective cost, the unknown harmonic input is reconstructed. Using the reconstructed input, the parameters of the adaptive feedback system are updated using recursive least squares. Results are presented for a rigid body, a damped rigid body, and a 2D missile with a three-loop autopilot topology.

Retrospective cost optimization for adaptive state estimation, input estimation, and model refinement

Abstract Retrospective cost optimization was originally developed for adaptive control. In this paper, we show how this technique is applicable to three distinct but related problems, namely, state estimation, input estimation, and model refinement. To illustrate these techniques, we give two examples. In the first example, retrospective cost model refinement is used with synthetic data to estimate the cooling dynamics that are missing from a model of the ionosphere-thermosphere. In the second example, retrospective cost adaptive state estimation is used with data from a satellite to estimate a solar driver in the ionosphere- thermosphere, with performance gauged by using data from a second satellite.

Retrospective-Cost-Based Adaptive State Estimation and Input Reconstruction for the Global Ionosphere-Thermosphere Model

We consider the problem of estimating the unknown solar driver F10.7 and physical states in the ionosphere and thermosphere using retrospective cost adaptive state estimation (RCASE). We interface RCASE with the Global Ionosphere Thermosphere Model (GITM) to demonstrate state estimation and F10.7 input reconstruction. We further examine the various factors that affect F10.7 estimation including saturation limits, initial estimates, and RCASE tuning parameters.

Consistent identification of Hammerstein systems using an ersatz nonlinearity

We develop a method for identifying SISO Ham merstein systems with an unknown static nonlinearity, linear dynamics, white input noise and colored output noise. We use least squares with a μ-Markov model to estimate the Markov parameters of the linear time-invariant dynamical system. Since the input to the linear system is not available, we use a substitute (ersatz) nonlinearity to transform the input for use in the regressor matrix. We prove that the Markov parameters of the system can be estimated consistently up to a constant scalar as the amount of data increases. This method is demonstrated with several numerical examples.

Sensor-to-sensor identification of Hammerstein systems

Traditional system identification uses measurements of the inputs, but when these measurements are not available, alternative methods, such as blind identification, output-only identification, or operational modal analysis, must be used. Yet another method is sensor-to-sensor identification (S2SID), which estimates pseudo transfer functions whose inputs are outputs of the original system. A special case of S2SID is transmissibility identification. Since S2SID depends on cancellation of the input, this approach does not extend to nonlinear systems. However, in the present paper we show that, for the case of a two-output Hammerstein system, the least-squares estimate of the PTF is consistent, that is, asymptotically correct, despite the presence of the nonlinearities.

Sliding window recursive quadratic optimization with variable regularization

In this paper, we present a sliding-window variable-regularization recursive least squares algorithm. In contrast to standard recursive least squares, the algorithm presented in this paper operates on a finite window of data, where old data are discarded as new data become available. This property can be beneficial for estimating time-varying parameters. Furthermore, standard recursive least squares uses time-invariant regularization. More specifically, the inverse of the initial covariance matrix in standard recursive least squares can be viewed as a regularization term, which weights the difference between the next estimate and the initial estimate. This regularization is fixed for all steps of the recursion. The algorithm derived in this paper allows for time-varying regularization. In particular, the present paper allows for time varying regularization in the weighting as well as what is being weighted. Specifically, the regularization term can weight the difference between the next estimate and a time-varying vector of parameters rather than the initial estimate.