Stoyan Kanev

Robustly asymptotically stable finite-horizon MPC

This paper presents a robustly stable finite-horizon model predictive control (MPC) scheme for linear uncertain systems, in which the uncertainty is not restricted to some specific uncertainty class (polytopic, affine, LFT, etc.). The only requirement is that the state-space matrices remain bounded over the uncertainty set. Suitable constraints are added to the MPC cost function to impose robust asymptotic stability and to deal with input/output constraints. The resulting optimization problem is solved at each time instant in a probabilistic framework using an iterative randomized ellipsoid algorithm (REA). The method is compared in simulation to the existing approach of Kothare, Balakrishnan and Morari [(1996). Robust constrained model predictive control using linear matrix inequalities. Automatica, 32(10), 1361-1379].

MODEL WEIGHT AND STATE ESTIMATION FOR MULTIPLE MODEL SYSTEMS APPLIED TO FAULT DETECTION AND IDENTIFICATION

Abstract A method is proposed for estimating both the weights and the state of a multiple model system with one common state vector. In this system, the weights are related to the activation of each individual model. For the resulting nonlinear estimation problem a method is developed that efficiently decomposes the total problem into two separate parts, one for estimating the model weights and one for estimating the state. The method has been validated on a component, actuator and sensor fault detection and identification problem for a linearized model of an aircraft.

MODEL WEIGHT ESTIMATION FOR FDI USING CONVEX FAULT MODELS

Abstract A method is proposed for modeling a large number of faults in a system by a convex combination of a limited number of fault models that form a model set. The fault models in this model set, correspond to the maximum and minimum expected faults for faults that can occur partially. In this way partial faults can be represented by a convex combination of the models from the model set. The identification of faults is performed by estimating the weights of the models from the model set. A set of linearized models of a Boeing 747 aircraft is used to display the effectiveness of the proposed method. This model set also includes models of the aircraft that correspond to faults that occurred during the disastrous crash of EL AL flight 1862 in 1992.

The Randomized Ellipsoid Algorithm for Constrained Robust Least Squares Problems

In this chapter a randomized ellipsoid algorithm is described that can be used for finding solutions to robust Linear Matrix Inequality (LMI) problems. The iterative algorithm enjoys the property that the convergence speed is independent on the number of uncertain parameters. Other advantages, as compared to the deterministic algorithms, are that the uncertain parameters can enter the LMIs in a general nonlinear way, and that very large systems of LMIs can be treated. Given an initial ellipsoid that contains the feasibility set, the proposed approach iteratively generates a sequence of ellipsoids with decreasing volumes, all containing the feasibility set. A method for finding an initial ellipsoid is also proposed based on convex optimization. For an important subclass of problems, namely for constrained robust least squares problems, analytic expressions are derived for the initial ellipsoid that could replace the convex optimization. The approach is finally applied to the problem of robust Kalman filtering.

Multiple model weight estimation for models with no common state

Abstract In this paper the problem of model weight estimation is considered for systems represented by convex combinations of a set of multiple linear models with time-varying weights. As opposed by the majority of the existing methods, the present paper considers the more general case when the models in the model set do not necessarily share the same state basis and may even have different state dimension. Basically the method collects a batch of input-output measurement data within some fixed time interval, which is subsequently projected in such a way, that the influence of the state vector is removed. The resulting nonlinear constraint optimization problem, that in a particular special case takes the form of a convex optimization problem, is then solved with respect to the model weights.

Vibration-Based Damage Assessment for Controller Reconfiguration: Application to an Oilpan

One of the objectives of the EU research project InMAR (“Intelligent Materials for Active Noise Reduction”) is to reduce car engine noise by active control. An oilpan of a passenger car serves as a demonstrator. A concern in the application of active control is that the controlled system may change during service life (e.g. due to damage), and hence, may degrade the control performance. This paper presents two vibration-based methods that are able to autonomously detect damage and yield updated experimental models of the structure. A first approach is based on (operational) modal analysis. Based on vibration measurements, the modal parameters of the structure are estimated. The idea is now to automate this process so that, without human intervention, a representative dynamic model of the structure is always available. A second approach uses multiple-model estimation in the case when the state-space models have different state dimensions. To this end, an existing non-interacting multiple-model estimator has been extended to make it alert to jumps from one model to another. Both techniques (“Automatic Modal Analysis” and “Alert Autonomous Multiple Model Estimator”) will be applied to experimental vibration data from an oilpan of a passenger car subjected to damage (loosening of bolts).

Multiple Model Weight Estimation for Models With No Common State

: In this paper the problem of model weight estimation is considered for systems represented by convex combinations of a set of multiple linear models with time-varying weights. As opposed by the majority of the existing methods, the present paper considers the more general case when the models in the model set do not necessarily share the same state basis and may even have different state dimension. Basically, the method collects a batch of input-output measurement data within some fixed time interval, which is subsequently projected in such a way, that the influence of the state vector is removed. The resulting nonlinear constraint optimization problem, that in a particular special case takes the form of a convex optimization problem, is then solved with respect to the model weights.

Model Weight Estimation for FDI Using Convex Fault Models

: A method is proposed for modeling a large number of faults in a system by a convex combination of a limited number of fault models that form a model set. The fault models in this model set, correspond to the maximum and minimum expected faults for faults that can occur partially. In this way, partial faults can be represented by a convex combination of the models from the model set. The identification of faults is performed by estimating the weights of the models from the model set. A set of linearized models of a Boeing 747 aircraft is used to display the effectiveness of the proposed method. This model set also includes models of the aircraft that correspond to faults that occurred during the disastrous crash of EL AL flight 1862 in 1992.