System Identification I

This dissertation focuses on efficiently forming reduced-order models for large, linear dynamic systems. Projections onto unions of Krylov subspaces lead to a class of reduced-order models known as rational interpolants. The cornerstone of this dissertation is a collection of theory relating Krylov projection to rational interpolation. Based on this theoretical framework, three algorithms for model reduction are proposed. The first
algorithm, dual rational Arnoldi, is a numerically reliable approach involving orthogonal projection matrices. The second, rational Lanczos, is an efficient generalization of existing Lanczos-based methods. The third, rational power Krylov, avoids orthogonalization and is suited for parallel or approximate computations. The performance of the three algorithms is compared via a combination of theory and examples. Independent of the precise algorithm, a host of supporting tools are also develop ed to form a complete model-reduction package. Techniques for choosing the matching frequencies, estimating the modeling error, insuring the model's stability, treating multiple-input multiple-output systems, implementing parallelism, and avoiding a need for exact factors of large matrix
pencils are all examined to various degrees

https://tel.archives-ouvertes.fr/tel-01711328/document

Krylov Projection Methods for Model Reduction

We consider the problem of security constrained optimal control for discrete-time, linear dynamical systems in which control and measurement packets are transmitted over a communication network. The packets may be jammed or compromised by a malicious adversary. For a class of denial-of-service (DoS) attack models, the goal is to find an (optimal) causal feedback controller that minimizes a given objective function subject to safety and power constraints. We present a semi-definite programming based solution for solving this problem. Our analysis also presents insights on the effect of attack models on solution of the optimal control problem.

Safe and Secure Networked Control Systems under Denial-of-Service Attacks

In this paper, we present two novel algorithms to realize a finite dimensional, linear time-invariant state-space model from input-output data. The algorithms have a number of common features. They are classified as one of the subspace model identification schemes, in that a major part of the identification problem consists of calculating specially structured subspaces of spaces defined by the input-output data. This structure is then exploited in the calculation of a realization. Another common feature is their algorithmic organization: an RQ factorization followed by a singular value decomposition and the solution of an overdetermined set (or sets) of equations. The schemes assume that the underlying system has an output-error structure and that a measurable input sequence is available. The latter characteristic indicates that both schemes are versions of the MIMO Output-Error State Space model identification (MOESP) approach. The first algorithm is denoted in particular as the (elementary MOESP scheme)...

Subspace model identification-Part 1. The output-error state-space model identification class of algorithms

Model predictive control (MPC) has demonstrated exceptional success for the high-performance control of complex systems [1], [2]. The conceptual simplicity of MPC as well as its ability to effectively cope with the complex dynamics of systems with multiple inputs and outputs, input and state/output constraints, and conflicting control objectives have made it an attractive multivariable constrained control approach [1]. MPC (a.k.a. receding-horizon control) solves an open-loop constrained optimal control problem (OCP) repeatedly in a receding-horizon manner [3]. The OCP is solved over a finite sequence of control actions {u0,u1,f,uN- 1} at every sampling time instant that the current state of the system is measured. The first element of the sequence of optimal control actions is applied to the system, and the computations are then repeated at the next sampling time. Thus, MPC replaces a feedback control law p(m), which can have formidable offline computation, with the repeated solution of an open-loop OCP [2]. In fact, repeated solution of the OCP confers an "implicit" feedback action to MPC to cope with system uncertainties and disturbances. Alternatively, explicit MPC approaches circumvent the need to solve an OCP online by deriving relationships for the optimal control actions in terms of an "explicit" function of the state and reference vectors. However, explicit MPC is not typically intended to replace standard MPC but, rather, to extend its area of application [4]-[6].

/pdf/stochastic-model-predictive-control-an-overview-and-1kyy9166uh.pdf

Stochastic Model Predictive Control: An Overview and Perspectives for Future Research

In this paper, we present a novel robust Iterative Learning Control (ILC) control strategy that is robust against model uncertainty as given by an additive uncertainty model. The design methodology hinges on H_inf optimization, but formulated such that the obtained ILC controller is not restricted to be causal, and inherently operates on a finite time interval. Optimization of the robust ILC (R-ILC) solution is accomplished for the situation where any information about structure in the uncertainty is discarded, and for the situation where the information about the structure in the uncertainty is explicitly taken into account. Subsequently, the convergence and performance properties of resulting R-ILC controlled system are analyzed. On an experimental set-up, we show that the presented robust ILC control strategy can outperform an existing linear-quadratic norm-optimal ILC approach and an existing causal robust ILC approach based on frequency domain H_inf synthesis. Click here to download the paper

Iterative learning control for uncertain systems : noncausal finite time-interval robust control design

In this paper, we consider residual vibration suppression in flexible structures performing a point-to-point motion, based on Hankel ILC. Initially, design freedom in Hankel ILC is discussed, including different choices for the actuation time window and the observation time window. Subsequently, a three input three output flexible beam is presented as an experimental setup for Hankel ILC. The different practical and theoretical issues related to implementation of Hankel ILC on the setup are discussed extensively. Thereby, versatility in the choice for the time windows is shown to be essential for a successful implementation. Experimental results illustrate the capability of Hankel ILC to suppress the residual vibrations in the flexible beam.

/pdf/hankel-iterative-learning-control-for-residual-vibration-2qrq3qi3gi.pdf

Hankel Iterative Learning Control for residual vibration suppression with MIMO flexible structure experiments

Measuring the higher order sinusoidal input describing functions of a non-linear plant operating in feedback

In approximate identification, the goal of the model should be taken into account when evaluating model quality. The purpose of this paper is the development of a system identification procedure, resulting in model sets that are suitable for subsequent robust control design. Incorporation of control relevance in the procedure results in a closed-loop frequency response-based multivariable system identification procedure. The model is represented as a coprime factorization, enabling the usage of stable model perturbations. The main result is the direct estimation of control-relevant coprime factors, exploiting knowledge of a stabilizing controller during the identification experiment. A numerically reliable iterative algorithm is devised, which is illustrated by means of experimental results.

/pdf/robust-control-relevant-coprime-factor-identification-a-jug0x9ev23.pdf

Robust-control-relevant coprime factor identification: A numerically reliable frequency domain approach

Deterministic approaches to model validation for robust control are investigated. In common deterministic model validation approaches, a trade-off between disturbances and model uncertainty is present, resulting in an ill-posed problem. In this paper, an approach to model validation is presented that attempts to remedy the ill-posedness. By employing accurate, non-parametric, deterministic disturbance models in conjunction with enforcing averaging properties of deterministic disturbances, a novel framework enabling model validation for robust control is obtained. The approach results in a realistically estimated model uncertainty and a disturbance model, and is illustrated in a simulation example.

/pdf/estimating-disturbances-and-model-uncertainty-in-model-4vc8ujmq5x.pdf

OH Okko Bosgra

Papers

Iterative learning control for uncertain systems : noncausal finite time-interval robust control design

Hankel Iterative Learning Control for residual vibration suppression with MIMO flexible structure experiments

Measuring the higher order sinusoidal input describing functions of a non-linear plant operating in feedback

Robust-control-relevant coprime factor identification: A numerically reliable frequency domain approach

Estimating disturbances and model uncertainty in model validation for robust control