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].

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

In this paper we present a full solution to the closed-loop model predictive control problem intrinsically using an observer and innovations feedback, a structure that turns out to be crucial to find its receding horizon implementation. Closed-loop MPC is a strategy in which a reference feedforward trajectory and a linear time varying feedback map are optimized simultaneously using convex optimization techniques. In this formulation, future disturbances are suppressed in an unconservative way by taking future measurements into account. Due to the finite horizon formulation one is forced to use a receding horizon implementation (as in open-loop model predictive control) and we will reveal how to do so.

A full solution to the constrained stochastic closed-loop MPC problem via state and innovations feedback and its receding horizon implementation

In this paper, we present a new approach for suppression of residual vibrations in point-to-point motions based on lifted iterative learning control (ILC). The approach is to add a signal to the command input during the point-to-point motion in order to compensate for residual vibrations. A special form of ILC with separate actuation and observation time windows is shown to converge to the required signal. Subsequently, we present ILC control strategies for residual vibration suppression in which convergence and performance specifications can be designed separately. Additionally, the designed controllers have the capability to constrain the amplitude of the command signal. The presented strategies are demonstrated on a flexible system and shown to be successful in the suppression of residual vibration while minimizing the maximum amplitude of the command signal. Copyright © 2007 John Wiley & Sons, Ltd.

Residual vibration suppression using Hankel iterative learning control

In this paper we will solve a closed-loop steady-state economic optimization problem for process operation by means of convex optimization techniques. The objective is the simultaneous optimization of controller parameters and steady-state operating condition maximizing the economic profit of the plant. The main point is, given the economic objective of the plant, to replace back-off selection by back-off optimization together with optimal tuning of controller parameters.

LMI-based closed-loop economic optimization of stochastic process operation under state and input constraints

The design of robust controllers for a compact disc mechanism is considered. Using mu synthesis, a controller has been designed for good track-following. The design problem involves time-domain constraints on signals and robustness requirements for norm-bounded structured plant uncertainty. It is shown that by using weighting functions in the mu framework this problem can be solved, but at the cost of many design iterations. The mu controller has been implemented in an experimental setup with a digitally controlled compact disc player. >

Robust control of a compact disc player

A technique is presented to design input signals for point-to-point control problems with the property of minimal excitation of parasitic system oscillations. This technique is compared to impulse based input design techniques in experiments performed on an industrial XY-positioning table. Impulse input shaping was formulated as a solution to an optimisation problem, which has been transformed for the case of point-to-point problems, resulting in a more time-optimal solution. The results from this new optimisation are very impressive considering the simplicity.

OH Okko Bosgra

Papers

A full solution to the constrained stochastic closed-loop MPC problem via state and innovations feedback and its receding horizon implementation

Residual vibration suppression using Hankel iterative learning control

LMI-based closed-loop economic optimization of stochastic process operation under state and input constraints

Robust control of a compact disc player

Input design for optimal discrete time point-to-point motion of an industrial XY-positioning table