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This article presents a statistical analysis of the Matrix Pencil method for estimating the mode and the amplitude of a single damped complex exponential. This study is based on a perturbation analysis of the mode and the amplitude, assuming a high signal-to-noise ratio. Closed-form expressions of the mean and variance of these perturbations are derived. It is shown that the estimates are unbiased...
Several subspace algorithms for the identification of bilinear systems have been proposed recently. A key practical problem with all of these is the very large size of the data-based matrices which must be constructed in order to ‘linearise’ the problem and allow parameter estimation essentially by regression. Another shortcoming of currently known subspace algorithms for bilinear systems is that...
A matrix form representation of discrete analogs of various forms of fractional differentiation and fractional integration is suggested. The suggested approach is new, and it can be used in all fields related to fractional-order dynamical systems and fractional-order control, including development of algorithms and software for real-time control, PIλDμ controllers, and modelling and simulation of...
In this paper we show how to spatially discretize a distributed port-Hamiltonian (pH) system, which describes the dynamics of an 1-D piezoelectric Euler-Bernoulli beam. Standard spatial discretization schemes for PDE systems have the disadvantage that they typically lead to a finite dimensional system which is not anymore in the pH form. So, there is a need for a spatial discretization scheme which...
In this paper, LPV identification and gain-scheduling (GS) control of a sewer system composed by a detention tank and a single reach sewer is proposed. First, a linear parameter-varying (LPV) control-oriented model for the single reach canal is presented and identified using LPV identification methods. Then, LPV GS theory is used to designing a PI GS controller guaranteeing performance and stability...
There are significant incentives in controlling the end-use properties in batch reactors to reduce the variability in the final product quality specifications. Here we define an approach for controlling the properties within a desired target region, instead of a set point, with an economic objective and with consideration of the model uncertainty. The approach to handling process-model mismatch is...
In this paper we show that for linear systems there is a strong relation between P.O.D. approximation and balanced truncation. Using this relation we obtain an error estimate for the P.O.D. approximation in the Hoc-norm. A small Hoc-norm is needed in order to guarantee that a controller design for the reduced system will perform well on the original system.
Nonlinear tomographic reconstruction algorithms are developed for inversion of data measured in scattering experiments in which the complex phase of the wavefields is modeled by an arbitrarily large (possibly infinite) number of terms in the Rytov series. The algorithms attain the form of a Volterra series of nonlinear operators, with the usual filtered backpropagation algorithm of Diffraction Tomography...
A new definition of Adaptive Neuro - Fuzzy Systems is presented in this paper for the identification of unknown nonlinear dynamical systems. The proposed scheme uses the concept of Adaptive Fuzzy Systems (AFS) operating in conjunction with High Order Neural Network Functions. Since the plant is considered unknown, we first propose its approximation by a special form of an adaptive fuzzy system and...
The problem of model reduction by moment matching for multimachine power systems is addressed and solved using the recently introduced notion of moment for nonlinear systems. It is shown that the reduced order model can be used to construct asymptotic estimates for the unmeasured states. The theory is illustrated by means of simulation on a 2-machine power system.
A new model class is proposed to use for identification purposes, which is able to approximate many nonlinear systems quite accurately. Conditions are given for the system to be representable by a linear-in-parameters equation, which allows to use effective linear methods to solve the identification problem. Finally an example is provided to illustrate the use of the proposed model class for identification...
The fractional differintegration problem is treated from the Signal Processing point of view. A brief review of the Laplace transform approach to differintegration is done. The continuous-time/discrete-time system conversion is discussed and presented a Grünwald-Letnikov integration.
We derive new projection formulas for the model reduction method based on the frequency-weighted Hankel norm approximation (FWHNA). These formulas extend the applicability of the FWHNA method to frequency weights expressed as antistable right/left invertible rational matrices. By computing the projections via the solution of appropriate generalized Sylvester equations, an inversion-free solution of...
Stabilization of mechanical control systems by the method of controlled Lagrangians in an approximate version, is used to analyze asymptotic stabilization of systems whose dynamics are governed by the Euler-Lagrange equations. The method is applied to the Furata pendulum. The approximation produces controlled near conservative stable orbits that can be asymptotically stabilized introducing dissipation.
In this paper, the author proposes an algorithm of dual predictive control for a system expressed by a linear ARX (auto-regressive and exogenous) model with uncertain plant model parameters. Previously, the author proposed a dual predictive control algorithm which first considered the uncertainties in future control input values and in future output values included in an ARX model. The future input...
We discuss an algebraic and computational framework for formally analyzing hybrid systems that attempts to avoid numerical integration by resorting to (algebraically) finding primitives, and inverting and (numerically) evaluating functions when needed. The goal of the paper is to start exploring a little bit deeper into this idea to try to find out (a) a methodology, (b) algebraic and computational...
In this paper, a new IMC-based PID controller design is proposed. The model reduction is employed to find the best PID controller approximation to the IMC controller. Compared with the existing IMC-based methods, the proposed design is applicable to a wider range of processes, and yields a control system with performance closer to the more sophisticated IMC counterpart. Furthermore, it can be made...
We develop a day-to-day route choice control method that is based on model predictive control (MPC). To influence the route choice of drivers we propose to use traffic control measures like variable speed limits or outflow control. In previous papers we have developed MPC for route choice control in the case of a constant demand. In this paper we consider the case of a time-varying demand. The resulting...
We present a convergence theorem for a com- putable continuous-time recursive maximum likelihood method with resetting, under realistic conditions. Resetting takes place if the estimator process hits the boundary of a pre-specified compact domain, or if the rate of change, in a stochastic sense, of the parameter process would hit a fixed threshold. The modified recursive maximum likelihood estimator...
A computational method for the approximation of reachable sets for non-linear dynamic systems is suggested. The method is based on a discretization of the interesting region and a projection onto grid points. The projections require to solve optimal control problems which are solved by a direct discretization approach. These optimal control problems allow a flexible formulation and it is possible...
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