A computational method for solving optimal control and parameter estimation of linear systems using Haar wavelets

Karimi, Hamid Reza; Lohmann, Boris; Maralani, P. Jabedar; Moshiri, Behzad

doi:10.1080/03057920412331272225

Cited by 55 publications

(20 citation statements)

References 7 publications

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“…This is evident from the vast amount of literature published over the last two decades [6]. The various systems of orthogonal functions may be classified into two categories: (1) piecewise constant basis functions such as Haar functions (HFs) [7]- [8], block pulse functions [9] and Walsh functions [10], and (2) orthogonal polynomials such as Legendre, Laguerre, Chebyshev, Jacobi, Hermite along with sinecosine functions [11]- [12]. It is noting that the main characteristic of the piecewise constant basis functions is that these problems are reduced to those of solving a system of algebraic equations for the solution of problems described by differential equations.…”

Section: Introductionmentioning

confidence: 99%

Vibration Control of a Base-Isolated Building using Wavelets

Karimi

2011

IFAC Proceedings Volumes

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This paper proposes a numerical approach for finding an optimal control based on wavelet functions for vibration reduction of a base-isolated building subjected to actual earthquakes. The objective is two-fold: (1) to find a computational method using properties of Haar functions, and (2) to calculate controller gains approximately by solving only algebraic equations instead of solving the Riccati differential. Simulation results are included to demonstrate the validity and applicability of the technique.

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Section: Introductionmentioning

confidence: 99%

Vibration Control of a Base-Isolated Building using Wavelets

Karimi

2011

IFAC Proceedings Volumes

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“…The characteristic of flat outputs for more general nonlinear systems can be found in [8]. Using the model Equation (17) and Equation (18) and its derivatives, we obtain the L-B isomorphic maps between the state/input and the flat output as follows.…”

Section: A Flat Chemical Reactor Modelmentioning

confidence: 99%

“…For example, a computationally-efficient method based on Haar wavelets for solving variational problems and optimal control of linear systems was developed in [17][18][19][20][21]. All of the system variables (input, state and output) are represented by a Haar wavelet series, which facilitates efficient integration using the integral operation matrix [22].…”

Section: Introductionmentioning

confidence: 99%

Fast Wavelet-Based Model Predictive Control of Differentially Flat Systems

2015

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A system is differentially flat if it is Lie-Bäcklund (L-B) equivalent to a free dynamical system that has dimensions equal to that of the input of the original system. Utilizing this equivalence, the problem of nonlinear model predictive control of a flat system can be reduced to a lower dimensional nonlinear programming problem with respect to the flat outputs. In this work, a novel computational method based on Haar wavelets in the time-domain for solving the resulting nonlinear programming problem is developed to obtain an approximation of the optimal flat output trajectory. The Haar wavelet integral operational matrix is utilized to transform the nonlinear programming problem to a finite dimensional nonlinear optimization problem. The proposed approach makes use of flatness as a structural property of nonlinear systems and the convenient mathematical properties of Haar wavelets to develop an efficient computational algorithm for nonlinear model predictive control of differentially flat systems. Further improvement on computational efficiency is achieved by providing solutions with multiple resolutions (e.g., obtaining high resolution solutions only for the near future, but allowing coarse approximation for the later stage in the prediction horizon).

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“…This is evident from the vast amount of literature published over the last two decades [6]. The various systems of orthogonal functions may be classified into two categories: (1) piecewise constant basis functions such as Haar functions (HFs) [7]- [8], block pulse functions [9] and Walsh functions [10], and (2) orthogonal polynomials such as Legendre, Laguerre, Chebyshev, Jacobi, Hermite along with sine-cosine functions [11]- [12]. It is noting that the main characteristic of the piecewise constant basis functions is that these problems are reduced to those of solving a system of algebraic equations for the solution of problems described by differential equations.…”

Section: Introductionmentioning

confidence: 99%

Wavelet-Based Optimal Control of a Wind Turbine System: A Computational Approach

Karimi

2011

JAMDSM

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This paper deals with a computational optimization approach to the problem of state-feedback control design for a wind turbine system. The first step of the study is to develop a reduced order model for the system by considering the most important physical phenomena of aerodynamics and structural dynamics. Moreover, the behavior of the system can be influenced by the coupled dynamics between the tower motions and the blade pitch and turbine speed which can cause instabilities in the control loops in the worst case. By using a suitable wavelet funcation, called Haar functions, a recursive computational procedure is established for finding the system dynamics approximately by solving only algebraic equations instead of solving the Riccati differential. Simulation results are given to illustrate the usefulness of the proposed control methodology.

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A computational method for solving optimal control and parameter estimation of linear systems using Haar wavelets

Cited by 55 publications

References 7 publications

Vibration Control of a Base-Isolated Building using Wavelets

Vibration Control of a Base-Isolated Building using Wavelets

Fast Wavelet-Based Model Predictive Control of Differentially Flat Systems

Wavelet-Based Optimal Control of a Wind Turbine System: A Computational Approach

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