Local convergence properties of an adaptive control algorithm that, under suitable assumptions, is known to be globally convergent to the optimal LQ regulator, are studied. In this connection, it is shown that, as in ...
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Local convergence properties of an adaptive control algorithm that, under suitable assumptions, is known to be globally convergent to the optimal LQ regulator, are studied. In this connection, it is shown that, as in more standard adaptive controllers, a “transfer function” H ( q ), depending on the innovation C ( q )-polynomial, plays a central role. The peculiarity of the algorithm under consideration is that the special form of the corresponding H ( q ) implies its positive realness. The interest of this result is in the relationship that it allows one to establish between the algorithm under consideration and other adaptive controllers, viz. MUSMAR, whose local convergence properties are known to be described by the same H ( q ).
The MUSMAR self-tuning controller was carefully examined with respect to its servo behaviour. In spite of its nice overall behaviour, several imperfections were discovered. A modified algorithm, without these imperfec...
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The MUSMAR self-tuning controller was carefully examined with respect to its servo behaviour. In spite of its nice overall behaviour, several imperfections were discovered. A modified algorithm, without these imperfections will be proposed. The proposed algorithm is also equipped with an offset estimation and an adaptation mechanism to avoid the burst effect. A comparison between the original and the modified algorithm is made. This will be illustrated with several simulation and real-time experiments.
The effects of multipredictor information in adaptive control are studied, particularly from the standpoint of plant structural uncertainties and umaodelled dynamics. It is shown, through a convergence analysis based ...
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The effects of multipredictor information in adaptive control are studied, particularly from the standpoint of plant structural uncertainties and umaodelled dynamics. It is shown, through a convergence analysis based on the O.D.E. method, that a multipredictor-based self-tuning regulator, viz. the MUSMAR algorithm, if it converges, always converges to the local minima of the cost, under any structural mismatching condition and plant unmodelled dynamics. Similarities and differences with a singlepredictor based self-tuner are pointed out.
This paper describes a system which can be used when designing control digital loops in real industrial processes, as well as for educational purposes.
This paper describes a system which can be used when designing control digital loops in real industrial processes, as well as for educational purposes.
A convergence rate estimate is derived for the homogeneous gradient-based adaptive linear estimator algorithm. This estimate involves the eigenvalues of the regression vector covariance matrix, yielding a useful measu...
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A convergence rate estimate is derived for the homogeneous gradient-based adaptive linear estimator algorithm. This estimate involves the eigenvalues of the regression vector covariance matrix, yielding a useful measure for the choice of input signals for adaptive parameter estimation. The connection between this criterion and those more familiar from nonadaptive system identification is made and comparisons are drawn between the two areas.
An analysis of robust recursive algorithms for dynamic system identification is presented. Problems related to the construction of optimal stochastic approximation algorithms in the min-max sense are demonstrated. Sta...
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An analysis of robust recursive algorithms for dynamic system identification is presented. Problems related to the construction of optimal stochastic approximation algorithms in the min-max sense are demonstrated. Starting from the definition of one class of robustified recursive identification algorithms, several procedures are derived through convenient approximations and initial assumptions. A detailed Monte Carlo analysis gives an insight into the practical robustness of these procedures indicating the most reliable ones. Important relationships between parameters describing the algorithms are pointed out.
An optimal estimation scheme is presented, which determines the satellite attitude using the gyro readings and the star tracker measurements of a commonly used satellite attitude measuring unit. The scheme is mainly b...
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An optimal estimation scheme is presented, which determines the satellite attitude using the gyro readings and the star tracker measurements of a commonly used satellite attitude measuring unit. The scheme is mainly based on the exponential Fourier densities that have the desirable closure property under conditioning. By updating a finite and fixed number of parameters, the conditional probability density, which is an exponential Fourier density, is recursively determined. Simulation results indicate that the scheme is more accurate and robust than extended Kalman filtering. It is believed that this approach is applicable to many other attitude measuring units. As no linearization and approximation are necessary in the approach, it is ideal for systems involving high levels of randomness and/or low levels of observability and systems for which accuracy is of overriding importance.
Two new square root Kalman filtering algorithms are presented. Both algorithms are based on the spectral V − Λ of the covariance matrix where V is the matrix whose columns are the eigenvectors of the covariance and ...
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Two new square root Kalman filtering algorithms are presented. Both algorithms are based on the spectral V − Λ of the covariance matrix where V is the matrix whose columns are the eigenvectors of the covariance and Λ is the diagonal matrix of its eigenvalues. The algorithms use the covariance mode in the time propagation stage and the information mode in the measurement update stage. This switch between modes, which is trivial in the V − Λ representation, increases the efficiency of the algorithms. In the first algorithm, which is a continuous/discrete one, the V and Λ 1 2 matrices are propagated in time in a continuous manner, while the measurement update is a discrete time procedure. In the second algorithm, which is a discrete/discrete one, the time propagation of the V − Λ 1 2 factors is performed in discrete time too, using a procedure which is similar to the one used for the discrete measurement update. The discrete propagation and the measurement update are based on singular value decomposition algorithms. The square root nature of the algorithms is demonstrated numerically through a typical example. While promising all the virtues of square root routines, the V − Λ filters are also characterized by their ability to exhibit singularities as they occur.
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