Stochastic Control and Tuning Methodologies

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Author Index
A B C D E F G H I
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S T U V W X Y Z

Integrating Identification with Robust Control: a Mixed H_2/H_(infinity) Approach

Authors:

Liuping Wang, Graham C. Goodwin,

Volume: 1, Page 3341 Paper number 1247

Abstract:

In previous work we have proposed an H_2 design procedure aimed at bringing robust control and system identification closer together by using statistical confidence bounds. The key idea was to change the nominal design so as to reduce the overall variability from an a-priori specified desired performance. However, due to the choice of cost function, the original design method did not necessarily produce a robust control system with guaranteed stability. This paper addresses the latter problem. First a control validation procedure is proposed based on an estimated error bound; then the stability problem is formulated as a mixed H_2/H_(infinity) problem. The solution to this problem is obtained in the frequency domain using a classical algorithm due to Lawson (1961). An alternative algorithm is also described which uses standard quadratic programming methods. Finally a simulation example is presented which shows how the robust design method can be used in conjunction with standard identification procedures.

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Automatic Tuning for Classical Step-Response Specifications Using Iterative Feedback Tuning

Authors:

Magnus AAkerblad, Anders Hansson, Bo Wahlberg,

Volume: 1, Page 3347 Paper number 9039

Abstract:

The objective of this contribution is to study how to tune PID controllers with respect to classical step-response specifications using iterative feedback tuning. Typically the closed-loop response is improved considerably using only six to nine closed-loop experiments.

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A Robustness Result for Stochastic Control

Authors:

Gino Favero, Wolfgang J. Runggaldier,

Volume: 1, Page 3349 Paper number 1024

Abstract:

The solution of a stochastic control problem depends on the underlying model, i.e., on the probability measure induced by the model. The real world model may not be known precisely, and so one solves the problem for a hypothetical model that induces a measure generally different but close to the real one. We investigate two ways to derive a bound on the suboptimality of the hypothetical optimal control when it is used in the real problem. Both bounds are in terms of the Radon-Nikodym derivative of the real world measure with respect to the hypothetical one.

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A Learning Algorithm for Markov Decision Process with Adaptive State Aggregation

Authors:

John S. Baras, Vivek S. Borkar,

Volume: 1, Page 3351 Paper number 1716

Abstract:

We propose a simulation-based algorithm for learning good policies for a Markov decision process with unknown transition law, with aggregated stated. The state aggregation itself can be adapted on a slower time scale by an auxiliary learning algorithm. Rigorous justifications are provided for both algorithms.

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An Asymptotic Expansion in A 3-Dimensional Degenerated Control Problem With Finite Horizon

Authors:

Charles Marchetti,

Volume: 1, Page 3357 Paper number 73

Abstract:

We Study a degenerate nonlinear optimal stochastic control problem with finite horizon ([2]), [8] and [9]). Using the Hamilton-Jacobi-Bellman equation, we find an asymptotic expansion for this solution of this problem

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Covariance Analysis, Positivity and the Yakubovich-Kalman-Popov Lemma

Authors:

Rolf Johansson, Anders Robertsson,

Volume: 1, Page 3363 Paper number 1280

Abstract:

This paper presents theory and algorithms for covariance analysis and stochastic realization without any minimality condition imposed. Also without any minimality conditions, we show that several properties of covariance factorization and positive realness hold. The results are significant for validation in system identification of state-space models from finite input-output sequences. Using the Riccati equation, we have designed a procedure to provide a reduced-order stochastic model that is minimal with respect to system order as well as the number of stochastic inputs thereby avoiding several problems appearing in standard application of stochastic realization to the model validation problem. The case considered includes the problem of rank-deficient residual covariance matrices, a case which is encountered in applications with mixed stochastic-deterministic input-output properties as well as for cases where outputs are linearly dependent, thus extending previous results in covariance analysis.

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Control for Bounded Pseudo ARMAX Stochastic Systems via Linear B-Spline Approximations

Authors:

Hong Wang,

Volume: 1, Page 3369 Paper number 1449

Abstract:

Following the recently developed algorithms for the control of the shape of the output probability density function for general dynamic stochastic systems (Wang, 1998; 1999 and 2000), this paper presents the modelling and control algorithms for pseudo ARMAX systems, where different from all the existing ARMAX systems the considered system is subjected to any arbitrary bounded random input and the purpose of the control input design is to make the output probability density function of the system output as close as possible to a given distribution function. At first, the relationship between the input noise distribution and the output distribution is established via linear B-spline approximations. This is then followed by the description on the control algorithm design and discussions on control of unstable systems and nonlinear ARMAX systems.

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