Fixed-structure robust controller synthesis based on sign definite condition by a special quantifier elimination

Anai, Hirokazu; Hara, Shinji

doi:10.1109/acc.2000.876713

Cited by 30 publications

(24 citation statements)

References 7 publications

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“…In this reference, the special structure afforded by piecewise linear functions is exploited to derive algorithms with very reasonable running times, reasonable enough to allow their application to realistic problems in network monitoring. For other cases of the application of symbolic methods to problems in control theory (equilibrium computation, stabilization, tracking) the reader is referred to [18], [27], and [28].…”

Section: )mentioning

confidence: 99%

Reachability Analysis of Discrete-Time Systems With Disturbances

Raković

Kerrigan

Mayne

et al. 2006

IEEE Trans. Automat. Contr.

156

108

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Abstract-This paper presents new results that allow one to compute the set of states that can be robustly steered in a finite number of steps, via state feedback control, to a given target set. The assumptions that are made in this paper are that the system is discrete-time, nonlinear and time-invariant and subject to mixed constraints on the state and input. A persistent disturbance, dependent on the current state and input, acts on the system. Existing results are not able to address state-and input-dependent disturbances and the results in this paper are, therefore, a generalization of previously published results. One of the key aims of this paper is to present results such that one can perform the relevant set computations using polyhedral algebra and computational geometry software, provided the system is piecewise affine and the constraints are polygonal. Existing methods are only applicable to piecewise affine systems that either have no control inputs or no disturbances, whereas the results in this paper remove this limitation. Some simple examples are also given that show that, even if all the relevant sets are convex and the system is linear, convexity of the set of controllable states cannot be guaranteed.

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Section: )mentioning

confidence: 99%

Reachability Analysis of Discrete-Time Systems With Disturbances

Raković

Kerrigan

Mayne

et al. 2006

IEEE Trans. Automat. Contr.

156

108

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“…Subsequently this enables us to achieve control system design with respect to SORPRP systematically. In fact, since the actual control design problems treated are recast as simple conditions on an univariate polynomial with parametric coefficients (one of them is a sign definite condition), we can utilize an efficient quantifier elimination algorithm using Sturm-Habicht sequence [1,10]. The proposed method is applied to an even polynomial derived from "linear quadratic regulator (LQR) problem" which is one of the main concerns in control theory.…”

Section: Introductionmentioning

confidence: 99%

“…As the controller C(s, q) has fixed-structure with some parameters q, what we have to do is to seek feasible controller parameters q which satisfy the controller design problem. For such problems, techniques in computer algebra have been successfully applied [9,14,1,2]. Stability is the first necessary requirement for control system design, and assigning roots of a certain polynomial within a desired region is an essential problem for stability study.…”

Section: Introductionmentioning

confidence: 99%

“…Applying real quantifier elimination (QE) to the sign definite condition, we can obtain possible regions of controller parameters q to meet D-stability. In particular, we can utilize an efficient quantifier elimination algorithm specialized to SDC [1,10]. These controller synthesis methods with respect to stability are implemented as functions in a MATLAB toolbox for robust parametric control [3] In this paper we focus on the sum of roots with positive real parts (SORPRP) of a given even polynomial, and provide another successful application of computer algebra to control design problem, where the SORPRP is related to certain index of "average" stability in optimal control.…”

Section: Introductionmentioning

confidence: 99%

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Sum of roots with positive real parts

Anai

Hara

Yokoyama

2005

Proceedings of the 2005 International Symposium on Symbolic and Algebraic Computation

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In this paper we present a method to compute or estimate the sum of roots with positive real parts (SORPRP) of a polynomial, which is related to a certain index of "average" stability in optimal control, without computing explicit numerical values of the roots. The method is based on symbolic and algebraic computations and enables us to deal with polynomials with parametric coefficients for their SORPRP. This leads to provide a novel systematic method to achieve optimal regulator design in control by combining the method with quantifier elimination. We also report some experimental result for a typical class of plants and confirm the effectiveness of the proposed method.

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“…Furthermore, using SyNRAC as a kernel, we are now pushing the further development of design tools based on computer algebra (in particular, QE) in various application fields: One successful attempt is the development of a toolbox for parametric robust control design on MATLAB [3] based on the authors' previous works concerning QE-based robust control design [4,5,6,7].…”

Section: Introductionmentioning

confidence: 99%