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Michael Basin - One of the best experts on this subject based on the ideXlab platform.

  • Discrete-time optimal control for stochastic nonlinear Polynomial Systems
    International Journal of General Systems, 2014
    Co-Authors: Miguel Hernandez-gonzalez, Michael Basin
    Abstract:

    This paper presents a solution to the discrete-time optimal control problem for stochastic nonlinear Polynomial Systems over linear observations and a quadratic criterion. The solution is obtained in two steps: the optimal control algorithm is developed for nonlinear Polynomial Systems by considering complete information when generating a control law. Then, the state estimate equations for discrete-time stochastic nonlinear Polynomial System over linear observations are employed. The closed-form solution is finally obtained substituting the state estimates into the obtained control law. The designed optimal control algorithm can be applied to both distributed and lumped Systems. To show effectiveness of the proposed controller, an illustrative example is presented for a second degree Polynomial System. The obtained results are compared to the optimal control for the linearized System.

  • Mean-square filter design for stochastic Polynomial Systems with Gaussian and Poisson noises
    International Journal of Systems Science, 2013
    Co-Authors: Michael Basin, Pablo Rodriguez-ramirez
    Abstract:

    This paper addresses the mean-square finite-dimensional filtering problem for Polynomial System states with both, Gaussian and Poisson, white noises over linear observations. A constructive procedure is established to design the mean-square filtering equations for System states described by Polynomial equations of an arbitrary finite degree. An explicit closed form of the designed filter is obtained in case of a third-order Polynomial System. The theoretical result is complemented with an illustrative example verifying performance of the designed filter.

  • optimal control for a Polynomial System with a quadratic criterion over infinite horizon
    American Control Conference, 2013
    Co-Authors: Michael Basin, Manuel Jimenezlizarraga, Pablo Rodriguezramirez, Celeste Rodriguezcarreon
    Abstract:

    This paper proposes an optimal control algorithm for a Polynomial System with a quadratic criterion over infinite horizon. The designed regulator gives a closed form solution to the infinite horizon optimal control problem for a Polynomial System with a quadratic criterion. The obtained solution consists in a feedback control law obtained by solving a Riccati algebraic equation dependent on the state. Numerical simulations in the example show advantages of the developed algorithm.

  • mean square filter design for nonlinear Polynomial Systems with poisson noise
    American Control Conference, 2011
    Co-Authors: Michael Basin, Juan J. Maldonado
    Abstract:

    This paper presents the mean-square filtering problem for incompletely measured Polynomial System states, confused with white Poisson noises, over linear observations. The problem is treated proceeding from the general expression for the stochastic Ito differential of the optimal estimate and the error variance. As a result, the Ito differentials for the optimal estimate and error variance corresponding to the stated filtering problem are first derived. The procedure for obtaining a closed System of the filtering equations for any Polynomial System state with white Poisson noises over linear observations is then established, which yields the explicit closed form of the filtering equations in the particular case of a third-order state equation. In the example, performance of the designed optimal filter is verified against the conventional mean-square Polynomial filter designed for Systems with white Gaussian noises.

  • CCA/ISIC - Sub-optimal risk-sensitive filtering for third degree Polynomial stochastic Systems
    2009 IEEE International Conference on Control Applications, 2009
    Co-Authors: Ma. Aracelia Alcorta G., Sonia G. Anguiano, Michael Basin, Juan J. Maldonado
    Abstract:

    The risk-sensitive filter design problem with respect to the exponential mean-square criterion is considered for stochastic Gaussian Systems with Polynomial drift terms and intensity parameters multiplying diffusion terms in the state and observations equations. The closed-form suboptimal filtering algorithm is obtained by linearizing a nonlinear third degree Polynomial System at the operating point and reducing the original problem to the optimal filter design for a first degree Polynomial System. The reduced filtering problem is solved using quadratic value functions as solutions to the corresponding Fokker-Planck-Kolmogorov equation. The performance of the obtained risk-sensitive filter for stochastic third degree Polynomial Systems is verified in a numerical example against the mean-square optimal third degree Polynomial filter and extended Kalman-Bucy filter, through comparing the exponential mean-square criteria values. The simulation results reveal strong advantages in favor of the designed risk-sensitive algorithm for large values of the intensity parameters.

Pablo Rodriguez-ramirez - One of the best experts on this subject based on the ideXlab platform.

  • Mean-square filter design for stochastic Polynomial Systems with Gaussian and Poisson noises
    International Journal of Systems Science, 2013
    Co-Authors: Michael Basin, Pablo Rodriguez-ramirez
    Abstract:

    This paper addresses the mean-square finite-dimensional filtering problem for Polynomial System states with both, Gaussian and Poisson, white noises over linear observations. A constructive procedure is established to design the mean-square filtering equations for System states described by Polynomial equations of an arbitrary finite degree. An explicit closed form of the designed filter is obtained in case of a third-order Polynomial System. The theoretical result is complemented with an illustrative example verifying performance of the designed filter.

Mikhail Skliar - One of the best experts on this subject based on the ideXlab platform.

  • optimal filtering for Polynomial System states with Polynomial multiplicative noise
    American Control Conference, 2006
    Co-Authors: Michael Basin, Jose P Perez, Mikhail Skliar
    Abstract:

    In this paper, the optimal filtering problem for Polynomial System states with Polynomial multiplicative noise over linear observations is treated proceeding from the general expression for the stochastic Ito differential of the optimal estimate and the error variance. As a result, the Ito differentials for the optimal estimate and error variance corresponding to the stated filtering problem are first derived. The procedure for obtaining a closed System of the filtering equations for any Polynomial state with Polynomial multiplicative noise over linear observations is then established, which yields the explicit closed form of the filtering equations in the particular cases of of a linear state equation with linear multiplicative noise and a bilinear state equation with bilinear multiplicative noise. In the example, performance of the designed optimal filter is verified for a quadratic state with a quadratic multiplicative noise over linear observations against the optimal filter for a quadratic state with a state-independent noise and a conventional extended Kalman-Bucy filter.

  • optimal filtering for Polynomial System states with Polynomial multiplicative noise
    International Journal of Robust and Nonlinear Control, 2006
    Co-Authors: Michael Basin, Jose P Perez, Mikhail Skliar
    Abstract:

    In this paper, the optimal filtering problem for Polynomial System states with Polynomial multiplicative noise over linear observations is treated proceeding from the general expression for the stochastic Ito differential of the optimal estimate and the error variance. As a result, the Ito differentials for the optimal estimate and error variance corresponding to the stated filtering problem are first derived. The procedure for obtaining a closed System of the filtering equations for any Polynomial state with Polynomial multiplicative noise over linear observations is then established, which yields the explicit closed form of the filtering equations in the particular cases of a linear state equation with linear multiplicative noise and a bilinear state equation with bilinear multiplicative noise. In the example, performance of the designed optimal filter is verified for a quadratic state with a quadratic multiplicative noise over linear observations against the optimal filter for a quadratic state with a state-independent noise and a conventional extended Kalman–Bucy filter. Copyright © 2006 John Wiley & Sons, Ltd.

  • optimal filtering for partially measured Polynomial System states
    American Control Conference, 2005
    Co-Authors: Michael Basin, Mikhail Skliar
    Abstract:

    In this paper, the optimal filtering problem for Polynomial Systems with partially measured linear part over linear observations is treated proceeding from the general expression for the stochastic Ito differential of the optimal estimate and the error variance. As a result, the Ito differentials for the optimal estimate and error variance corresponding to the stated filtering problem are first derived. The procedure for obtaining a closed System of the filtering equations for any Polynomial state with partially measured linear part over linear observations with delay is then established, which yields the explicit closed form of the filtering equations in the particular case of a bilinear System state. In the example, performance of the designed optimal filter is verified for a quadratic-linear state with unmeasured linear part over linear observations against the conventionally designed extended Kalman-Bucy filter.

Zhang Weinian - One of the best experts on this subject based on the ideXlab platform.

Philippe Trébuchet - One of the best experts on this subject based on the ideXlab platform.

  • Border Basis for Polynomial System Solving and Optimization
    2016
    Co-Authors: Philippe Trébuchet, Bernard Mourrain, Marta Abril Bucero
    Abstract:

    We describe the software package borderbasix dedicated to the computation of border bases and the solutions of Polynomial equations. We present the main ingredients of the border basis algorithm and the other methods implemented in this package: numerical solutions from multiplication matrices, real radical computation, Polynomial optimization. The implementation parameterized by the coefficient type and the choice function provides a versatile family of tools for Polynomial computation with modular arithmetic, floating point arithmetic or rational arithmetic. It relies on linear algebra solvers for dense and sparse matrices for these various types of coefficients. A connection with SDP solvers has been integrated for the combination of relaxation approaches with border basis computation. Extensive benchmarks on typical Polynomial Systems are reported, which show the very good performance of the tool.

  • stable normal forms for Polynomial System solving
    Theoretical Computer Science, 2008
    Co-Authors: Bernard Mourrain, Philippe Trébuchet
    Abstract:

    The paper describes and analyzes a method for computing border bases of a zero-dimensional ideal I. The criterion used in the computation involves specific commutation Polynomials, and leads to an algorithm and an implementation extending the ones in [B. Mourrain, Ph. Trebuchet, Generalised normal forms and Polynomial System solving, in: M. Kauers (Ed.), Proc. Intern. Symp. on Symbolic and Algebraic Computation, ACM Press, New-York, 2005, pp. 253-260]. This general border basis algorithm weakens the monomial ordering requirement for Grobner bases computations. It is currently the most general setting for representing quotient algebras, embedding into a single formalism Grobner bases, Macaulay bases and a new representation that does not fit into the previous categories. With this formalism, we show how the syzygies of the border basis are generated by commutation relations. We also show that our construction of normal form is stable under small perturbations of the ideal, if the number of solutions remains constant. This feature has a huge impact on practical efficiency, as illustrated by the experiments on classical benchmark Polynomial Systems, at the end of the paper.

  • Stable normal forms for Polynomial System solving
    Theoretical Computer Science, 2008
    Co-Authors: Bernard Mourrain, Philippe Trébuchet
    Abstract:

    This paper describes and analyzes a method for computing border bases of a zero-dimensional ideal $I$. The criterion used in the computation involves specific commutation Polynomials and leads to an algorithm and an implementation extending the one provided in [MT'05]. This general border basis algorithm weakens the monomial ordering requirement for \grob bases computations. It is up to date the most general setting for representing quotient algebras, embedding into a single formalism Gröbner bases, Macaulay bases and new representation that do not fit into the previous categories. With this formalism we show how the syzygies of the border basis are generated by commutation relations. We also show that our construction of normal form is stable under small perturbations of the ideal, if the number of solutions remains constant. This new feature for a symbolic algorithm has a huge impact on the practical efficiency as it is illustrated by the experiments on classical benchmark Polynomial Systems, at the end of the paper.

  • generalized normal forms and Polynomial System solving
    International Symposium on Symbolic and Algebraic Computation, 2005
    Co-Authors: Bernard Mourrain, Philippe Trébuchet
    Abstract:

    This paper describes a new method for computing the normal form of a Polynomial modulo a zero-dimensional ideal I. We give a detailed description of the algorithm, a proof of its correctness, and finally experimentations on classical benchmark Polynomial Systems. The method that we propose can be thought as an extension of both the Grobner basis method and the Macaulay construction. We have weaken the monomial ordering requirement for bases computations, which allows us to construct new type of representations for the quotient algebra. This approach yields more freedom in the linear algebra steps involved, which allows us to take into account numerical criteria while performing the symbolic steps. This is a new feature for a symbolic algorithm, which has a huge impact on the practical efficiency.