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J C Geromel - One of the best experts on this subject based on the ideXlab platform.

  • differential linear matrix inequality in optimal sampled data control
    Automatica, 2019
    Co-Authors: J C Geromel, Patrizio Colaneri, P Bolzern
    Abstract:

    This paper addresses the design of optimal sampled-data output feedback full order controllers for linear continuous-time invariant systems. First, H2 and H∞ performance indices are determined and expressed through differential linear matrix inequalities (DLMIs). Second, in each scenario, the optimal sampled-data controller of the aforementioned class is determined from a Convex Programming Problem expressed by DLMIs. Theoretical achievements are based on the direct application of the celebrated Bellman’s Principle of Optimality expressed in terms of the dynamic Programming equation associated to the time interval corresponding to two successive sampling instants. The design Problems to be dealt with are Convex and are solved by converting all constraints to LMI and adopting a piecewise linear solution. The possibility of aperiodic sampling is considered and briefly discussed. Finally, academic examples are solved for illustration.

  • brief continuous time state feedback h2 control of markovian jump linear systems via Convex analysis
    Automatica, 1999
    Co-Authors: O L V Costa, J Do B R Val, J C Geromel
    Abstract:

    Continuous-time H"2-control Problem for the class of linear systems with Markovian jumps (MJLS) using Convex analysis is considered in this paper. The definition of the H"2-norm for continuous-time MJLS is presented and related to the appropriate observability and controllability Gramians. A Convex Programming formulation for the H"2-control Problem of MJLS is developed. That enables us to tackle the optimization Problem of MJLS under the assumption that the transition rate matrix @P=[@p"i"j] for the Markov chain may not be exactly known, but belongs to an appropriate Convex set. An equivalence between the Convex formulation when @P is exactly known and the usual dynamic Programming approach of quadratic optimal control of MJLS is established. It is shown that there exists a solution for the Convex Programming Problem if and only if there exists the mean-square stabilizing solution for a set of coupled algebraic Riccati equations. These results are compared with other related works in the current literature.

  • on a Convex parameter space method for linear control design of uncertain systems
    Siam Journal on Control and Optimization, 1991
    Co-Authors: J C Geromel, Pedro L D Peres, J Bernussou
    Abstract:

    This paper presents a new procedure for continuous and discrete-time linear control systems design. It consists of the definition of a Convex Programming Problem in the parameter space that, when solved, provides the feedback gain. One of the most important features of the procedure is that additional design constraints are easily incorporated in the original formulation, yielding solutions to Problems that have raised a great deal of interest within the last few years. This is precisely the case of the decentralized control Problem and the quadratic stabilizability Problem of uncertain systems with both dynamic and input uncertain matrices. In this last case, necessary and sufficient conditions for the existence of a linear stabilizing gain are provided and, to the authors’ knowledge, this is one of the first numerical procedures able to handle and solve this interesting design Problem for high-order, continuous-time or discrete-time linear models. The theory is illustrated by examples.

P Bolzern - One of the best experts on this subject based on the ideXlab platform.

  • differential linear matrix inequality in optimal sampled data control
    Automatica, 2019
    Co-Authors: J C Geromel, Patrizio Colaneri, P Bolzern
    Abstract:

    This paper addresses the design of optimal sampled-data output feedback full order controllers for linear continuous-time invariant systems. First, H2 and H∞ performance indices are determined and expressed through differential linear matrix inequalities (DLMIs). Second, in each scenario, the optimal sampled-data controller of the aforementioned class is determined from a Convex Programming Problem expressed by DLMIs. Theoretical achievements are based on the direct application of the celebrated Bellman’s Principle of Optimality expressed in terms of the dynamic Programming equation associated to the time interval corresponding to two successive sampling instants. The design Problems to be dealt with are Convex and are solved by converting all constraints to LMI and adopting a piecewise linear solution. The possibility of aperiodic sampling is considered and briefly discussed. Finally, academic examples are solved for illustration.

Patrizio Colaneri - One of the best experts on this subject based on the ideXlab platform.

  • differential linear matrix inequality in optimal sampled data control
    Automatica, 2019
    Co-Authors: J C Geromel, Patrizio Colaneri, P Bolzern
    Abstract:

    This paper addresses the design of optimal sampled-data output feedback full order controllers for linear continuous-time invariant systems. First, H2 and H∞ performance indices are determined and expressed through differential linear matrix inequalities (DLMIs). Second, in each scenario, the optimal sampled-data controller of the aforementioned class is determined from a Convex Programming Problem expressed by DLMIs. Theoretical achievements are based on the direct application of the celebrated Bellman’s Principle of Optimality expressed in terms of the dynamic Programming equation associated to the time interval corresponding to two successive sampling instants. The design Problems to be dealt with are Convex and are solved by converting all constraints to LMI and adopting a piecewise linear solution. The possibility of aperiodic sampling is considered and briefly discussed. Finally, academic examples are solved for illustration.

  • The static output feedback stabilization Problem as a concave-Convex Programming Problem
    Proceedings of the 2004 American Control Conference, 2004
    Co-Authors: Alessandro Astolfi, Patrizio Colaneri
    Abstract:

    It is shown that the static output feedback stabilization Problem for linear multi-input single-output (MISO) systems can be posed as a concave-Convex Programming Problem. This allows the potential design of minimization algorithms yielding a stabilizing static output feedback gain, if it exists, or showing that the Problem is not solvable at all.

Masahiro Inuiguchi - One of the best experts on this subject based on the ideXlab platform.

  • an inner approximation method incorporating with a penalty function method for a reverse Convex Programming Problem
    Journal of Computational and Applied Mathematics, 2002
    Co-Authors: S Yamada, Tetsuzo Tanino, Masahiro Inuiguchi
    Abstract:

    In this paper, we consider a reverse Convex Programming Problem constrained by a Convex set and a reverse Convex set which is defined by the complement of the interior of a compact Convex set X. When X is not necessarily a polytope, an inner approximation method has been proposed (J. Optim. Theory Appl. 107(2) (2000) 357). The algorithm utilizes inner approximation of X by a sequence of polytopes to generate relaxed Problems. Then, every accumulation point of the sequence of optimal solutions of relaxed Problems is an optimal solution of the original Problem. In this paper, we improve the proposed algorithm. By underestimating the optimal value of the relaxed Problem, the improved algorithms have the global convergence.

  • inner approximation method for a reverse Convex Programming Problem
    Journal of Optimization Theory and Applications, 2000
    Co-Authors: Seiji Yamada, Tetsuzo Tanino, Masahiro Inuiguchi
    Abstract:

    In this paper, we consider a reverse Convex Programming Problem constrained by a Convex set and a reverse Convex set, which is defined by the complement of the interior of a compact Convex set X. We propose an inner approximation method to solve the Problem in the case where X is not necessarily a polytope. The algorithm utilizes an inner approximation of X by a sequence of polytopes to generate relaxed Problems. It is shown that every accumulation point of the sequence of optimal solutions of the relaxed Problems is an optimal solution of the original Problem.

  • An inner approximation method for a reverse Convex Programming Problem
    IEEE SMC'99 Conference Proceedings. 1999 IEEE International Conference on Systems Man and Cybernetics (Cat. No.99CH37028), 1999
    Co-Authors: S Yamada, Teruo Tanino, Masahiro Inuiguchi, K. Tatsumi
    Abstract:

    In this paper, we consider a reverse Convex Programming Problem constrained by a Convex set and a reverse Convex set which is defined by the complement of the interior of a compact Convex set X. We propose an inner approximation method to solve the Problem in the case where X is not necessarily a polytope. The algorithm utilizes inner approximation of X by a sequence of polytopes to generate relaxed Problems. It is shown that every accumulation point of the sequence of optimal solutions of relaxed Problems is an optimal solution of the original Problem.

Steve B Jiang - One of the best experts on this subject based on the ideXlab platform.

  • gpu based ultra fast direct aperture optimization for online adaptive radiation therapy
    Physics in Medicine and Biology, 2010
    Co-Authors: Chunhua Men, Xun Jia, Steve B Jiang
    Abstract:

    Online adaptive radiation therapy (ART) has great promise to significantly reduce normal tissue toxicity and/or improve tumor control through real-time treatment adaptations based on the current patient anatomy. However, the major technical obstacle for clinical realization of online ART, namely the inability to achieve real-time efficiency in treatment re-planning, has yet to be solved. To overcome this challenge, this paper presents our work on the implementation of an intensity-modulated radiation therapy (IMRT) direct aperture optimization (DAO) algorithm on the graphics processing unit (GPU) based on our previous work on the CPU. We formulate the DAO Problem as a large-scale Convex Programming Problem, and use an exact method called the column generation approach to deal with its extremely large dimensionality on the GPU. Five 9-field prostate and five 5-field head-and-neck IMRT clinical cases with 5 × 5 mm2 beamlet size and 2.5 × 2.5 × 2.5 mm3 voxel size were tested to evaluate our algorithm on the GPU. It takes only 0.7–3.8 s for our implementation to generate high-quality treatment plans on an NVIDIA Tesla C1060 GPU card. Our work has therefore solved a major Problem in developing ultra-fast (re-)planning technologies for online ART.