Papers by Ricardo Takahashi
We find a searching method on ordered lists that surprisingly outperforms binary searching with r... more We find a searching method on ordered lists that surprisingly outperforms binary searching with respect to average query complexity while retaining minmax optimality. The method is shown to require O(log2 log2 n) queries on average while never exceeding dlog2 ne queries in the worst case, i.e. the minmax bound of binary searching. Our average results assume a uniform distribution hypothesis similar to those of previous authors under which the expected query complexity of interpolation search of O(log2 log2 n) is known to be optimal. Hence our method turns out to be optimal with respect to both minmax and average performance. We further provide robustness guarantees and perform several numerical experiments with both artificial and real data. Our results suggest that time savings range roughly from a constant factor of 10% to 50% to a logarithmic factor spanning orders of magnitude when different metrics are considered.
This paper presents a less conservative approach to compute, with any prescribed accuracy, the H∞... more This paper presents a less conservative approach to compute, with any prescribed accuracy, the H∞ guaranteed cost of time-delay continuous-time linear time-invariant systems subjected to polytopic uncertainties. The proposed analysis approach is based on a branch-and-bound algorithm that incorporates a recent LMI-based analysis formulation and a new polytope partition strategy. In the branch-and-bound algorithm, the upper bound function is defined as the worst case guaranteed H∞ disturbance attenuation level computed for the subpolytopes achieved with successive partitions of the polytope which describes the uncertainty domain. The lower bound function is defined as the worst case H∞ norm computed in the polytope and subpolytope vertices. The difference between the upper and lower bound functions converges to zero as the initial polytope is split into smaller subpolytopes resulting in the H∞ guaranteed cost for the whole initial polytope with the required accuracy. It is also presen...
ACM Transactions on Mathematical Software, 2021
We identify a class of root-searching methods that surprisingly outperform the bisection method o... more We identify a class of root-searching methods that surprisingly outperform the bisection method on the average performance while retaining minmax optimality. The improvement on the average applies for any continuous distributional hypothesis. We also pinpoint one specific method within the class and show that under mild initial conditions it can attain an order of convergence of up to 1.618, i.e., the same as the secant method. Hence, we attain both an improved average performance and an improved order of convergence with no cost on the minmax optimality of the bisection method. Numerical experiments show that, on regular functions, the proposed method requires a number of function evaluations similar to current state-of-the-art methods, about 24% to 37% of the evaluations required by the bisection procedure. In problems with non-regular functions, the proposed method performs significantly better than the state-of-the-art, requiring on average 82% of the total evaluations required ...
Proceedings IECON '91: 1991 International Conference on Industrial Electronics, Control and Instrumentation
IEEE Control Systems, 1997
This article presents a methodology for sub-optimal design of PID compensators for systems subjec... more This article presents a methodology for sub-optimal design of PID compensators for systems subject to disturbance signals and to parametric uncertainties of polytope type. The adopted optimality criteria are the H2 and H∞ norms of the transfer matrices from the disturbance inputs and from the reference input to the controlled output error. Time constant constraints are also employed in the
Proceedings of the 44th IEEE Conference on Decision and Control
This paper presents a less conservative approach to compute, with any prescribed accuracy, the H∞... more This paper presents a less conservative approach to compute, with any prescribed accuracy, the H∞guaranteed cost of time-delay continuous-time linear time-invariant systems subjected to polytopic uncertainties. The proposed analysis approach is based on a branch-and-bound algorithm that incorporates a recent LMI-based analysis formulation and a new polytope partition strategy. In the branch-and-bound algorithm, the upper bound function is defined as
12th Biennial IEEE Conference on Electromagnetic Field Computation, CEFC 2006, 2006
This work studies the design of broadband Yagi-Uda antennas considering 3 conflicting specificati... more This work studies the design of broadband Yagi-Uda antennas considering 3 conflicting specifications in 3 different frequencies, thus, a 9 objectives optimization problem. This multiobjective problem was solved using the cone of efficient direction algorithm and the multiobjective line search. Results for 6 elements antennas are presented
2010 IEEE/ACM 14th International Symposium on Distributed Simulation and Real Time Applications, 2010
Page 1. An Evolutionary Dynamic Approach for Designing Wireless Sensor Networks for Real Time Mon... more Page 1. An Evolutionary Dynamic Approach for Designing Wireless Sensor Networks for Real Time Monitoring Flávio VC Martins ∗ , Eduardo G. Carrano , Elizabeth F. Wanner , Ricardo HC Takahashi and Geraldo R. Mateus § ...
2006 IEEE International Conference on Evolutionary Computation
This paper studies the issue of defining the fitness function for ranking-based selection. Two fa... more This paper studies the issue of defining the fitness function for ranking-based selection. Two families of parametric nonlinear functions are considered, for reaching different selection pressures, controlled by the function parameter. Both the static versions and some dynamic varying versions of such functions are considered. The usual linear fitness function is shown to be systematically outperformed by several instances of
Environmental and Ecological Statistics, 2014
Journal of Applied Mathematics, 2013
A heuristic algorithm is proposed for a class of stochastic discrete-time continuous-variable dyn... more A heuristic algorithm is proposed for a class of stochastic discrete-time continuous-variable dynamic programming problems submitted to non-Gaussian disturbances. Instead of using the expected values of the objective function, the randomness nature of the decision variables is kept along the process, while Pareto fronts weighted by all quantiles of the objective function are determined. Thus, decision makers are able to choose any quantile they wish. This new idea is carried out by using Monte Carlo simulations embedded in an approximate algorithm proposed to deterministic dynamic programming problems. The new method is tested in instances of the classical inventory control problem. The results obtained attest for the efficiency and efficacy of the algorithm in solving these important stochastic optimization problems.
International Journal of Systems Science, 2004
IEE Proceedings - Control Theory and Applications, 1998
IEEE Transactions on Magnetics, 1999
This paper presents an adaptive deep cut algorithm for the ellipsoid method. The formulation prop... more This paper presents an adaptive deep cut algorithm for the ellipsoid method. The formulation proposed employs a variable cut depth which depends on an estimate of the current ellipsoid center distance to the solution. These adaptations in the formulation provide an enhanced convergence in the algorithm without losing robustness. The results of an analytical problem and benchmark problem 22 indicate
IEEE Transactions on Magnetics, 2006
Evolutionary Computation, 2014
Recent works raised the hypothesis that the assignment of a geometry to the decision variable spa... more Recent works raised the hypothesis that the assignment of a geometry to the decision variable space of a combinatorial problem could be useful both for providing meaningful descriptions of the fitness landscape and for supporting the systematic construction of evolutionary operators (the geometric operators) that make a consistent usage of the space geometric properties in the search for problem optima. This paper introduces some new geometric operators that constitute the realization of searches along the combinatorial space versions of the geometric entities descent directions and subspaces. The new geometric operators are stated in the specific context of the wireless sensor network dynamic coverage and connectivity problem (WSN-DCCP). A genetic algorithm (GA) is developed for the WSN-DCCP using the proposed operators, being compared with a formulation based on integer linear programming (ILP) which is solved with exact methods. That ILP formulation adopts a proxy objective funct...
ArXiv, 2021
Current state-of-the-art multi-objective optimization solvers, by computing gradients of all m ob... more Current state-of-the-art multi-objective optimization solvers, by computing gradients of all m objective functions per iteration, produce after k iterations a measure of proximity to critical conditions that is upperbounded by O (1/ √ k) when the objective functions are assumed to have L−Lipschitz continuous gradients; i.e. they require O (m/ε2) gradient and function computations to produce a measure of proximity to critical conditions bellow some target ε . We reduce this toO (1/ε2) with a method that requires only a constant number of gradient and function computations per iteration; and thus, we obtain for the first time a multi-objective descent-type method with a query complexity cost that is unaffected by increasing values ofm. For this, a brand new multi-objective descent direction is identified, which we name the central descent direction, and, an incremental approach is proposed. Robustness properties of the central descent direction are established, measures of proximity t...
IEEE Transactions on Magnetics, 2001
This paper presents a strategy for robust H2/H∞ dynamic output-feedback control synthesis, with r... more This paper presents a strategy for robust H2/H∞ dynamic output-feedback control synthesis, with regional pole placement, based on a multiobjective optimization algorithm applied directly in the space of controller parameters. The H2 and H∞ norms, computed in all polytope vertices and in “worst case” interior points are taken as the optimization objectives. An a posteriori LMI-based guaranteed cost computation algorithm is applied for worst-case performance assessment. Keywords— Robust H2/H∞ control, dynamic output feedback, regional pole placement, multiobjective optimization, non-differentiable optimization. Resumo— Este artigo apresenta uma estratégia para śıntese de controladores robustos H2/H∞ por realimentação dinâmica da sáıda, com alocação regional de pólos, baseada em um algoritmo de otimização multi-objetivo aplicado diretamente no espaço de parâmetros do controlador. As normas H2 e H∞, calculadas em todos os vértices do politopo e, em certos casos, em pontos interiores com...
This paper presents a strategy for robust H2/H∞ dynamic outputfeedback control synthesis, with re... more This paper presents a strategy for robust H2/H∞ dynamic outputfeedback control synthesis, with regional pole placement, applied to linear continuous-time time-invariant systems with polytope-bounded uncertainty. The proposed synthesis approach is based on a multiobjective optimization algorithm applied directly in the space of controller parameters. The H2 and H∞ norms, computed in all polytope vertices and in possible “worst case” interior points are taken as the optimization objectives. A branch-and-bound algorithm based on LMI guaranteed cost formulation is applied to validate the controller design. Examples are presented to show the effectiveness of the proposed strategy, including examples of full order and low order, centralized and decentralized control systems. Copyright c ©2005 IFAC.
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Papers by Ricardo Takahashi