Hiro Mukai received a bachelor's degree in electrical engineering from Waseda University. He then received his master's degree and a doctorate in electrical engineering and computer sciences, both from the University of California, Berkeley. After brief service as a post-doctoral engineer at Berkeley, he joined Washington University as an assistant professor in 1975. In 1982, while on a sabbatical leave, he taught at the University of California, Berkeley and worked as a full-time consultant in San Francisco for the Pacific Gas and Electric, a local utility company for most of northern California. In 1997-98, while on a sabbatical leave, he taught at the University of Namur in Belgium and worked as a researcher at the University of Ghent in Belgium. He is currently Professor of Engineering and Applied Science, Associate Chair, and Director of the Master of Control Engineering Program in the Department of Electrical and Systems Engineering at Washington University in St. Louis.
Hiro Mukai's research activities involve development of new computational methods for both unconstrained and constrained optimization as well as for monitoring and controlling engineering systems such as electrical power networks. His recent interests focus on computation methods for differential games and dynamic estimation.
Differential Games: We investigate a numerical method for computing a local Nash (saddle-point) solution to a zero-sum differential game for a nonlinear system. Given a solution estimate to the game, we define a subproblem, which is obtained from the original problem by linearizing its system dynamics around the solution estimate and expanding its payoff function to quadratic terms around the same solution estimate. We then apply the standard Riccati equation method to the linear-quadratic subproblem and compute its saddle solution. We then update the current solution estimate by adding the computed saddle solution of the subproblem multiplied by a small positive constant (a step size) to the current solution estimate for the original game. We repeat this process and successively generate better solution estimates. Our applications of this sequential method to air combat simulations demonstrate experimentally that the solution estimates converge to a local Nash (saddle) solution of the original game.
Stochastic Discrete Optimization: A stochastic search method has been designed for finding a global solution to the stochastic discrete optimization problem in which the objective function must be estimated through a probabilistic model. The variables are discrete, thus making the traditional approach of gradient-type methods inapplicable. Although there are many practical problems of this type, no nonheuristic methods have been proposed for such stochastic discrete problems. The designed method is very simple, yet it finds the global optimum solution. The method exploits the randomness of the probabilistic model and generates a sequence of solution estimates. This generated sequence turns out to be a nonstationary Markov chain, and it is shown that the Markov chain is strongly ergodic and that the probability that the current solution estimate is global optimum converges to one.
Optimization Algorithm with Probabilistic Estimation: A stochastic continuous optimization algorithm has been developed based on the idea of the gradient method which incorporates a new adaptive-precision technique. The variables are continuous, but probabilistic elements are present. Hence, there will be a need for fine-tuning various parameters in using traditional optimization methods. Because of this new technique, unlike recent methods, the proposed algorithm adaptively selects the precision without any need for prior knowledge on the speed of convergence of the generated sequence. With this new technique, the algorithm can avoid increasing the estimation precision unnecessarily, yet it retains its favorable convergence properties.
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