An Ordinal Optimization Approach to Optimal Control Problems
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An Ordinal Optimization Approach to Optimal Control Problems
An Ordinal Optimization Approach to Optimal Control Problems’Mei (May) Deng® and Yu-Chi Ho’ABSTRACT - We introduce an ordinal optimization approach to An Ordinal Optimization Approach to Optimal Control Problemso the study of optimal control law design. As illustration of the methodology, we find the optimal feedback control law for a simple LQG problem without the benefit of theory. For the famous unsolved Witsenhausen problem (1968). a solution that is 50% better than the Witsenbausen solution is found.K An Ordinal Optimization Approach to Optimal Control ProblemsEYWORDS: Artificial Intelligence. Optimal Control. Optimization. Search Methods. Stochastic Systems. Simulation1.IntroductionOrdinal Optimization (OO)An Ordinal Optimization Approach to Optimal Control Problems
is a method of speeding up the process of stochastic optimization via parametric simulation (Deng-Ho-Hu. 1992; Ho. 1994; Ho-Larson. 1995; Ho-Deng. 19An Ordinal Optimization Approach to Optimal Control Problems’Mei (May) Deng® and Yu-Chi Ho’ABSTRACT - We introduce an ordinal optimization approach to An Ordinal Optimization Approach to Optimal Control Problemss is intuitively reasonable. To determine whether A is greater or less than B is a simpler task than to determine the value of A-B in stochastic situations. Recent results actually quantified this advantage (Dai. 1997; Lau-Ho. 1997; Xie. 1997). (ii) SOFTENING THE GOAL OF OPTIMIZATION ALSO MAKES THE An Ordinal Optimization Approach to Optimal Control ProblemsPROBLEM EASIER Instead of asking the "best for sure" we settle for the "good enough with high probability". For example, consider a search on design sAn Ordinal Optimization Approach to Optimal Control Problems
pace 0. We can define the "good enough" subset. Gp0. as the top-l% of the design space based on system performances, and the "selected" subset, spo. aAn Ordinal Optimization Approach to Optimal Control Problems’Mei (May) Deng® and Yu-Chi Ho’ABSTRACT - We introduce an ordinal optimization approach to An Ordinal Optimization Approach to Optimal Control Problemswing the search from 0 to s we are not "throwing out the baby with the bath water". This again has been quantitatively reported in (Deng. 1995. Lau-Ho. 1997; Lee-Lau-Ho. 1998).Many examples of the use of oo to speed up the simulation optimization processes by orders of magnitude in computation have An Ordinal Optimization Approach to Optimal Control Problemsbeen demonstrated in the past few years (Ganz-Wang. 1994; Ho-Larson. 1995; Ho-Deng. 1994; Ho-Sreenivas-Vakih. 1992; Lau-Ho. 1997; Patsis-Chen-Larson.An Ordinal Optimization Approach to Optimal Control Problems
1997; Wieseltheir-Barnhart-Ephremides. 1995). However, oo still has limitations as it stands. One key drawback is the fact that 0 for many problems caAn Ordinal Optimization Approach to Optimal Control Problems’Mei (May) Deng® and Yu-Chi Ho’ABSTRACT - We introduce an ordinal optimization approach to An Ordinal Optimization Approach to Optimal Control Problemsis still IO3 away from the optimum. This is often of scant comfort to optimizers. The purpose of this note is to address this limitation through iterative use of 00 very much in the spirit of hill climbing in traditional optimization.2.Model and ConceptsConsider the expected performance function J(0 An Ordinal Optimization Approach to Optimal Control Problems) = E[L(x(t: 0. CD] i E[L(0. c>]. where L(x(t; 0. CD represents some sample performance function evaluated tlirough the realization of a system trajecAn Ordinal Optimization Approach to Optimal Control Problems
tory X(t; 0. c> under the design parameter 0. Here c represents all the random effects of the system. Denote by 0. a huge but finite set. the set of aAn Ordinal Optimization Approach to Optimal Control Problems’Mei (May) Deng® and Yu-Chi Ho’ABSTRACT - We introduce an ordinal optimization approach to An Ordinal Optimization Approach to Optimal Control Problems.1(9) has little analytical structure but large uncertainty and must be estimated through repeated simulation’ The wAn Ordinal Optimization Approach to Optimal Control Problems
abs. Roon 1L-20S. 101 Crautoids Comer Roa± Hohudel. NJ 07733. (732) 949-7624. (Fax) (732) 919-1720. mdav@att.catn.• Division of Applied Science. HarvaAn Ordinal Optimization Approach to Optimal Control Problems’Mei (May) Deng® and Yu-Chi Ho’ABSTRACT - We introduce an ordinal optimization approach to An Ordinal Optimization Approach to Optimal Control Problems often equivalently,https://khothuvien.cori!The principal claim of oo is that performance order IS relatively robust with respect to very small K or t«x (We shall use s on simulation 01 small number of replications interchangeably here after to indicate that the confidence interval of the An Ordinal Optimization Approach to Optimal Control ProblemsAn Ordinal Optimization Approach to Optimal Control Problems’Mei (May) Deng® and Yu-Chi Ho’ABSTRACT - We introduce an ordinal optimization approach toGọi ngay
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