Satisficing Optimization Methods In Control Systems

Satisfaction optimization, as a branch of the optimization theory and methodology, has received a lot of attention recently. It has been widely used in many applications such as systems engineering, economic planning, production, management, transportation, military scheduling, system analysis, and so on. From the viewpoints of science, technology, engineer-ing, and mathematics, we focus on the study of several aspects of satisfaction optimization. Specifically, we mainly investigate the properties and structure of satisfaction optimization, satisfaction theory, the involved stability and algorithm analysis.Based on the difference and relation of satisfaction optimization and the traditional one, some basic structures and properties for satisfaction optimization question are presented. For uncertain multiple index problem of control system, two types of sample statistics and feature selection satisfactory degree functions are established by combining some satisfactory degree functions such as Harrington and Suich methods.Addressing the problem of multivariate constraint controls, we investigate the model, criteria, and structure and existence of solution of satisfactory optimization for fuzzy theory, measure theory, and utility theory.First of all, we give a new kind of gλfuzzy measure, Sugeno integral and Choquet inte-gral. They reduce the complexity of calculation and improve the convergence speed compared with the traditional fuzzy control. An index satisfactory optimization method with fuzzy mea-sure is established according to the Choquet integral with random samples of statistics. This method has a scroll mechanism and characteristics of human-computer interaction, and it affords more flexibility. Contrasting to the fuzzy comprehensive evaluation of multiple objec-tive problems, we use the Delphi law to establish the analytic hierarchy target choice plan.Secondly, we observe that the Goodrich’s satisfactory solution expressed by mathemat-ical expectation in measure space has a weak anti-jamming ability and its transition function is hard to determine. Accordingly, we propose the satisfactory criteria, fuzzy and probability measure space, the fuzzy measure function sequence on response indexes in measure space. Mathematically, we derive the conditions of σ-addition and bounded closed convex closure. Based on the results aforementioned, we establish the satisfactory optimization method and algorithm. The examples of single-loop control system show that the proposed algorithm has a good convergence.In addition, inspired by the ideas of utility theory in the feed back control system due to Goodrich, Levi and Stirling, we establish the utility strategy in the multiple indicators measure space. This method can be used to achieve the satisfactory coordination of the target domain, and thus improve the boundary adjustment method by Xi et al. In order to construct the satisfactory control method of the control system, the utility policies are developed for the control variables measuring functions. In addition, thanks to the work of Curtis and Bi-nazadeh, we obtain the utility satisfaction policy based on CLF stable strategy, and derive the conditions of non-empty, uniqueness and the condition of global asymptotic stability of a closed-loop system. The simulation results of the predictive control for rotary wing aircraft shows the algorithm has a good convergence property and anti-jamming capabilities.As far as the algorithm analysis is concerned, we propose a sensitivity analysis method for satisfactory degree function aiming at the inverse problem of satisfactory optimization by Jin. Based on the target augmentation way of the sensitivity, we present a satisfaction func-tion coordination algorithm. By the new algorithm, we can effectively determine the feasible region of some optimization problems. Furthermore, we propose the quantum probability gate algorithm which improves the quantum rotating gate iteration algorithm. We prove that the proposed algorithm has a faster speed of convergence. Based on the basic logic of algo-rithm, we analyze the feasible solution of overall importance probability and demonstrate that probability gate quantum evolution algorithm has a better global optimization capability. The compared results with several kind of model test functions are also given.