Interactive multi-objective programming as a framework for computer-aided control system design
After an introduction, which presents the problem and the organization of the book, in chapter 2, the author describes various design methods and provides a characterization of those methods. In chapter 3 interactive multi-objective programming is formulated. The multiple objectives are represented by a vector of performance indices. The set of feasible solutions is the set of the feasible decision. For the generation of the efficient solutions (Pareto solutions) different scalarizations of the vector of performance indices are used and an interactive algorithm is defined. Chapter 4 presents four search-based control system design methods: Zakian's method of inequalities, semi-infinite optimization (Polak, Mayne a.s.o.), multiple-objective programming, with a distinguished formulation as a constrained minimax optimization problem (Nye and Tits) and performance vector optimization. For all of these methods evaluations are presented. In chapter 5 the author discusses the transcription of a design problem into one of interactive multi-objective programming; then he formulates a set of design principles and realization strategies. Chapter 6 describes a set of tools for the generation of candidate solutions for two stages of the strategy: in one of them the formulation of constrained minimax optimization is used, due to Nye and Tits. The other stage uses either Zakian's inequality formulation, or Wierzbicki's achievement function formulation. For the generation of candidate solutions, in all cases, iterative numerical search methods are used. Chapter 7 describes the two tools which help the designer to understand the design possibilities revealed in the sample efficient subset, in graphical form, and to prescribe index bounds. For the comparison of a large number of candidate solutions, in chapter 8, the SQL language is used. With extensions to its syntax, a language for evaluation is obtained. To illustrate the use of the design strategy, the author describes in chapter 9 two examples in the design of linear time-invariant multivariable controllers. In both examples, hard constraints were not explicitly formulated, but were included in the set of performance indices instead. Chapter 10 presents the author's contributions to this work and suggestions for future work.
linear time-invariant multivariable controllers
scientific article; zbMATH DE number 194928