Abstract
This paper introduces an iterative approach for the design of an optimum switching gain controller for a linear time invariant single input/single output (SISO) systems. The controller parameters are determined at different switching instants so as to improve the dynamic characteristics of a closed loop system and satisfy a set of inequalities. The approach is based on solving a constrained parameter optimization problem. Optimization is carried out based on the genetic algorithm (GA) in order to find the optimum number of switching, optimum switching instants and optimum controller parameters vector. All that in the sense of minimizing a certain time based objective function and satisfying a set of parametric and operating constraints. Constraints imposed on the controlled system may be in the form of design specifications and/or performance requirements. The technique is applicable for any controller structure, and gives a set of an optimum parameter values switched at optimum switching instants. Parameter values are function of the system states at these instants. Different systems are examined to show the applicability of the presented approach. 
 
Highlights
Switching systems are considered as a specified division of hybrid systems
[12,13,14,15], the modern heuristic search optimization techniques developed in the past decades, such as the genetic algorithms (GA), particle swarm optimization (PSO), ant colony optimization (ACO), artificial bee colony (ABC), artificial foraging optimization (AFO), differential evolution (DE), and other population-based learning techniques are gaining high acceptance to be the standard approach used for tuning and optimizing the controllers in modern control problems [16,17,18,19]
The design was implemented by using the genetic algorithm as one of the most successfully evolutionary optimization algorithms used for control problems
Summary
Switching systems are considered as a specified division of hybrid systems. It is composed of various subsystems with switching control rules that coordinate the active subsystem at certain instants of time [1,2,3,4]. Recent computational methods for optimal control problems associated with switching systems is based on the type of switching. If the controller is considered in the process of switching for a single system model rather than for subsystem models, a special class of optimal switching systems is generated. This class of problems with the present advances in optimization algorithms is not well mentioned in the literature. This paper presents an iterative general state space approach for the design of any controller structure that might be subjected to any set of practical and operating constraints.
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