Abstract
Abstract For at least fifty years, the inverted pendulum has been the most popular benchmark, among others, in nonlinear control theory. The fundamental focus of this work is to enhance the wealth of this robotic benchmark and provide an overall picture of historical and current trend developments in nonlinear control theory, based on its simple structure and its rich nonlinear model. In this review, we will try to explain the high popularity of such a robotic benchmark, which is frequently used to realize experimental models, validate the efficiency of emerging control techniques and verify their implementation. We also attempt to provide details on how many standard techniques in control theory fail when tested on such a benchmark. More than 100 references in the open literature, dating back to 1960, are compiled to provide a survey of emerging ideas and challenging problems in nonlinear control theory accomplished and verified using this robotic system. Possible future trends that we can envision based on the review of this area are also presented.
Highlights
Control theory is a field dealing with disciplines and methods that lead to an automatic decision process in order to improve the performance of a control system
This paper proposes to enhance the wealth of the pendulum benchmark and attempt to provide an overall picture of historical, current and trend developments in nonlinear control theory based on its simple structure and its rich nonlinear model
It has been shown that the inverted pendulum system is a fundamental benchmark in nonlinear control theory
Summary
Control theory is a field dealing with disciplines and methods that lead to an automatic decision process in order to improve the performance of a control system. Concerning engineering systems, many robotic benchmarks of high interest exist in the literature. They are frequently used to realize experimental models, validate the efficiency of emerging control techniques and verify their implementation. In spite of its simple structure, the inverted pendulum is considered, among the last examples, the most fundamental benchmark. This paper proposes to enhance the wealth of the pendulum benchmark and attempt to provide an overall picture of historical, current and trend developments in nonlinear control theory based on its simple structure and its rich nonlinear model. Trends and challenges will be addressed in the last section
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