Variable-Structure Interval-Based Duffing Oscillator

The paper deals with the design of a variablestructure chaotic oscillator for path-planning applications of autonomous mobile vehicles. This oscillator is designed as a result of analysis of the generalized dynamical system. We use interval methods to model such a system and take into consideration its nonlinearities. Our approach offers to replace exactly defined system nonlinear functions with domains where these functions are localized. We define lower and upper boundaries for these domains by using piecewise linear functions. The usage of these functions allows us to rewrite initial nonlinear system equations into linear-like form with linear terms that are defined in some intervals and thus simplify the system model. Piecewise linearity of this model gives us the possibility to analyze the system features by using various control methods. Such a model can be used in both real and complex domains. The consideration of system dynamics in a complex domain allows us to increase the order of the considered system and define a set of operation modes to design a variable-structure system. We show the benefits of our approach by studying the Duffing pendulum and designing its base variable-structure system.