Abstract
In recent years, many applications, as well as theoretical properties of interval analysis have been investigated. Without any claim for completeness, such applications and methodologies range from enclosing the effect of round-off errors in highly accurate numerical computations over simulating guaranteed enclosures of all reachable states of a dynamic system model with bounded uncertainty in parameters and initial conditions, to the solution of global optimization tasks. By exploiting the fundamental enclosure properties of interval analysis, this paper aims at computing invariant sets of nonlinear closed-loop control systems. For that purpose, Lyapunov-like functions and interval analysis are combined in a novel manner. To demonstrate the proposed techniques for enclosing invariant sets, the systems examined in this paper are controlled via sliding mode techniques with subsequently enclosing the invariant sets by an interval based set inversion technique. The applied methods for the control synthesis make use of a suitably chosen Gröbner basis, which is employed to solve Bézout’s identity. Illustrating simulation results conclude this paper to visualize the novel combination of sliding mode control with an interval based computation of invariant sets.
Highlights
During the last few decades, interval analysis has been shown to provide efficient numerical approaches for solving various tasks in scientific computing, as well as in application-oriented disciplines in which numerical techniques with a result verification are helpful or required
Illustrating simulation results conclude this paper to visualize the novel combination of sliding mode control with an interval based computation of invariant sets
The possibility of interval analysis to treat the effects of round-off and truncation errors of numerical solution techniques is exploited [8,9,10]
Summary
During the last few decades, interval analysis has been shown to provide efficient numerical approaches for solving various tasks in scientific computing, as well as in application-oriented disciplines in which numerical techniques with a result verification are helpful or required In such a way, they help to solve problems in control engineering, robotics, including rigorous methods for localization and/or path planning, as well as guaranteed obstacle avoidance, computational (bio-)mechanics, civil engineering, or bio-engineering, just to mention a few of the large number of different areas [1,2,3,4,5,6,7]. These paths are assumed to be described in terms of a sliding surface for a nonlinear dynamic system This control design procedure is interfaced with techniques from the field of interval analysis that are employed to determine enclosures of the invariant sets of the resulting controlled system in a reliable and computationally efficient way.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
