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Article

Using Interval Analysis to Compute the Invariant Set of a Nonlinear Closed-Loop Control System

1
Chair of Mechatronics, University of Rostock, D-18059 Rostock, Germany
2
Lab-STICC of ENSTA Bretange, 29806 Brest, France
3
Chair of Mechatronics, University of Rostock, D-18059 Rostock, Germany
*
Authors to whom correspondence should be addressed.
Received: 30 October 2019 / Revised: 2 December 2019 / Accepted: 3 December 2019 / Published: 6 December 2019
(This article belongs to the Special Issue Algorithms for Reliable Estimation, Identification and Control)
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. View Full-Text
Keywords: interval analysis; Lyapunov stability; sliding mode control; invariant sets interval analysis; Lyapunov stability; sliding mode control; invariant sets
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MDPI and ACS Style

Romig, S.; Jaulin, L.; Rauh, A. Using Interval Analysis to Compute the Invariant Set of a Nonlinear Closed-Loop Control System. Algorithms 2019, 12, 262. https://0-doi-org.brum.beds.ac.uk/10.3390/a12120262

AMA Style

Romig S, Jaulin L, Rauh A. Using Interval Analysis to Compute the Invariant Set of a Nonlinear Closed-Loop Control System. Algorithms. 2019; 12(12):262. https://0-doi-org.brum.beds.ac.uk/10.3390/a12120262

Chicago/Turabian Style

Romig, Swantje, Luc Jaulin, and Andreas Rauh. 2019. "Using Interval Analysis to Compute the Invariant Set of a Nonlinear Closed-Loop Control System" Algorithms 12, no. 12: 262. https://0-doi-org.brum.beds.ac.uk/10.3390/a12120262

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