Robustly Complete Reach-and-Stay Control Synthesis for Switched Systems via Interval Analysis

2018 ◽  
Author(s):  
Yinan Li ◽  
Jun Liu
Keyword(s):  
Interval Analysis ◽  
Switched Systems ◽  
Control Synthesis

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

Algorithms ◽  
2019 ◽  
Vol 12 (12) ◽  
pp. 262 ◽  
Author(s):  
Swantje Romig ◽  
Luc Jaulin ◽  
Andreas Rauh
Keyword(s):  
Interval Analysis ◽  
Closed Loop ◽  
Sliding Mode ◽  
Initial Conditions ◽  
Invariant Sets ◽  
Control Synthesis ◽  
Closed Loop Control ◽  
Loop Control ◽  
Loop Control System ◽  
Bézout’S Identity

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.

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