On Two-Sided Approximations of Reachable Sets of Control Systems with Geometric Constraints on the Controls

2021 ◽  
Vol 313 (S1) ◽  
pp. S211-S227
Author(s):  
V. N. Ushakov ◽  
M. V. Pershakov
Keyword(s):  
Control Systems ◽  
Geometric Constraints ◽  
Reachable Sets

A Note on the Reachable Sets of Control Systems

1991 ◽  
pp. 113-119 ◽  
Author(s):  
Rosa Maria Bianchini ◽  
Gianna Stefani
Keyword(s):  
Control Systems ◽  
Reachable Sets

A numerical method for the approximation of reachable sets of linear control systems

2017 ◽  
Vol 36 (2) ◽  
pp. 423-441 ◽  
Author(s):  
Lizhen Shao ◽  
Fangyuan Zhao ◽  
Guangda Hu
Keyword(s):  
Numerical Method ◽  
Control Systems ◽  
Optimization Problems ◽  
Approximation Error ◽  
Outer Approximation ◽  
Reachable Sets ◽  
Linear Control ◽  
Superior Performance ◽  
Linear Control Systems ◽  
Inner Approximation

Abstract In this article, a numerical method for the approximation of reachable sets of linear control systems is discussed. First a continuous system is transformed into a discrete one with Runge–Kutta methods. Then based on Benson’s outer approximation algorithm for solving multiobjective optimization problems, we propose a variant of Benson’s algorithm to sandwich the reachable set of the discrete system with an inner approximation and an outer approximation. By specifying an approximation error, the quality of the approximations measured in Hausdorff distance can be directly controlled. Furthermore, we use an illustrative example to demonstrate the working of the algorithm. Finally, computational experiments illustrate the superior performance of our proposed algorithm compared to a recent algorithm in the literature.

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