Convergent under-approximations of reachable sets and tubes: A piecewise constant approach |
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| Authors: | Mohamed Serry |
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| Affiliation: | 1. The School of Information and Control Engineering, Liaoning Shihua University, Fushun 113000, PR China;2. The Institute of Intelligence Science and Engineering, Shenzhen Polytechnic, Shenzhen 518055, PR China;3. National Laboratory of Industrial Control Technology, Institute of Cyber-Systems and Control, Zhejiang University, Yuquan Campus, Hangzhou Zhejiang 310027, PR China;1. College of Applied Mathematics, Shanxi University of Finance and Economics, Taiyuan 030006, PR China;2. College of Information, Shanxi University of Finance and Economics, Taiyuan 030006, PR China;3. School of Mathematics and Statistics, Changsha University of Science and Technology, Changsha 410076, PR China;1. Fair Friend Institute of Intelligent Manufacturing, Hangzhou Vocational and Technical College, Hangzhou 310018, PR China;2. Institute of Information and Control, Hangzhou Dianzi University, Hangzhou 310018, PR China;1. School of Information Science and Engineering, Southeast University, Nanjing 210096, China;2. School of Cyber Science and Engineering, Southeast University, Nanjing 210096, China;3. School of Mathematics, Southeast University, Nanjing 210096, China |
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| Abstract: | In this paper, a method to under-approximate finite-time reachable sets and tubes for a class of continuous-time linear uncertain systems is proposed. The class under consideration is the linear time-varying (LTV) class with time-varying integrable system matrices and uncertain initial and input values belonging to known convex compact sets. The proposed method depends upon the iterative use of constant-input reachable sets, which results in convergent under-approximations in the sense of the Hausdorff distance. As a consequence of the convergence, it is shown that interior points of reachable sets are attainable using piecewise constant inputs. The computational complexity of a zonotopic implementation of the proposed method is discussed and comparisons with existing under-approximation methods are established. Finally, the proposed approach is illustrated through two numerical examples. |
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