Safety preserving control synthesis for sampled data systems |
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| Institution: | 1. Department of Computer Science, University of British Columbia, Canada;2. Department of Electrical Engineering & Computer Science, University of California, Berkeley, United States;3. Department of Electrical & Computer Engineering, University of New Mexico, United States;1. Department of Electrical and Computer Engineering, Louisiana State University, Baton Rouge, LA 70803-5901, United States;2. Department of Electronic and Computer Engineering, Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong;1. University of Applied Sciences Erfurt, Department of Civil Engineering, Germany;2. University of Bremen, Centre for Industrial Mathematics, P.O. Box 330440, 28334 Bremen, Germany;1. College of Information Sciences and Technology, Donghua University, Shanghai 201620, China;2. Polytechnic School of Engineering, New York University, New York 11201, USA;3. Engineering Research Center of Digitized Textile & Fashion Technology, Ministry of Education, Donghua University, Shanghai 201620, China;4. China Ship Development and Design Center, Wuhan 430064, China;5. College of Computer Sciences and Technology, Donghua University, Shanghai 201620, China;1. School of Mathematics and Computational Science, Sun Yat-Sen University, Guangzhou 510275, PR China;2. College of Mathematics and Computer Science, Fuzhou University, Fuzhou 350108, PR China |
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| Abstract: | In sampled data systems the controller receives periodically sampled state feedback about the evolution of a continuous time plant, and must choose a constant control signal to apply between these updates; however, unlike purely discrete time models the evolution of the plant between updates is important. In this paper we describe an abstract algorithm for approximating the discriminating kernel (also known as the maximal robust control invariant set) for a sampled data system with continuous state space, and then use this operator to construct a switched, set-valued feedback control policy which ensures safety. We show that the approximation is conservative for sampled data systems. We then demonstrate that the key operations–the tensor products of two sets, invariance kernels, and a pair of projections–can be implemented in two formulations: one based on the Hamilton–Jacobi partial differential equation which can handle nonlinear dynamics but which scales poorly with state space dimension, and one based on ellipsoids which scales well with state space dimension but which is restricted to linear dynamics. Each version of the algorithm is demonstrated numerically on a simple example. |
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| Keywords: | Nonlinear systems Sampled data Control synthesis Continuous reachability Hamilton–Jacobi equations Viability Ellipsoids |
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