Abstract
In this article, we propose a tractable family of remainder-form mixed-monotone decomposition functions that are useful for overapproximating the image set of nonlinear mappings in reachability and estimation problems. Our approach applies to a new class of nonsmooth, discontinuous nonlinear systems that we call either-sided locally Lipschitz semicontinuous systems, which we show to be a strict superset of locally Lipschitz continuous systems, thus expanding the set of systems that are formally known to be mixed-monotone. In addition, we derive lower and upper bounds for the overapproximation error and show that the lower bound is achieved with our proposed approach, i.e., our approach constructs the tightest, tractable remainder-form mixed-monotone decomposition function. Moreover, we introduce a set inversion algorithm that along with the proposed decomposition functions can be used for constrained reachability analysis and guaranteed state estimation for continuous- and discrete-time systems with bounded noise.
Original language | English (US) |
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Pages (from-to) | 7057-7072 |
Number of pages | 16 |
Journal | IEEE Transactions on Automatic Control |
Volume | 68 |
Issue number | 12 |
DOIs | |
State | Published - Dec 1 2023 |
Externally published | Yes |
Keywords
- ELLS systems
- Nonlinear dynamical systems
- mixed-monotonicity
- one-sided decomposition functions
- reachability analysis
ASJC Scopus subject areas
- Electrical and Electronic Engineering
- Control and Systems Engineering
- Computer Science Applications