ﻻ يوجد ملخص باللغة العربية
In this paper, we propose an incremental abstraction method for dynamically over-approximating nonlinear systems in a bounded domain by solving a sequence of linear programs, resulting in a sequence of affine upper and lower hyperplanes with expanding operating regions. Although the affine abstraction problem can be solved offline using a single linear program, existing approaches suffer from a computation space complexity that grows exponentially with the state dimension. Hence, the motivation for incremental abstraction is to reduce the space complexity for high-dimensional systems, but at the cost of yielding potentially worse abstractions/overapproximations. Specifically, we start with an operating region that is a subregion of the state space and compute two affine hyperplanes that bracket the nonlinear function locally. Then, by incrementally expanding the operating region, we dynamically update the two affine hyperplanes such that we eventually yield hyperplanes that are guaranteed to over-approximate the nonlinear system over the entire domain. Finally, the effectiveness of the proposed approach is demonstrated using numerical examples of high-dimensional nonlinear systems.
We consider the covariance steering problem for nonlinear control-affine systems. Our objective is to find an optimal control strategy to steer the state of a system from an initial distribution to a target one whose mean and covariance are given. Du
Robust control is a core approach for controlling systems with performance guarantees that are robust to modeling error, and is widely used in real-world systems. However, current robust control approaches can only handle small system uncertainty, an
This paper studies the extremum seeking control (ESC) problem for a class of constrained nonlinear systems. Specifically, we focus on a family of constraints allowing to reformulate the original nonlinear system in the so-called input-output normal f
Atangana and Baleanu proposed a new fractional derivative with non-local and no-singular Mittag-Leffler kernel to solve some problems proposed by researchers in the field of fractional calculus. This new derivative is better to describe essential asp
Numerical tools for constraints solving are a cornerstone to control verification problems. This is evident by the plethora of research that uses tools like linear and convex programming for the design of control systems. Nevertheless, the capability