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Autonomous system (mathematics)
About: Autonomous system (mathematics) is a research topic. Over the lifetime, 1648 publications have been published within this topic receiving 38373 citations.
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TL;DR: It is proved that for certain types of functions g(t, y) the "generalized" positive limit sets of (P) also are invariant with respect to (A), which contains previous theorems of Markus, Opial, and Yoshizawa.
Abstract: for large t. I f the solutions of (A) are uniquely de termined by initial conditions, then it is well-known [6] that all positive limit sets ~(x0) of (A) are invariant with respect to (A). We shall prove (Theorem 2.4) that for certain types of functions g(t, y) the \"generalized\" positive limit sets of (P) also are invariant with respect to (A). This result contains previous theorems of Markus [7], Opial [8], and Yoshizawa [11]. An application to stability is given in Section 3 (Corollary 3.3).
59 citations
TL;DR: An on-line, Newton-like optimization algorithm is proposed that recomputes the control variable by attempting to optimize the cost-to-go at equally-spaced epochs and can vary from sublinear to quadratic depending on its computing rate and the state estimation error.
Abstract: This paper considers an optimization problem in the setting of switched-mode hybrid dynamical systems, where the control variable (independent variable) consists of the mode-switching times, and the performance criterion is a cost functional defined on the system's state trajectory. The system is deterministic, nonlinear, and autonomous, and its state variable cannot be measured and hence it has to be estimated. We propose an on-line, Newton-like optimization algorithm that recomputes the control variable by attempting to optimize the cost-to-go at equally-spaced epochs. The main result concerns the algorithm's convergence rate, which can vary from sublinear to quadratic depending on its computing rate and the state estimation error.
59 citations
TL;DR: In this paper, a piecewise-linear 4D autonomous system with hyperchaotic behavior is proposed and analyzed by constructing a 2D return map and giving theoretical evidence for hyperchaos generation.
Abstract: A piecewise-linear 4-D autonomous system with hyperchaotic behavior is proposed. The system is analyzed by constructing a 2-D return map. We describe this map explicitly and give theoretical evidence for hyperchaos generation. An implementation example is also provided, and its chaotic behavior is demonstrated.
57 citations
TL;DR: It is shown that for constructing the set of initial states that can be driven to the origin asymptotically, one can restrict the search to a polyhedral set in the unstable subspace of the autonomous system, which yields a drastic reduction in the computational burden.
57 citations
TL;DR: A cycle-time model for class-based storage policies is proposed for automated unit load Storage and Retrieval systems that use autonomous vehicle technology to achieve sufficient accuracy and computational efficiency for system design conceptualisation applications.
Abstract: A cycle-time model for class-based storage policies is proposed for automated unit load Storage and Retrieval (S/R) systems that use autonomous vehicle technology. The model is based on a queuing network approach to achieve sufficient accuracy and computational efficiency for system design conceptualisation applications. It is illustrated through a series of realistic case problems.
57 citations