作者：
Sakamoto, NNagoya Univ
Grad Sch Engn Dept Aerosp Engn Chikusa Ku Nagoya Aichi 4648603 Japan
In this paper, the geometric property and structure of the Hamilton-Jacobi equation arising from nonlinear control theory are investigated using symplectic geometry. The generating function of symplectic transforms pl...
详细信息
In this paper, the geometric property and structure of the Hamilton-Jacobi equation arising from nonlinear control theory are investigated using symplectic geometry. The generating function of symplectic transforms plays an important role in revealing the structure of the Hamilton Jacobi equation. It is seen that many fundamental properties of the Riccati equation can be generalized in the Hamilton-Jacobi equation, and, therefore, the theory of the Hamilton-Jacobi equation naturally contains that of the Riccati equation.
In an empirical context, a method to use nonlinear control theory in the dynamic analysis of supply chain resilience is developed and tested. The method utilises block diagram development, transfer function formulatio...
详细信息
In an empirical context, a method to use nonlinear control theory in the dynamic analysis of supply chain resilience is developed and tested. The method utilises block diagram development, transfer function formulation, describing function representation of nonlinearities and simulation. Using both shock' or step response and filter' or frequency response lenses, a system dynamics model is created to analyse the resilience performance of a distribution centre replenishment system at a large grocery retailer. Potential risks for the retailer's resilience performance include the possibility of a mismatch between supply and demand, as well as serving the store inefficiently and causing on-shelf stock-outs. Thus, resilience is determined by investigating the dynamic behaviour of stock and shipment responses. The method allows insights into the nonlinear system control structures that would not be evident using simulation alone, including a better understanding of the influence of control parameters on dynamic behaviour, the identification of inventory offsets potentially leading to drift', the impact of nonlinearities on supply chain performance and the minimisation of simulation experiments.
For at least fifty years, the inverted pendulum has been the most popular benchmark, among others, in nonlinear control theory. The fundamental focus of this work is to enhance the wealth of this robotic benchmark and...
详细信息
For at least fifty years, the inverted pendulum has been the most popular benchmark, among others, in nonlinear control theory. The fundamental focus of this work is to enhance the wealth of this robotic benchmark and provide an overall picture of historical and current trend developments in nonlinear control theory, based on its simple structure and its rich nonlinear model. In this review, we will try to explain the high popularity of such a robotic benchmark, which is frequently used to realize experimental models, validate the efficiency of emerging control techniques and verify their implementation. We also attempt to provide details on how many standard techniques in controltheory fail when tested on such a benchmark. More than 100 references in the open literature, dating back to 1960, are compiled to provide a survey of emerging ideas and challenging problems in nonlinear control theory accomplished and verified using this robotic system. Possible future trends that we can envision based on the review of this area are also presented.
The present paper is a continuation of the series of papers [1-4]. In [1], weconsidered some constructions that can be used when developing the foundations of the theory ofnonlinearcontrol dynamical systems. Such con...
详细信息
The present paper is a continuation of the series of papers [1-4]. In [1], weconsidered some constructions that can be used when developing the foundations of the theory ofnonlinearcontrol dynamical systems. Such constructions (either implicit or explicit) are used inany mathematical theory (group theory, theory of linear spaces, etc.). They have categorical *** are niorphisnis, that is, mappings relating control systems and reduced systems (isomorphicsystems, subsystems, quotient systems), i.e., in a sense, simplified models of the original controlsystem. In [1], we also represented mathematical techniques for the analysis of these constructionsfor nonlinearcontrol systems; these techniques have differential-geometric and group-theoreticcharacter. In [2], we used the notion of quotient system in a certain category of nonlinearcontrolsystems for the solution of a number of problems of controltheory (problems of observability,implementation, invariance under perturbations, and autonomy). The role of the notion of a subsystemwas demonstrated in [3] in a certain category of nonlinearcontrol systems (the terminal controlproblem and the control problem with equality-like constraints on the phase variables). In [4], weconsidered symmetries, that is, self-mappings of the phase space of the control system that takephase trajectories to phase trajectories.
The article focuses on the construction of symmetry algebras for the canonical forms that can be used when developing the theory of nonlinear dynamical control systems. It represents a mathematical technique for the a...
详细信息
The article focuses on the construction of symmetry algebras for the canonical forms that can be used when developing the theory of nonlinear dynamical control systems. It represents a mathematical technique for the analysis of such constructions for nonlinearcontrol systems. It also uses the notion of quotient system in a certain category of nonlinearcontrol systems to solve problems in controltheory.
The present paper is a continuation of [1, 2]. In [1], we considered someconstructions that can be used in developing the foundations of the theory of nonlinearcontroldynamical systems. Such constructions are used (e...
详细信息
The present paper is a continuation of [1, 2]. In [1], we considered someconstructions that can be used in developing the foundations of the theory of nonlinearcontroldynamical systems. Such constructions are used (either explicitly or implicitly) in eachmathematical theory (group theory, theory of linear spaces, etc.). They are of categorical *** are morphisms, i.e., mappings relating the control systems and reduced systems (isomorphicsystems, subsystems, quotient systems), i.e., in a sense, simplified models of the original controlsystem. A mathematical technique for the investigation of such constructions for nonlinearcontrolsystems was represented in [1]; it is of differential-geometric and group-theoretic character. Thenotion of a quotient system in a certain category of nonlinearcontrol systems was used in [2] forthe solution of a number of important problems of controltheory. Below we illustrate the role ofthe notion of a subsystem in a certain category of nonlinearcontrol systems.
Ultrafast quantum dynamics of interband transitions in monolayer graphene initiated by strong laser radiation is investigated. A microscopic theory describing nonlinear interaction beyond the Dirac cone approximation ...
详细信息
Ultrafast quantum dynamics of interband transitions in monolayer graphene initiated by strong laser radiation is investigated. A microscopic theory describing nonlinear interaction beyond the Dirac cone approximation and applicable to the full Brillouin zone of the hexagonal nanostructure with tight-binding electronic states is developed. Coherent effects toward the control of macroscopic quantum states in graphene are considered. In particular, we consider Rabi oscillations, rapid adiabatic passage for population transfer, and multiphoton excitation of the Fermi-Dirac sea in a monolayer graphene.
暂无评论