Fuzzy model-based control for dynamic variable structure systems

In this study, a new fuzzy system structure that reduces the number of inputs is proposed for dynamic system identification applications. Algebraic fuzzy systems have some disadvantages due to many inputs. As the number of inputs increase, the number of parameters in the training process increase and hence the classical fuzzy system becomes more complex. In the conventional fuzzy system structure, the past information of both inputs and outputs are also regarded as inputs for dynamic systems, therefore the number of inputs may not be manageable even for “single input and single output” systems. The new dynamic fuzzy system module (DFM) proposed here has only a single input and a single output. We have carried out identification simulations to test the proposed approach and shown that the DFM can successfully identify non-linear dynamic systems and it performs better than the classical fuzzy system.

Dramatic progress in computing capabilities has resulted in the synthesis and implementation of increasingly complex dynamical systems. Since such systems frequently exhibit simultaneously several kinds of dynamic behavior in different parts of the system, they are referred to as hybrid dynamical systems. Such systems frequently defy traditional modeling and analysis techniques since the different system components may evolve along different notions of "time", including real time, discrete time, and discrete events. Most investigations of such systems to date involve ad hoc models and tailor-made analysis results. In some recent work, however, a general model has been proposed which contains most of the different classes of hybrid dynamical systems considered in the literature as special cases. At the core of this general model of hybrid dynamical system, which is defined on an arbitrary metric space, is a notion of generalized time. For this class of general hybrid dynamical systems, a variety of Lyapunov and Lagrange stability results have been established and made public in a scattering of publications and workshop records. Our objective in this paper is to present a unified overview of the more important aspects of this work.

As charge carrier of the macroscopic superconductivity, the Cooper pair is a composite particle of two paired electrons, which has both center-of-mass and inner-pair degrees of freedom. In most cases, these two different degrees of freedom can be well described by the macroscopic Ginzburg-Landau theory and the microscopic Bardeen-Cooper-Schrieffer (BCS) theory, respectively. Near the superconducting phase transition where the Cooper pair is fragile and unstable because of the small binding energy, there are non-trivial couplings between these two different degrees of freedom due to such as finite energy and/or momentum transfer. The non-trivial couplings make the original derivation of the Ginzburg-Landau theory from the BCS theory fail in principle as where these two different degrees of freedom should not be decoupled. In this article, we will present a renormalization formalism for an extended Ginzburg-Landau action for the superconducting phase transition where there is finite energy transfer between the center-of-mass and the inner-pair degrees of freedom of Cooper pairs. This renormalization formalism will provide a theoretical tool to study the unusual dynamical effects of the inner-pair time-retarded physics on the superconducting phase transition.

An atmospheric imaging system based on quantum hyper-entanglement has been developed. Hyper-entanglement refers to entanglement in more than one degree of freedom, e.g. polarization, energy-time and orbital angular momentum (OAM). The system functions at optical or infrared frequencies. Only the signal photon propagates in the atmosphere, the ancilla photon is retained within the detector. This results in loss being essentially classical, giving rise to stronger forms of entanglement. Bell state generation and Bell state measurement, i.e. the ability to distinguish the various Bell states is discussed. A mathematical representation of Bell state generation and the Bell state analyzer, including a projection operator describing the measurement process is provided. Signatures for unique detection of the various Bell states are developed. A method and design for creating states hyper-entangled in polarization, energy-time, OAM and the radial quantum number is examined. Hermite-Gaussian (HG) modes, Laguerre-Gaussian (LG) modes, OAM dependence of the LG modes and a method of mode conversion are discussed. A projection operator that represents the combined measurements between the different degrees of freedom is provided. A model of generation and detection efficiencies for the different degrees of freedom and the implications for signal to noise ratio (SNR), signal to interference ratio (SIR), the quantum Cramer-Rao lower bound, and the measurement time are provided in closed form. A formula describing how hyper-entanglement greatly improves the maximum detection range of the system is derived. The formalism permits random noise and entangled or non-entangled sources of interference to be modeled.

With the expansion of floating photovoltaics, rigid connectors offer advantages over polyester ropes by reducing the relative motion of floats and simplifying the layout of the connection system. However, the overall stability and safety of the floating photovoltaic system may be compromised if a wave crest occurs at the connection point of the rigid connector during motion. Furthermore, the rigid connectors with different degrees of freedom significantly impact the motion of the floats and their connection loads. In this study, three types of single-rod rigid connector models with varying constraints are established through numerical simulation to explore the feasibility of applying single-rod rigid connectors with different degrees of freedom in photovoltaic systems. Based on their degrees of freedom, these connectors are classified as cardan, purely rigid, and hinged. An analysis of float motion and connector loads in two-floating, four-floating, and eight-floating systems shows that as the number of floats increases, the axial distance between them decreases, resulting in more intense motion. Despite this, the eight-floating system maintains a certain safety distance. The maximum load on the connectors occurs in the middle of the multi-floating system, and releasing degrees of freedom can help mitigate some of the load effects.

Encoding many qubits in different degrees of freedom (DOFs) of single photons is one of the routes toward enlarging the Hilbert space spanned by a photonic quantum state. Hyperentangled photon states (that is, states showing entanglement in multiple DOFs) have demonstrated significant implications for both fundamental physics tests and quantum communication and computation. Increasing the number of qubits of photonic experiments requires miniaturization and integration of the basic elements, and functions to guarantee the setup stability, which motivates the development of technologies allowing the precise control of different photonic DOFs on a chip. We demonstrate the contextual use of path and polarization qubits propagating within an integrated quantum circuit. We tested the properties of four-qubit linear cluster states built on both DOFs, and we exploited them to perform the Grover's search algorithm according to the one-way quantum computation model. Our results pave the way toward the full integration on a chip of hybrid multi-qubit multiphoton states.

The structural stability of the optical system in an off-axis four-mirror space telescope is critical to maintaining its optical performance and avoiding potential system failure. Structural deformation can cause variations of the optical path within the telescope, with different degrees of freedom (DOFs) of mirror displacement exerting varying degrees of influence on the optical path. This study develops a model to analyze the impact of multi-DOF rigid body displacements of mirrors on the optical path and predicts the sensitivity of each DOF. The findings are validated through simulations using Zemax, identifying the sensitive DOFs, which are further confirmed through experiments. The results reveal that the effects of displacements vary across different mirrors and DOFs. For instance, in the primary mirror, translation along the Z-axis, translation along the Y-axis, and rotation around the X-axis have the most significant impacts on the optical path and are identified as sensitive directions. In the rotation direction around the X axis, the optical path variation caused by the primary mirror's displacement is significantly greater than that of the secondary mirror. These sensitive directions should receive special attention during the design and testing phases of the telescope. This research provides essential technical support and methodological references for ultra-high-precision multi-DOF structural stability measurements in gravitational wave telescopes. It also offers valuable guidance for the design of ultra-stable structures.

Towards a general class of hybrid dynamical system with free terminal states a global optimal control problem is proposed in this paper. And we bring forward the mathematical method to solve the above problem?HDS? global maximum principle. Then we prove the theorem by means of general variational principle.

This paper proposes a hybrid controller with an event-based switching design for complex network systems, and analyzes the convergence result with network hybrid automaton models. Specifically, the main contributions of the paper are fourfold. First, a hybrid controller design is proposed for a wide spectrum of complex network systems. Second, a class of hybrid dynamical systems is described via a hybrid automaton model; and some invariance convergence results for this class of hybrid dynamical systems are proposed. Third, a network automaton model is presented to capture the details of the closed-loop system; and the convergence results are proved. Finally, the hybrid network controller is applied to the Kunder's two-area, four-machine power system, the implementation of the hybrid network controller for the power network in Simulink is presented, and the simulation is conducted to show the efficacy of the proposed hybrid controller design.

This paper proposes a manipulability servoing control method in null space for redundant bilateral control system with different degrees of freedom (DOF). In the redundant bilateral system, the error of manipulability in work space is arised by different DOF between master and slave systems. As a result, it is difficult to achieve the precise motion control. In order to solve this problem, a bilateral control method based on null space with the manipulability measure is proposed. This paper verifies the effectiveness of the proposed method by simulation and experimental results.

This study presents an attitude of female students studying B.Ed. third year towards physical education and sports within Kathmandu valley. Initially, it was hypothesized that there is no significance difference in attitude of physical education and sports among female students of different campuses. From these 6 campuses, 184 female students were randomly selected. A five-point Likert-type scale was applied for data collection from the selected students who studied in B.Ed. third year. Altogether five opinion statements were used for data collection. It was found that all respondents showed positive attitudes towards physical education and sports. In order to test whether there is significant interdependence in score among the respondents in different perspectives. The chi-square test score was applied as statistical test at the 0.05 level of significance. The chi-test under contingency table: independent of opinion among the respondent, if (χ2>α=0.05 in different degree of freedom) and independent if (χ2≤ α=0.05 in different degree of freedom). For the measurement of attitude for physical education and sports,it has enough evidence in the data to accept alternatives hypothesis; there is relation or interdependence of attitude towards physical education and sports among the respondents. Because, the score is very high among the response of respondent. The study suggests that the university teacher must be accountable to construct professional environment.

The Wishart distribution with two different degrees of freedom

Stability of Dynamic Hybrid Systems With Descriptor Systems as Dynamic Model

This paper deals with the characterization of the stability and instability matrices for a class of unilaterally constrained dynamical systems, represented as linear evolution variational inequalities (LEVI). Such systems can also be seen as a sort of differential inclusion, or (in special cases) as linear complementarity systems, which in turn are a class of hybrid dynamical systems. Examples show that the stability of the unconstrained system and that of the constrained system, may drastically differ. Various criteria are proposed to characterize the stability or the instability of LEVI.

The Complementarity Class of Hybrid Dynamical Systems