Conditions for realizing one-point interactions from a multi-layer structure model

A heterostructure composed of N parallel homogeneous layers is studied in the limit as their widths l1, . . . , lN shrink to zero. The problem is investigated in one dimension and the piecewise constant potential in the Schrödinger equation is given by the strengths V1, . . . , VN as functions of l1, . . . , lN, respectively. The key point is the derivation of the conditions on the functions V1(l1), . . . , VN(lN) for realizing a family of one-point interactions as l1, . . . , lN tend to zero along available paths in the N-dimensional space. The existence of equations for a squeezed structure, the solution of which determines the system parameter values, under which the non-zero tunneling of quantum particles through a multi-layer structure occurs, is shown to exist and depend on the paths. This tunneling appears as a result of an appropriate cancellation of divergences.

Extended state observer-based control with an adjustable parameter for a large ground-based telescope

The high-precision requirements will always be constrained due to the complicated operating conditions of the ground-based telescope. Owing to various internal and external disturbances, it is necessary to study a control method, which should have a good ability on disturbance rejection and a good adaptability on system parameter variation. The traditional proportional-integral (PI) controller has the advantage of simple and easy adjustment, but it cannot deal with the disturbances well in different situations. This paper proposes a simplified active disturbance rejection control law, whose debugging is as simple as the PI controller, and with better disturbance rejection ability and parameter adaptability. It adopts a simplified second-order extended state observer (ESO) with an adjustable parameter to accommodate the significant variation of the inertia during the different design stages of the telescope. The gain parameter of the ESO can be adjusted online with a recursive least square estimating method once the system parameter has changed significantly. Thus, the ESO can estimate the total disturbances timely and the controller will compensate them accordingly. With the adjustable parameter of the ESO, the controller can always achieve better performance in different applications of the telescope. The simulation and experimental verification of the control law was conducted on a 1.2-meter ground based telescope. The results verify the necessity of adjusting the parameter of the ESO, and demonstrate better disturbance rejection ability in a large range of speed variations during the design stages of the telescope.

Tuxedo: Maximizing Smart Contract Computation in PoW Blockchains

Proof-of-Work (PoW) based blockchains typically allocate only a tiny fraction (e.g., less than 1% for Ethereum) of the average interarrival time (I) between blocks for validating smart contracts present in transactions. In such systems, block validation and PoW mining are typically performed sequentially, the former by CPUs and the latter by ASICs. A trivial increase in validation time (τ) introduces the popularly known Verifier's Dilemma, and as we demonstrate, causes more forking and hurts fairness. Large τ also reduces the tolerance for safety against a Byzantine adversary. Solutions that offload validation to a set of non-chain nodes (a.k.a. off-chain approaches) suffer from trust and performance issues that are non-trivial to resolve. In this paper, we present Tuxedo, the first on-chain protocol to theoretically scale τ/I ≈1 in PoW blockchains. The key innovation in Tuxedo is to perform CPU-based block processing in parallel to ASIC mining. We achieve this by allowing miners to delay validation of transactions in a block by up to ζ blocks, where ζ is a system parameter. We perform security analysis of Tuxedo considering all possible adversarial strategies in a synchronous network with maximum end-to-end delay Δ and demonstrate that Tuxedo achieves security equivalent to known results for longest chain PoW Nakamoto consensus. Our prototype implementation of Tuxedo atop Ethereum demonstrates that it can scale τ without suffering the harmful effects of naive scaling up of τ/I in existing blockchains

Output-Feedback Position Tracking Servo System with Feedback Gain Learning Mechanism via Order-Reduction Speed-Error-Stabilization Approach

This paper presents a novel trajectory-tracking technique for servo systems treating only the position measurement as the output subject to practical concerns: system parameter and load uncertainties. There are two main contributions: (a) the use of observers without system parameter information for estimating the position reference derivative and speed and acceleration errors and (b) an order reduction exponential speed error stabilizer via active damping injection to enable the application of a feedback-gain-learning position-tracking action. A hardware configuration using a QUBE-servo2 and myRIO-1900 experimentally validates the closed-loop improvement under various scenarios.

INVESTIGATION OF THE NORMAL VIBRATION MODES STABILITY IN SOME ESSENTIALLY NONLINEAR SYSTEMS

In the paper stability of nonlinear normal modes is analyzed by two approaches. One of them is the method of Ince algebraization, when a new independent variable associated with the unperturbed solution is introduced in the problem. In this case equations in variations are transformed to equations with singular points. The problem of determination of solutions corresponding to boundaries of the stability/ instability regions is reduced here to the problem of determination of functions that have singularity at the mentioned points. Such solutions can be obtained in the form of power series, which coefficients are satisfying a system of homogeneous linear algebraic equations. The condition ensuring the existence non-trivial solutions for such systems determines the boundaries between the stability / instability regions in the system parameter space. An advantage of the Ince algebraization is that we do not use the time-presentation of the solution when studying its stability. Other approach to investigating steady state stability is associated with the classical Lyapunov definition of stability. The analytical-numerical test proposed in the paper can be applied to a stability problem when the problem has no analytical solution. It also allows to obtain boundaries between the stability / instability regions in the system parameter space. In the present paper the first approach is used to analyze stability of normal vibration modes in the system of connected oscillators on the essentially nonlinear elastic support, and the second one is used to analyze stability of a horizontal vibration mode in the so-called stochastic absorber.

Dynamical integrity assessment of stable equilibria: a new rapid iterative procedure

A new algorithm for the estimation of the robustness of a dynamical system’s equilibrium is presented. Unlike standard approaches, the algorithm does not aim to identify the entire basin of attraction of the solution. Instead, it iteratively estimates the so-called local integrity measure, that is, the radius of the largest hypersphere entirely included in the basin of attraction of a solution and centred in the solution. The procedure completely overlooks intermingled and fractal regions of the basin of attraction, enabling it to provide a significant engineering quantity in a very short time. The algorithm is tested on four different mechanical systems of increasing dimension, from 2 to 8. For each system, the variation of the integrity measure with respect to a system parameter is evaluated, proving the engineering relevance of the results provided. Despite some limitations, the algorithm proved to be a viable alternative to more complex and computationally demanding methods, making it a potentially appealing tool for industrial applications.

A Three-Stage Data-Driven Approach for Determining Reaction Wheels’ Remaining Useful Life Using Long Short-Term Memory

Reaction wheels are widely used in the attitude control system of small satellites. Unfortunately, reaction wheels failure restricts the efficacy of a satellite, and it is one of the many reasons leading to premature abandonment of the satellites. This study observes the measurable system parameter of a faulty reaction wheel induced with incipient fault to estimate the remaining useful life of the reaction wheels. We achieve this goal in three stages, as none of the observable system parameters are directly related to the health of a reaction wheel. In the first stage, we identify the necessary observable system parameter and predict the future of these parameters using sensor acquired data and a long short-term memory recurrent neural network. In the second stage, we estimate the health index parameter using a multivariate long short-term memory network. In the third stage, we predict the remaining useful life of reaction wheels based on historical data of the health index parameter. Normalized root mean squared error is used to evaluate the performance of the various models in each stage. Additionally, three different timespans (short, moderate, and extended in the scale of small satellite orbit times) are simulated and tested for the performance of the proposed methodology regarding the malfunction of reaction wheels. Furthermore, the robustness of the proposed method to missing values, input frequency, and noise is studied. The results show promising performance for the proposed scheme with accuracy in predicting health index parameter around 0.01–0.02 normalized root mean squared error, the accuracy in prediction of RUL of 1%–2.5%, and robustness to various uncertainty factors, as discussed above.