Data-driven asymptotic stabilization for discrete-time nonlinear systems

In this paper, we propose a data-driven feedback controller design method based on Lyapunov approach, which can guarantee the asymptotic stability of the closed-loop and enlarge the estimate of domain of attraction (DOA) for the closed-loop. First, sufficient conditions for a feedback controller asymptotically stabilizing the discrete-time nonlinear plant are proposed. That is, if a feedback controller belongs to an open set consisting of pairs of control input and state, whose elements can make the difference of a control Lyapunov function (CLF) to be negative-definite, then the controller asymptotically stabilizes the plant. Then, for a given CLF candidate, an algorithm, to estimate the open set only using data, is proposed. With the estimate, it is checked whether the candidate is or is not a CLF. If it is, a feedback controller is designed just using data, which satisfies sufficient conditions mentioned above. Finally, the estimate of DOA for closed-loop is enlarged by finding an appropriate CLF from a CLF candidate set based on data. Because the controller is designed directly from data, complexity in building the model and modeling error are avoided.     

Transient Stability Enhancement of Multi–Machine Power Systems: Synchronization via Immersion of a Pendular System

In this paper the problem of designing excitation controllers to improve the transient stability of multi‐machine power systems is addressed adopting two new perspectives. First, instead of the standard formulation of stabilization of an equilibrium point, we aim here at the more realistic objective of keeping the difference between the generators rotor angles bounded and their speeds equal—which is called synchronization in the power literature—and translates into a problem of stabilization of a set. Second, we adopt the classical viewpoint of power systems as a set of coupled nonlinear pendula, and express our control objective as ensuring that some suitable defined pendula dynamics are (asymptotically) immersed into the power system dynamics. Our main contribution is the explicit computation of a control law for the two–machine system that achieves global synchronization. The same procedure is applicable to the n–machine case, for which the existence of a locally stabilizing solution is established.     

光学镜头调制传递函数的测试

为了定量、客观、全面地评价光学镜头的像质,介绍了光学镜头调制传递函数的测试。先简要叙述了测试的原理,并给出计算公式;然后介绍了测试步骤,其中包括固定、穿轴、测试中心视场和测试轴外视场;最后介绍了测试时的注意事项,包括对测试工装的要求、对测试平面的要求和正、负轴外视场测试值相差较大时的处理办法。     

A New Derivation of the Cubature Kalman Filters

This paper investigates the cubature Kalman filtering (CKF) for nonlinear dynamic systems. This third‐degree rule based filter employs a spherical‐radial cubature rule to numerically compute the integrals encountered in nonlinear filtering problems, thereby removing the requirements of explicitly computing the Jacobians. The cubature rule, however, requires computing the intractable integrals over a high‐dimensional spherical region for multidimensional applications. Moreover, the cubature formula that has been used to construct the spherical cubature formula has some demerits, most notably its inconvenient properties in computation and low estimation accuracy. Aimed at these issues, a general class of CKFs that uses only cubature rules is derived in this paper. It can be shown that the conventional CKF is a special case of the proposed algorithm. The paper also includes higher‐degree CKFs, especially two representative types of the fifth‐degree CKFs. Performance of the proposed algorithms is demonstrated via two target tracking problems. The experimental results, presented herein, illustrate the superior performance of higher‐degree CKFs to conventional nonlinear filters.     

On the Design of Observer for Nonlinear Time‐Delay Systems

This paper suggests a new method to design observers in a class of nonlinear time‐delay systems with delays in system states. The method is based on an extension of the well‐known state‐dependent Riccati equation (SDRE) technique. The conditions for locally asymptotic stability of the proposed observer are investigated. Some numerical simulations are provided to show the design procedure and the flexibility of the proposed observer.     

EFFICIENT DESIGNS FOR NONLINEAR MODELING

In the modeling of physical systems, such as chemical reactions, nonlinear models in a set of unknown parameters are commonly developed. Using the method of least squares for model fitting the efficiency of the process is measured by the large sample variance of the parameter estimates. Designs which yield desirable properties in the linear case, such as factorial and central composite designs, are often utilized in the nonlinear model setting. In this paper a method for transforming these standard designs, yielding more efficient estimators, in the nonlinear model case is proposed. The procedure is demonstrated on a typical kinetic reaction model.     

Modeling and control of Wiener-type processes

We develop a simple relay feedback method to identify Wiener-type nonlinear processes. It separates the identification problem of the nonlinear static function from that of the linear dynamic subsystem to simplify the identification procedure significantly. Owing to the separation, the unmeasurable output of the linear dynamic subsystem can be obtained in a straightforward manner. Then, determining the model structure of the nonlinear static function becomes very simple and the estimates are robust to additive output noises. We can identify the whole activated region of the nonlinear static function as well as the ultimate information of the linear dynamic subsystem from only one relay feedback test. More information on the linear dynamic subsystem can be estimated by well-established linear system identification methods from additional tests. We use a nonlinear control strategy to compensate the nonlinear dynamics of the Wiener process so that the design parameters can be determined by usual tuning rules developed for linear processes and a high control performance can be achievable as in linear processes.     

A STUDY OF EXPERIMENTAL DESIGN OPTIMALITY FOR WIENER SYSTEMS

In the context of nonlinear dynamic system identification for Hammerstein systems, Rollins et al. (2003a) studied the information efficiency of the following two competing experimental design approaches: statistical design of experiments (SDOE) and pseudo-random sequences design (PRSD). The focus of this study is the Wiener system and evaluates SDOE against PRS under D-optimal efficiency. Three cases are evaluated and the results strongly support SDOE as the better approach.     

Capillary jet instability under the influence of gravity

The focus of this paper is on the effect of gravity stretching on disturbed capillary jet instability. Break-up and droplet formation under low flows are simulated using finite difference solution of a one-dimensional approximation of disturbed capillary jet instability chosen from the work by Eggers and Dupont (J. Fluid Mech. 155 (1994) 289). Experiments were conducted using water and aqueous glycerol solutions to compare with simulations. We use a gravity parameter, G, which quantifies gravity stretching by relating flow velocity, orifice size and acceleration and is the reciprocal of the Froude number. The optimum disturbance frequency was found to be inversely proportional to G. However, this relationship appears to be complex for the range of G's investigated. At low G, the relationship between and G appears to be linear but takes on a weakly decaying like trend as G increases. As flows are lowered, the satellite-free regime decreases, although experimental observation found that merging of main and satellite drops sometimes offset this effect to result in monodispersed droplet trains post break-up. Viscosity did not significantly affect the relationship between the disturbance frequency and G, although satellite drops could be seen more clearly close to the upper limit for instability at high G's. It is possible to define regimes of satellite formation under low flows by considering local wavenumbers at the point of instability.     

Fundamental Optical Absorption Edge of Sputter-Deposited Zirconia and Yttria

Zirconia and yttria films were sputter deposited onto unheated fused silica substrates using a metal target and rare gas-oxygen discharges. Double-beam spectrophotometry was used to measure the transmission and reflection as a function of incident photon energy, E , from which the absorption coefficient, α( E ), was calculated. An indirect interband transition at E _i= 4.70 eV and two direct interband transitions at E _g1= 5.17 eV and E _g2= 5.93 eV occur in monoclinic zirconia. Two direct interband transitions at E _g1= 5.07 eV and E _g2= 5.73 eV occur in cubic yttria. The absorption edge structure is modified when unusual phases, such as tetragonal zirconia, and zirconia and yttria with no longrange crystallographic order, are present.