Unscented MPSP for Optimal Control of a Class of Uncertain Nonlinear Dynamic Systems

2019 ◽  
Vol 141 (6) ◽  
Author(s):  
S. Mathavaraj ◽  
Radhakant Padhi
Keyword(s):  
Optimal Control ◽  
Initial Conditions ◽  
Mean Value ◽  
Control Synthesis ◽  
Benchmark Problems ◽  
Computationally Efficient ◽  
Efficient Manner ◽  
The Mean ◽  
Low Dimensional ◽  
Time Invariant

A new computationally efficient nonlinear optimal control synthesis technique, named as unscented model predictive static programming (U-MPSP), is presented in this paper that is applicable to a class of problems with uncertainties in time-invariant system parameters and/or initial conditions. This new technique is a fusion of two recent ideas, namely MPSP and Riemann–Stieltjes optimal control problems. First, unscented transform is utilized to construct a low-dimensional finite number of deterministic problems. The philosophy of MPSP is utilized next so that the solution can be obtained in a computational efficient manner. The control solution not only ensures that the terminal constraint is met accurately with respect to the mean value, but it also ensures that the associated covariance matrix (i.e., the error ball) is minimized. Significance of U-MPSP has been demonstrated by successfully solving two benchmark problems, namely the Zermelo problem and inverted pendulum problem, which contain parametric and initial condition uncertainties.

scholarly journals Robust multi-fidelity design of a micro re-entry unmanned space vehicle

2011 ◽  
Vol 225 (11) ◽  
pp. 1195-1209 ◽  
Author(s):  
E Minisci ◽  
M Vasile ◽  
H Liqiang
Keyword(s):  
Neural Networks ◽  
Optimal Control ◽  
Thermal Protection ◽  
Space Vehicle ◽  
Mean Value ◽  
Maximum Heat ◽  
Direct Transcription ◽  
Maximum Heat Flux ◽  
The Neural Networks ◽  
The Mean

This article addresses the preliminary robust design of a small-scale re-entry unmanned space vehicle by means of a hybrid optimization technique. The approach, developed in this article, closely couples an evolutionary multi-objective algorithm with a direct transcription method for optimal control problems. The evolutionary part handles the shape parameters of the vehicle and the uncertain objective functions, while the direct transcription method generates an optimal control profile for the re-entry trajectory. Uncertainties on the aerodynamic forces and characteristics of the thermal protection material are incorporated into the vehicle model, and a Monte-Carlo sampling procedure is used to compute relevant statistical characteristics of the maximum heat flux and internal temperature. Then, the hybrid algorithm searches for geometries that minimize the mean value of the maximum heat flux, the mean value of the maximum internal temperature, and the weighted sum of their variance: the evolutionary part handles the shape parameters of the vehicle and the uncertain functions, while the direct transcription method generates the optimal control profile for the re-entry trajectory of each individual of the population. During the optimization process, artificial neural networks are utilized to approximate the aerodynamic forces required by the optimal control solver. The artificial neural networks are trained and updated by means of a multi-fidelity approach: initially a low-fidelity analytical model, fitted on a waverider type of vehicle, is used to train the neural networks, and through the evolution a mix of analytical and computational fluid dynamic, high-fidelity computations are used to update it. The data obtained by the high-fidelity model progressively become the main source of updates for the neural networks till, near the end of the optimization process, the influence of the data obtained by the analytical model is practically nullified. On the basis of preliminary results, the adopted technique is able to predict achievable performance of the small spacecraft and the requirements in terms of thermal protection materials.

scholarly journals Polynomial Representations of High-Dimensional Observations of Random Processes

Mathematics ◽  
2021 ◽  
Vol 9 (2) ◽  
pp. 123
Author(s):  
Pavel Loskot
Keyword(s):  
Random Variables ◽  
Mean Value ◽  
Weighted Sum ◽  
Computationally Efficient ◽  
First Order ◽  
Statistical Measures ◽  
Polynomial Representations ◽  
Univariate Polynomial ◽  
The Mean ◽  
Numerical Complexity

The paper investigates the problem of performing a correlation analysis when the number of observations is large. In such a case, it is often necessary to combine random observations to achieve dimensionality reduction of the problem. A novel class of statistical measures is obtained by approximating the Taylor expansion of a general multivariate scalar symmetric function by a univariate polynomial in the variable given as a simple sum of the original random variables. The mean value of the polynomial is then a weighted sum of statistical central sum-moments with the weights being application dependent. Computing the sum-moments is computationally efficient and amenable to mathematical analysis, provided that the distribution of the sum of random variables can be obtained. Among several auxiliary results also obtained, the first order sum-moments corresponding to sample means are used to reduce the numerical complexity of linear regression by partitioning the data into disjoint subsets. Illustrative examples provided assume the first and the second order Markov processes.

scholarly journals PENERAPAN METODE SUGESTOPEDIA UNTUK MENINGKATKAN KEMAMPUAN MENULIS PUISI SISWA KELAS V SEKOLAH DASAR

2018 ◽  
Vol 5 (2) ◽  
pp. 106
Author(s):  
Sri Wulan Anggraeni ◽  
Yayan Alpian
Keyword(s):  
Research Methodology ◽  
Initial Conditions ◽  
Research Result ◽  
Mean Value ◽  
Vocational School ◽  
Student Needs ◽  
Average Value ◽  
Study Results ◽  
The Mean ◽  
Bahasa Indonesia

Penelitian ini bertujuan untuk mengetahui peningkatan kemampuan menulis puisi siswa SDN Muktiwari 02 melalui penerapan metode sugestopedia. Metode penelitian yang digunakan adalah penelitian tindakan kelas. Penelitian ini dilakukan sebanyak tiga siklus yang setiap siklusnya melalui proses pengkajian yang terdiri dari empat tahap, yaitu merencanakan, melakukan tindakan, mengamati, dan melakukan refleksi. Hasil penelitian ini menunjukkan bahwa pembelajaran menulis puisi dengan menerapkan metode sugestopedia dapat meningkatkan kemampuan menulis puisi siswa. Terbukti dengan aktivitas dan hasil belajar menulis puisi siswa pada kondisi awal pra siklus dengan nilai rata-rata 51,88. Setelah dilakukan tindakan dengan menerapkan metode sugestopedia mengalami peningkatan yaitu pada siklus I dengan nilai rata-rata 62,5,siklus II dengan nilai rata-rata 68,95, dan pada siklus III nilai rata-rata 75,2. Oleh karena itu, pembelajaran dengan menerapkan metode sugestopedia dapat meningkatkan kemampuan menulis puisi. Implikasi penelitian ini ditujukan kepada pendidik, peneliti, dan lembaga atau intansi yang terkait khususnya pihak sekolah agar dapat lebih peka terhadap  kebutuhan siswa dan meningkatkan kreativitas pendidik dalam proses pembelajaran terutama pembelajaran bahasa Indonesia khusunya pembelajaran menulis puisi.Kata kunci: kemampuan menulis puisi, metode sugestopedia. APPLICATION OF SUGESTOPEDIA METHODS TO IMPROVE THE WRITING POETRY ABILITY OF VOCATIONAL SCHOOL OF ELEMENTARY SCHOOLAbstractThis study is aimed to know students’ ability in increasing their poem writing at SDN muktiwari 02 by using method of sugestopedia. Research methodology used is classroom action research. The study is done in three of any cycles through research repeated, consisting of four stage, the plan, take action, observing, and reflection. This research result indicates that learning wrote poems by applying a method of sugestopedia can improve the ability of students writing poetry. Proven with the activity and study results wrote poems students on initial conditions pre cycle the average value of 51,88. After conducted the act of by applying method sugestopedia increased where the cycle I the average value of 62.5, cycle II the average value of 68,95, and in cycle III  the mean value of the 75,2. Hence, learning by applying method sugestopedia can improve the ability wrote poems. Implication this research shown to educator, researchers, and institution or intansi related especially the school that can more vulnerable to student needs and creative educator in learning especially learning the indonesian language especially learning wrote poems.

Optimal stationary control of diesel engines using periodic control

2016 ◽  
Vol 231 (4) ◽  
pp. 457-475 ◽  
Author(s):  
Martin Sivertsson ◽  
Lars Eriksson
Keyword(s):  
Optimal Control ◽  
Optimal Solution ◽  
Mean Value ◽  
Operating Point ◽  
Improve Performance ◽  
Periodic Control ◽  
The Mean ◽  
Operating Points ◽  
Stationary Control ◽  
Optimal Stationary Control

Measurements and optimal control are used to study whether the fuel economy of a diesel engine can be improved through periodic control of the wastegate, illustrating how modern optimal control tools can be used to identify non-trivial solutions that can improve performance. The measurements show that the pumping torque of the engine is changed when the wastegate is controlled in a periodic manner versus stationary even if the mean position is the same. If this decreases the fuel consumption or not is seen to be frequency and operating point dependent. The measurements indicate that the phenomenon occurs in the time scales capturable by mean value engine models (MVEM). The operating points are further analyzed using a MVEM and optimal control. It is shown that whether the optimal solution exhibits periodic oscillations or not is operating point dependent, but is not due to the instantaneous nature of the controls. Even if an actuator model is added the oscillations persist for reasonable time constants, the frequency of the oscillations is however affected. Further it is shown that the periodic control can be predicted by optimal periodic control theory and that the frequency of the control affects the resulting efficiency.

The masses of 18 pairs of double neutron stars and implications for their origin

2018 ◽  
Vol 14 (S346) ◽  
pp. 474-477
Author(s):  
ChengMin Zhang ◽  
YiYan Yang
Keyword(s):  
Neutron Star ◽  
Neutron Stars ◽  
Mass Distribution ◽  
Binary Stars ◽  
Formation Process ◽  
Initial Conditions ◽  
Mean Value ◽  
Solar Mass ◽  
The Mean ◽  
The Masses

AbstractFor the observed 18 pairs of double neutron star (DNS) systems, we find that DNS mass distribution is very narrow and its mean value (about 1.34 solar mass) is less than the mean of all measured pulsars of about 1.4 solar mass. To interpret the special DNS mass characteristics, we analyze the DNS formation process, via the phases of HMXBs, by investigating the evolution of massive binary stars. Moreover, in DNSs, two classes of NSs are taken into account, formed by supernova (SN) and electron capture (EC), respectively, and generally the NS mass by SN is bigger than that by EC. Quantitatively, with various initial conditions of binary stars, the observed special DNS distribution can be satisfactorily explained.

scholarly journals On Asymmetric Periodic Solutions of the Plane Restricted Problem of Three Bodies, and Bifurcations of Families

1978 ◽  
Vol 41 ◽  
pp. 319-323
Author(s):  
P.J. Message ◽  
D.B. Taylor
Keyword(s):  
Periodic Solutions ◽  
Periodic Orbits ◽  
Restricted Problem ◽  
Initial Conditions ◽  
Characteristic Exponent ◽  
Mean Value ◽  
Mirror Image ◽  
Mean Values ◽  
Major Semi Axis ◽  
The Mean

Previous work on the plane circular restricted problem of three bodies (Message 1953, 1959, 1970, and Fragakis 1973) has shown the existence, in association with each of the commensurabilities 2:1 and 3:1 of the orbital periods, of a pair of families of asymmetric periodic solutions, branching from the stable series of symmetric periodic solutions of Poincaré’s second sort associated with that commensurability. (Each solution of either family is the mirror image, in the line of the two finite bodies, of a member of the other family of solutions associated with the commensurability.) The stability is transferred at the bifurcation to the two series of asymmetric orbits, each of which is therefore stable. Recent numerical integrations carried out by one of us (P.J.M.) have found such asymmetric periodic orbits associated also with the 4:1 commensurability, and quantities describing orbits of one of the two series are given in Table 1, showing the run of such orbits up to a second bifurcation with the same series of symmetric periodic orbits from which it sprang. Quantities describing some members of this series of symmetric orbits are given in Table 2. It is seen that stability is transferred back to the symmetric series at the second bifurcation. (The unit of distance is the distance between the two finite bodies, the unit of speed is the speed, of their relative motion, and the initial conditions given (x°, ẋ°, ẏ°) are for a crossing of the line of the two finite bodies, this line being taken as axis of “x” in a rotating Cartesian frame in the usual way. The mean values of the major semi-axis and eccentricity are denoted by ā and ē, respectively, C is Jacobi’s constant, and ȳ2 is the mean value of the critical argument ȳ2 = 4λ – λ′ – 3ω. The mass ratio used is 0.000954927, T is the period of the solution in units of the period of the motion of the two finite bodies, and 2π c/T is the non-zero characteristic exponent.)

scholarly journals Image Processing Method Based on Chaotic Encryption and Wavelet Transform for Planar Design

2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
Yiying Liu ◽  
Young Chun Ko
Keyword(s):  
Image Processing ◽  
Wavelet Transform ◽  
Chaotic System ◽  
Graphic Design ◽  
Initial Conditions ◽  
Mean Value ◽  
Processing Method ◽  
Chaotic Encryption ◽  
Characteristic Analysis ◽  
The Mean

This paper provides an in-depth study and analysis of image processing for graphic design through chaotic encryption combined with a wavelet transform algorithm. Firstly, the traditional Mallat algorithm is optimized; since the mean value of the transform coefficients generated after the wavelet transform of the image is used as the initial value of the chaotic system to iterate, when the image is modified, then the mean value of the wavelet coefficients will also change, and the final iteration comes out as two different sequences using the property that the chaotic system is extremely sensitive to the initial conditions, so the algorithm has a certain sensitivity to tampering and localization effect. The image of the encrypted graphic design is decrypted by the chaos decryption system, and the final image information of the graphic design is obtained. In terms of the security of the graphic design image itself, the complex dynamical properties of chaos are fully utilized to encrypt it, and the algorithm has a good encryption effect after statistical characteristic analysis, attack complexity, difference analysis, adjacent pixel correlation analysis, and key sensitivity analysis. The plaintext image is decomposed in odd-even sequence using the boosting algorithm to get the sequence with an even index and the sequence with an odd index; then, the diffusion algorithm is applied to the two sequences by the prediction and update algorithm, and this process is repeated many times to get the two ciphertext sequences after scrambling, merging these two sequences, and matrixing them to get the ciphertext image. Finally, the testing of the embedded planar designed image revolves around four aspects, namely, image processing, tamper sensitivity, robustness, and imperceptibility, to examine the designed planar designed image system. In the diffusion manipulation, the key matrix for diffusion is obtained using the threshold processing method of the Local Binary Pattern (LBP) algorithm for the matrices generated by the Logistic Chaos system, which improves the randomness of the algorithm. The experimental results verify the effectiveness and security of the algorithm.

scholarly journals A Comparison of Perturbed Initial Conditions and Multiphysics Ensembles in a Severe Weather Episode in Spain

2012 ◽  
Vol 51 (3) ◽  
pp. 489-504 ◽  
Author(s):  
Francisco J. Tapiador ◽  
Wei-Kuo Tao ◽  
Jainn Jong Shi ◽  
Carlos F. Angelis ◽  
Miguel A. Martinez ◽  
...  
Keyword(s):  
Land Surface ◽  
Initial Conditions ◽  
Mean Value ◽  
Severe Weather ◽  
Rain Intensity ◽  
Precipitation Field ◽  
Operational Forecasts ◽  
The Mean ◽  
The Individual ◽  
Physical Parameterizations

AbstractEnsembles of numerical model forecasts are of interest to operational early warning forecasters as the spread of the ensemble provides an indication of the uncertainty of the alerts, and the mean value is deemed to outperform the forecasts of the individual models. This paper explores two ensembles on a severe weather episode in Spain, aiming to ascertain the relative usefulness of each one. One ensemble uses sensible choices of physical parameterizations (precipitation microphysics, land surface physics, and cumulus physics) while the other follows a perturbed initial conditions approach. The results show that, depending on the parameterizations, large differences can be expected in terms of storm location, spatial structure of the precipitation field, and rain intensity. It is also found that the spread of the perturbed initial conditions ensemble is smaller than the dispersion due to physical parameterizations. This confirms that in severe weather situations operational forecasts should address moist physics deficiencies to realize the full benefits of the ensemble approach, in addition to optimizing initial conditions. The results also provide insights into differences in simulations arising from ensembles of weather models using several combinations of different physical parameterizations.

CW Argon-ion Laser Crystallization of a-Si:H Thin Films

2001 ◽  
Vol 664 ◽  
Author(s):  
A. Sunda-Meya ◽  
D. Gracin ◽  
J. Dutta ◽  
B. Vlahovic ◽  
R.J. Nemanich
Keyword(s):  
Crystal Size ◽  
Crystallization Process ◽  
Mean Value ◽  
Laser Crystallization ◽  
Irradiation Energy ◽  
Ion Laser ◽  
The Mean ◽  
Low Dimensional ◽  
Argon Ion ◽  
Dimensional Crystal

ABSTRACTThin a-Si:H films, with a thickness of 1 µm, with different hydrogen concentrations, prepared by hot wire deposition were crystallized by 514.5 nm cw Ar ion laser radiation, with a power density between 150 and 270 kW/cm2. The crystallization was continuously monitored by Raman spectroscopy for exposures up to hours. The analysis of crystallization process using Johnson-Mehl phenomenological equations showed an apparent crystallization energy of around 0.5 eV and low dimensional crystal growth. The mean value of the crystal size decreases with increasing irradiation energy and initial hydrogen content and varies between 3 and 6 nm.

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