scholarly journals A Discrete Control Lyapunov Function for Exponential Orbital Stabilization of the Simplest Walker

2017 ◽  
Vol 9 (5) ◽  
Author(s):  
Pranav A. Bhounsule ◽  
Ali Zamani
Keyword(s):  
Lyapunov Function ◽  
Rate Of Convergence ◽  
Basin Of Attraction ◽  
Discrete Control ◽  
Control Lyapunov Function ◽  
Foot Placement ◽  
Modeling Errors ◽  
Orbital Stabilization ◽  
One Step ◽  
The One

Abstract In this paper, we demonstrate the application of a discrete control Lyapunov function (DCLF) for exponential orbital stabilization of the simplest walking model supplemented with an actuator between the legs. The Lyapunov function is defined as the square of the difference between the actual and nominal velocity of the unactuated stance leg at the midstance position (stance leg is normal to the ramp). The foot placement is controlled to ensure an exponential decay in the Lyapunov function. In essence, DCLF does foot placement control to regulate the midstance walking velocity between successive steps. The DCLF is able to enlarge the basin of attraction by an order of magnitude and to increase the average number of steps to failure by 2 orders of magnitude over passive dynamic walking. We compare DCLF with a one-step dead-beat controller (full correction of disturbance in a single step) and find that both controllers have similar robustness. The one-step dead-beat controller provides the fastest convergence to the limit cycle while using least amount of energy per unit step. However, the one-step dead-beat controller is more sensitive to modeling errors. We also compare the DCLF with an eigenvalue-based controller for the same rate of convergence. Both controllers yield identical robustness but the DCLF is more energy-efficient and requires lower maximum torque. Our results suggest that the DCLF controller with moderate rate of convergence provides good compromise between robustness, energy-efficiency, and sensitivity to modeling errors.

Robust Control of Semi-passive Biped Dynamic Locomotion based on a Discrete Control Lyapunov Function

Robotica ◽  
2019 ◽  
Vol 38 (8) ◽  
pp. 1345-1358
Author(s):  
Chengju Liu ◽  
Jing Yang ◽  
Kang An ◽  
Ming Liu ◽  
Qijun Chen
Keyword(s):  
Robust Control ◽  
Lyapunov Function ◽  
Control Method ◽  
External Disturbance ◽  
Discrete Control ◽  
Gait Transition ◽  
Control Lyapunov Function ◽  
Walking Gait ◽  
Foot Strike ◽  
Passive Model

SUMMARYThis paper focuses on robust control of a simplest passive model, which is established on a DCLF (discrete control Lyapunov function) -based control system, and presents gait transition method based on the study of purely passive walker. Firstly, the DCLF is introduced to stabilize walking process between steps exponentially by modulating the length of next step. Next, the swing leg trajectory from mid-stance position to foot-strike can be planned. Then the control law is calculated to resist external disturbance. Besides, an impulse is added just before foot-strike to realize a periodic walking pattern on flat or uphill ground. With walking terrain varying, the robot can transit to an adaptive walking gait in a few steps. With different push or pull disturbances acting on hip joint and the robot gait transiting on a continuously slope-changing downhill, the effectiveness of the presented DCLF-based method is verified using simulation experiments. The ability to walk on a changing environment is also presented by simulation results. The insights of this paper can help to develop a robust control method and adaptive walking of dynamic passive locomotion robots.

scholarly journals Global Stabilization of a Reaction Wheel Pendulum: A Discrete-Inverse Optimal Formulation Approach via A Control Lyapunov Function

Symmetry ◽  
2020 ◽  
Vol 12 (11) ◽  
pp. 1771
Author(s):  
Oscar Danilo Montoya ◽  
Walter Gil-González ◽  
Juan A. Dominguez-Jimenez ◽  
Alexander Molina-Cabrera ◽  
Diego A. Giral-Ramírez
Keyword(s):  
Optimal Control ◽  
Lyapunov Function ◽  
Time Domain ◽  
Discrete Control ◽  
Global Stabilization ◽  
Inverse Optimal Control ◽  
Reaction Wheel ◽  
Control Lyapunov Function ◽  
Control Approach ◽  
Optimal Control Approach

This paper deals with the global stabilization of the reaction wheel pendulum (RWP) in the discrete-time domain. The discrete-inverse optimal control approach via a control Lyapunov function (CLF) is employed to make the stabilization task. The main advantages of using this control methodology can be summarized as follows: (i) it guarantees exponential stability in closed-loop operation, and (ii) the inverse control law is optimal since it minimizes the cost functional of the system. Numerical simulations demonstrate that the RWP is stabilized with the discrete-inverse optimal control approach via a CLF with different settling times as a function of the control gains. Furthermore, parametric uncertainties and comparisons with nonlinear controllers such as passivity-based and Lyapunov-based approaches developed in the continuous-time domain have demonstrated the superiority of the proposed discrete control approach. All of these simulations have been implemented in the MATLAB software.

A Study on the Rearrangement of Dialkyl 1-Aryl-1-hydroxymethylphosphonates to Benzyl Phosphates

2020 ◽  
Vol 24 (4) ◽  
pp. 465-471 ◽  
Author(s):  
Zita Rádai ◽  
Réka Szabó ◽  
Áron Szigetvári ◽  
Nóra Zsuzsa Kiss ◽  
Zoltán Mucsi ◽  
...  
Keyword(s):  
Quantum Chemical ◽  
Room Temperature ◽  
Phase Transfer ◽  
One Pot ◽  
Substrate Dependence ◽  
Triethylbenzylammonium Chloride ◽  
One Step ◽  
The Pudovik Reaction ◽  
The One ◽  
Solid Liquid

The phospha-Brook rearrangement of dialkyl 1-aryl-1-hydroxymethylphosphonates (HPs) to the corresponding benzyl phosphates (BPs) has been elaborated under solid-liquid phase transfer catalytic conditions. The best procedure involved the use of triethylbenzylammonium chloride as the catalyst and Cs2CO3 as the base in acetonitrile as the solvent at room temperature. The substrate dependence of the rearrangement has been studied, and the mechanism of the transformation under discussion was explored by quantum chemical calculations. The key intermediate is an oxaphosphirane. The one-pot version starting with the Pudovik reaction has also been developed. The conditions of this tandem transformation were the same, as those for the one-step HP→BP conversion.

scholarly journals One-Year Clinical Evaluation of the Bonding Effectiveness of a One-Step, Self-Etch Adhesive in Noncarious Cervical Lesion Therapy

2015 ◽  
Vol 2015 ◽  
pp. 1-5 ◽  
Author(s):  
Babacar Faye ◽  
Mouhamed Sarr ◽  
Khaly Bane ◽  
Adjaratou Wakha Aidara ◽  
Seydina Ousmane Niang ◽  
...  
Keyword(s):  
Clinical Performance ◽  
Retention Rate ◽  
Recall Rate ◽  
Acid Etching ◽  
Significant Difference ◽  
Usphs Criteria ◽  
One Step ◽  
One Year ◽  
The One ◽  
Self Etch

This study evaluated the one-year clinical performance of a one-step, self-etch adhesive (Optibond All-in-One, Kerr, CA, USA) combined with a composite (Herculite XRV Ultra, Kerr Hawe, CA, USA) to restore NCCLs with or without prior acid etching. Restorations performed by the same practitioner were evaluated at baseline and after 3, 6, and 12 months using modified USPHS criteria. At 6 months, the recall rate was 100%. The retention rate was 84.2% for restorations with prior acid etching, but statistically significant differences were observed between baseline and 6 months. Without acid etching, the retention rate was 77%, and no statistically significant difference was noted between 3 and 6 months. Marginal integrity (93.7% with and 87.7% without acid etching) and discoloration (95.3% with and 92.9% without acid etching) were scored as Alpha or Bravo, with better results after acid etching. After one year, the recall rate was 58.06%. Loss of pulp vitality, postoperative sensitivity, or secondary caries were not observed. After one year retention rate was of 90.6% and 76.9% with and without acid conditioning. Optibond All-in-One performs at a satisfactory clinical performance level for restoration of NCCLs after 12 months especially after acid etching.

scholarly journals Building up cyclodextrins from scratch – templated enzymatic synthesis of cyclodextrins directly from maltose

2021 ◽  
Author(s):  
Dennis Larsen ◽  
Sophie R. Beeren
Keyword(s):  
Enzymatic Synthesis ◽  
Combinatorial Libraries ◽  
One Step ◽  
The One ◽  
Kinetic Trapping

Template-induced kinetic trapping of specific cyclodextrins in enzyme-mediated dynamic combinatorial libraries of linear and cyclic α-glucans enables the one-step synthesis of cyclodextrins from maltose in water.

scholarly journals Efficient Cryopreservation of Populus tremula by In Vitro-Grown Axillary Buds and Genetic Stability of Recovered Plants

Plants ◽  
2021 ◽  
Vol 10 (1) ◽  
pp. 77
Author(s):  
Elena O. Vidyagina ◽  
Nikolay N. Kharchenko ◽  
Konstantin A. Shestibratov
Keyword(s):  
Survival Rate ◽  
Axillary Buds ◽  
Long Term Storage ◽  
Average Survival ◽  
Transgenic Lines ◽  
Ssr Loci ◽  
One Step ◽  
The One

Axillary buds of in vitro microshoots were successfully frozen at –196 °C by the one-step freezing method using the protective vitrification solution 2 (PVS2). Microshoots were taken from 11 transgenic lines and three wild type lines. Influence of different explant pretreatments were analyzed from the point of their influence towards recovery after cryopreservation. It was found out that the use of axillary buds as explants after removal of the apical one increases recovery on average by 8%. The cultivation on growth medium of higher density insignificantly raises the regenerants survival rate. Pretreatment of the osmotic fluid (OF) shows the greatest influence on the survival rate. It leads to the increase in survival rate by 20%. The cryopreservation technology providing regenerants average survival rate of 83% was developed. It was based on the experimental results obtained with explant pretreatment. Incubation time in liquid nitrogen did not affect the explants survival rate after thawing. After six months cryostorage of samples their genetic variability was analyzed. Six variable simple sequence repeat (SSR) loci were used to analyze genotype variability after the freezing-thawing procedure. The microsatellite analysis showed the genetic status identity of plants after cryopreservation and of the original genotypes. The presence of the recombinant gene in the transgenic lines after cryostorage were confirmed so as the interclonal variation in the growth rate under greenhouse conditions. The developed technique is recommended for long-term storage of various breeding and genetically modified lines of aspen plants, as it provides a high percentage of explants survival with no changes in genotype.

scholarly journals Understanding mathematics of Grover’s algorithm

2021 ◽  
Vol 20 (5) ◽  
Author(s):  
Paweł J. Szabłowski
Keyword(s):  
Phase Change ◽  
Unitary Operator ◽  
Mathematical Structure ◽  
Complex Numbers ◽  
Unitary Operators ◽  
Grover’S Algorithm ◽  
Great Probability ◽  
Grover's Algorithm ◽  
One Step ◽  
The One

AbstractWe analyze the mathematical structure of the classical Grover’s algorithm and put it within the framework of linear algebra over the complex numbers. We also generalize it in the sense, that we are seeking not the one ‘chosen’ element (sometimes called a ‘solution’) of the dataset, but a set of m such ‘chosen’ elements (out of $$n>m)$$ n > m ) . Besides, we do not assume that the so-called initial superposition is uniform. We assume also that we have at our disposal an oracle that ‘marks,’ by a suitable phase change $$\varphi $$ φ , all these ‘chosen’ elements. In the first part of the paper, we construct a unique unitary operator that selects all ‘chosen’ elements in one step. The constructed operator is uniquely defined by the numbers $$\varphi $$ φ and $$\alpha $$ α which is a certain function of the coefficients of the initial superposition. Moreover, it is in the form of a composition of two so-called reflections. The result is purely theoretical since the phase change required to reach this heavily depends on $$\alpha $$ α . In the second part, we construct unitary operators having a form of composition of two or more reflections (generalizing the constructed operator) given the set of orthogonal versors. We find properties of these operations, in particular, their compositions. Further, by considering a fixed, ‘convenient’ phase change $$\varphi ,$$ φ , and by sequentially applying the so-constructed operator, we find the number of steps to find these ‘chosen’ elements with great probability. We apply this knowledge to study the generalizations of Grover’s algorithm ($$m=1,\phi =\pi $$ m = 1 , ϕ = π ), which are of the form, the found previously, unitary operators.

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