Multivariable control based on incomplete models via feedback linearization and continuous‐time derivative estimation

2021 ◽  
Author(s):  
Diogo Rodrigues ◽  
Ali Mesbah
Keyword(s):  
Continuous Time ◽  
Feedback Linearization ◽  
Time Derivative ◽  
Multivariable Control ◽  
Derivative Estimation ◽  
Incomplete Models

scholarly journals Next-Point Prediction for Direct Touch Using Finite-Time Derivative Estimation

2018 ◽  
Author(s):  
Mathieu Nancel ◽  
Stanislav Aranovskiy ◽  
Rosane Ushirobira ◽  
Denis Efimov ◽  
Sebastien Poulmane ◽  
...  
Keyword(s):  
Finite Time ◽  
Time Derivative ◽  
Derivative Estimation

scholarly journals Prooving Identities with Computer-Algebra -- Example: Algebraic Time-Derivative Estimation

PAMM ◽  
2008 ◽  
Vol 8 (1) ◽  
pp. 10905-10906 ◽  
Author(s):  
Johann Reger ◽  
Jérôme Jouffroy
Keyword(s):  
Computer Algebra ◽  
Time Derivative ◽  
Derivative Estimation

Noise Tolerant Iterative Learning Control and Identification for Continuous-Time Systems With Unknown Bounded Input Disturbances

2007 ◽  
Vol 129 (6) ◽  
pp. 825-836 ◽  
Author(s):  
Tae-Hyoung Kim ◽  
Xiaoguang Zheng ◽  
Toshiharu Sugie
Keyword(s):  
Continuous Time ◽  
Iterative Learning Control ◽  
Time Derivative ◽  
Learning Control ◽  
Iterative Learning ◽  
Measurement Noise ◽  
Continuous Time Systems ◽  
Noise Tolerant ◽  
Time Systems ◽  
Bounded Input

This paper considers the problems of both noise tolerant iterative learning control (ILC) and iterative identification for a class of continuous-time systems with unknown bounded input disturbance and measurement noise. To this aim, we first propose a formulation of an extended ILC scheme using sampled input∕output (I∕O) data. The proposed ILC method has distinctive features as follows. Its learning law works in a prescribed finite-dimensional parameter space and employs I∕O data of all past trials efficiently. Also, the time derivative of tracking error is not required. Then, it is presented how the uncertain parameters can be identified by using the proposed ILC algorithm and how robust it is against measurement noise through a numerical example. Furthermore, its experimental evaluation is performed to demonstrate the effectiveness of the proposed identification scheme.

scholarly journals Noise-tolerant continuous-time Zhang neural networks for time-varying Sylvester tensor equations

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Sun Min ◽  
Liu Jing
Keyword(s):  
Neural Networks ◽  
Continuous Time ◽  
Time Derivative ◽  
Time Varying ◽  
Gradient Based ◽  
Noise Tolerant ◽  
Derivative Information ◽  
Residual Errors ◽  
Theoretical Analyses ◽  
Zhang Neural Networks

Abstract In this paper, to solve the time-varying Sylvester tensor equations (TVSTEs) with noise, we will design three noise-tolerant continuous-time Zhang neural networks (NTCTZNNs), termed NTCTZNN1, NTCTZNN2, NTCTZNN3, respectively. The most important characteristic of these neural networks is that they make full use of the time-derivative information of the TVSTEs’ coefficients. Theoretical analyses show that no matter how large the unknown noise is, the residual error generated by NTCTZNN2 converges globally to zero. Meanwhile, as long as the design parameter is large enough, the residual errors generated by NTCTZNN1 and NTCTZNN3 can be arbitrarily small. For comparison, the gradient-based neural network (GNN) is also presented and analyzed to solve TVSTEs. Numerical examples and results demonstrate the efficacy and superiority of the proposed neural networks.

scholarly journals THE EVOLUTION OF ONE- AND TWO-LOCUS SYSTEMS

Genetics ◽  
1976 ◽  
Vol 83 (3) ◽  
pp. 583-600
Author(s):  
Thomas Nagylaki
Keyword(s):  
Continuous Time ◽  
Time Derivative ◽  
Second Order ◽  
Rate Of Change ◽  
Evolutionary Significance ◽  
Multiple Alleles ◽  
Mean Fitness ◽  
The Mean ◽  
Change In Mean ◽  
Continuous Time Models

ABSTRACT Assuming age-independent fertilities and mortalities and random mating, continuous-time models for a monoecious population are investigated for weak selection. A single locus with multiple alleles and two alleles at each of two loci are considered. A slow-selection analysis of diallelic and multiallelic two-locus models with discrete nonoverlapping generations is also presented. The selective differences may be functions of genotypic frequencies, but their rate of change due to their explicit dependence on time (if any) must be at most of the second order in s, (i.e., O(s  2)), where s is the intensity of natural selection. Then, after several generations have elapsed, in the continuous time models the time-derivative of the deviations from Hardy-Weinberg proportions is of O(s  2), and in the two-locus models the rate of change of the linkage disequilibrium is of O(s  2). It follows that, if the rate of change of the genotypic fitnesses is smaller than second order in s (i.e., o(s  2)), then to O(s  2) the rate of change of the mean fitness of the population is equal to the genic variance. For a fixed value of s, however, no matter how small, the genic variance may occasionally be smaller in absolute value than the (possibly negative) lower order terms in the change in fitness, and hence the mean fitness may decrease. This happens if the allelic frequencies are changing extremely slowly, and hence occurs often very close to equilibrium. Some new expressions are derived for the change in mean fitness. It is shown that, with an error of O(s), the genotypic frequencies evolve as if the population were in Hardy-Weinberg proportions and linkage equilibrium. Thus, at least for the deterministic behavior of one and two loci, deviations from random combination appear to have very little evolutionary significance.

scholarly journals A Shake Table Frequency-Time Control Method Based on Inverse Model Identification and Servoactuator Feedback-Linearization

Vibration ◽  
2020 ◽  
Vol 3 (4) ◽  
pp. 425-447
Author(s):  
José Ramírez Senent ◽  
Jaime H. García-Palacios ◽  
Iván M. Díaz
Keyword(s):  
Feedback Linearization ◽  
Control Method ◽  
Time Derivative ◽  
Shake Table ◽  
Pressure Force ◽  
Structural Dynamic ◽  
Target Acceleration ◽  
Resonance Frequencies ◽  
Force Time ◽  
Acceleration Profile

Shake tables are one of the most widespread means to perform vibration testing due to their ability to capture structural dynamic behavior. The shake table acceleration control problem represents a challenging task due to the inherent non-linearities associated to hydraulic servoactuators, their low hydraulic resonance frequencies and the high frequency content of the target signals, among other factors. In this work, a new shake table control method is presented. The procedure relies on identifying the Frequency Response Function between the time derivative of pressure force exerted on the actuator’s piston rod and the resultant acceleration at the control point. Then, the Impedance Function is calculated, and the required pressure force time variation is estimated by multiplying the impedance by the target acceleration profile in frequency domain. The pressure force time derivative profile can be directly imposed on an actuator’s piston by means of a feedback linearization scheme, which approximately cancels out the actuator’s non-linearities leaving only those related to structure under test present in the control loop. The previous architecture is completed with a parallel Three Variable Controller to deal with disturbances. The effectiveness of the proposed method is demonstrated via simulations carried over a non-linear model of a one degree of freedom shake table, both in electrical noise free and contaminated scenarios. Numerical experiments results show an accurate tracking of the target acceleration profile and better performance than traditional control approaches, thus confirming the potential of the proposed method for its implementation in actual systems.

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