Optimal design of nonlinear model predictive controller based on new modified multitracker optimization algorithm

The controller design for the robotic manipulator faces different challenges such as the system's nonlinearities and the uncertainties of the parameters. Furthermore, the tracking of different linear and nonlinear trajectories represents a vital role by the manipulator. This paper suggests an optimal design for the nonlinear model predictive control (NLMPC) based on a new improved intelligent technique and it is named modified multitracker optimization algorithm (MMTOA). The proposed modification of the MTOA is carried out based on opposition-based learning (OBL) and quasi OBL approaches. This modification improves the exploration behavior of the MTOA to prevent it from becoming trapped in a local optimum. The proposed method is applied on the robotic manipulator to track different linear and nonlinear trajectories. The NLMPC parameters are tuned by the MMTOA rather than the trial and error method of the designer. The proposed NLMPC based on MMTOA is compared with the original MTOA, genetic algorithm, and cuckoo search algorithm in literature. The superiority and effectiveness of the proposed controller are confirmed to track different linear and nonlinear trajectories. Furthermore, the robustness of the proposed method is emphasized against the uncertainties of the parameters.     

A stiffness parameter and truncation error criterion for adaptive path following in structural mechanics

We explore a truncation error criterion to steer adaptive step length refinement and coarsening in incremental-iterative path following procedures, applied to problems in large-deformation structural mechanics. Elaborating on ideas proposed by Bergan and collaborators in the 1970s, we first describe an easily computable scalar stiffness parameter whose sign and rate of change provide reliable information on the local behavior and complexity of the equilibrium path. We then derive a simple scaling law that adaptively adjusts the length of the next step based on the rate of change of the stiffness parameter at previous points on the path. We show that this scaling is equivalent to keeping a local truncation error constant in each step. We demonstrate with numerical examples that our adaptive method follows a path with a significantly reduced number of points compared to an analysis with uniform step length of the same fidelity level. A comparison with Abaqus illustrates that the truncation error criterion effectively concentrates points around the smallest-scale features of the path, which is generally not possible with automatic incrementation solely based on local convergence properties.     

Filtered adaptive constrained sampled-data control for uncertain multivariable nonlinear systems

A filtered adaptive constrained sampled-data controller for uncertain multivariable nonlinear systems in the presence of various constraints is synthesized in this paper. A piecewise constant adaptive law drives that estimation error dynamics to zero at each sampling time instant yields adaptive parameters. The filtered control scheme consists of two components. Based on an estimation/cancellation strategy, a disturbance rejection control law is designed to compensate the nonlinear uncertainties within the bandwidth of low-pass filters, whereas a constraint violation avoidance control law is designed to solve an online constrained optimization problem. Although a reduced sampling time helps to minimize the estimation error caused by the neglect of unknowns, the resulting aggressive signals put more restrictions on the control law. Greater sacrifice of tracking performance is required to satisfy the constraints. The constraints violation avoidance control law is in favor of a larger sampling time. Sufficient conditions are given to guarantee the stability of the closed-loop system with the sampled-data controller, where the input/output signals are held constant over the sampling period. Numerical examples are provided to validate the theoretical results, comparisons between the constrained sampled-data controller and unconstrained adaptive controller with the implementation of different sampling times are carried out.     

Temperature- and frequency-dependent hysteresis scaling behaviour and phase transitions in a [001]c 0.73Pb(Mg1/3Nb2/3)O3-0.27PbTiO3 single crystal

The dielectric properties and bipolar polarization-electric field (P-E) and strain-electric field (S-E) dynamic hysteresis of a relaxor [001]_c 0.73Pb(Mg_1/3Nb_2/3)O₃-0.27PbTiO₃ (PMN-0.27PT) single crystal were investigated to reveal more details of the temperature-induced phase transitions. Different linear scaling relations for ferroelectric hysteresis area <A>, coercive field E_c, saturation polarization P_s and remnant polarization P_r versus temperature τ were measured in different temperature regions. For each measurement frequency f, all hysteresis parameters were found to decrease linearly with temperature in the temperature range of the single rhombohedral (R) phase or tetragonal (T) phase, and the rate of decrease in the T phase was observed to be much larger than the corresponding rate in the R phase. In the temperature range near the R-T phase transition, the exponent α in the power law <A>∝f ^α for the R phase was found to be smaller than that for the T phase, and the magnitude of α depended strongly on temperature when the crystal was in the R-T coexisting phase state. Our experimental and theoretical results indicate that the difference in the activation energy and dipole moment in the R and T phases may lead to the observed discrepancy for the P-E and S-E hysteresis behaviour in different temperature regions.     

Systematic convergence of nonlinear stochastic estimators on the Special Orthogonal Group SO(3)

This paper introduces two novel nonlinear stochastic attitude estimators developed on the Special Orthogonal Group with the tracking error of the normalized Euclidean distance meeting predefined transient and steady‐state characteristics. The tracking error is confined to initially start within a predetermined large set such that the transient performance is guaranteed to obey dynamically reducing boundaries and decrease smoothly and asymptotically to the origin in probability from almost any initial condition. The proposed estimators produce accurate attitude estimates with remarkable convergence properties using measurements obtained from low‐cost inertial measurement units. The estimators proposed in continuous form are complemented by their discrete versions for the implementation purposes. The simulation results illustrate the effectiveness and robustness of the proposed estimators against uncertain measurements and large initialization error, whether in continuous or discrete form.     

An original approximate method for estimating the invariant probability distribution of a large class of multi-dimensional nonlinear stochastic oscillators

This paper proposes an original method for obtaining analytical approximations of the invariant probability density function of multi-dimensional Hamiltonian dissipative dynamic systems under Gaussian white noise excitations, with linear non-conservative parts and nonlinear conservative parts. The method is based on an exact result and a heuristic argument. Its pertinence is attested by numerical tests.     

Characteristic Features of the Optimal Processing of the Results of Measurements in the Case of a Random Observation Function

An analysis is made of the characteristic features and problems of the optimal processing of the results of measurements in the case of a random observation function utilizing a nonlinear Kalman filter. A method is proposed for increasing the convergence domain of the filter with additional processing of measurements in the frequency domain.     

双频抽运提高SBS相位共轭保真度

相位共轭保真度是相位共轭镜技术用于强激光系统中的一个重要指标。采用四波混频加强SBS的方法 ,其相干拍频驱动声子场 ,能提高SBS相位共轭保真度。对于双频单池结构 ,使用列阵相机测量激光束能量远场角分布 ,在SBS转换效率最佳时 ,对相干驱动SBS相位共轭保真度进行了实验研究     

一种实现最佳用户检测的非线性优化神经网络

本文提出并讨论了实现码分多址（CDMA）系统上最佳多用户检测（MUD）的一种神经网络方法。该方法通过将最佳多用户检测视为非线性优化组合问题，利用神经网络能有效求解非线性优化问题的优势，导出了一种非线性优化神经网络来实现最佳多用户检测，理论分析和计算机模拟表明，所提出的神经网络具有可实时应用的动态性能和较传统方法优越得多的误码率性能和抗多址干扰的性能。