A symplectic direct method for motion-driven optimal control of mechanical systems

Shi, Boyang; Peng, Haijun; Wang, Xinwei; Zhong, Wanxie

doi:10.1016/j.cnsns.2022.106501

Cited by 5 publications

(2 citation statements)

References 36 publications

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“…This method provides a unified framework for solving the trajectory tracking control problem of a multi-body dynamic system of a robot. Shi et al [28] established the optimal control problem of a motion-driven mechanical system. A symplectic preservation method is presented to solve the optimal control problem of motion-driven systems.…”

Section: = Kmentioning

confidence: 99%

Stabilization Strategy of a Novel Car-Following Model with Time Delay and Memory Effect of the Driver

et al. 2022

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In this paper, a novel car-following model is established integrating the drivers’ memory of previous information. The drivers’ memory of the vehicle ahead is introduced as an influencing factor on the drivers’ expected behavior. The time delay feedback control term is added to the model to increase the stability interval of the system. By comparing the stability intervals of the controlled and uncontrolled models, the necessity of adding a delay feedback control item is demonstrated. The validity and feasibility of the time delay feedback control strategy are proved by numerical simulations. In this paper, the stability interval of the system is determined by the definite integral stability method (DISM) and the Hopf bifurcation analysis method. According to the number of unstable eigenvalues derived from the system eigenvalue equation, the appropriate time delay feedback control parameters are set. By choosing the optimal parameters, the new model can optimize the traffic flow to the maximum extent, eliminate the stop-and-go of vehicles, and make the traffic stable. Numerical examples close to actual traffic conditions are given to verify the feasibility of the control strategy using the verified design steps. Next generation simulation (NGSIM) measurements are used to conduct parameter calibration of the new model.

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Section: = Kmentioning

confidence: 99%

Stabilization Strategy of a Novel Car-Following Model with Time Delay and Memory Effect of the Driver

et al. 2022

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“…Optimization is finding a suitable set of variable values to minimize (maximize) the value of some optimization objective under certain constraints. Optimization algorithms are widely used in engineering design 1 – 3 , engineering practice 4 – 6 , motion control 7 – 9 , and task scheduling in the real world 10 – 12 . At this stage, algorithms for solving optimization problems contain two main categories 13 .…”

Section: Introductionmentioning

confidence: 99%

Symmetric projection optimizer: concise and efficient solving engineering problems using the fundamental wave of the Fourier series

Su,

Dong,

Liu

et al. 2024

Sci Rep

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The fitness function value is a kind of important information in the search process, which can be more targeted according to the guidance of the fitness function value. Most existing meta-heuristic algorithms only use the fitness function value as an indicator to compare the current variables as good or bad but do not use the fitness function value in the search process. To address this problem, the mathematical idea of the fitting is introduced into the meta-heuristic algorithm, and a symmetric projection optimizer (SPO) is proposed to solve numerical optimization and engineering problems more efficiently. The SPO algorithm mainly utilizes a new search mechanism, the symmetric projection search (SP) method. The SP method quickly completes the fitting of the projection plane, which is located through the symmetry of the two points and finds the minima in the projection plane according to the fitting result. Fitting by using the fitness function values allows the SP to find regions where extreme values may exist more quickly. Based on the SP method, exploration and exploitation strategies are constructed, respectively. The exploration strategy is used to find better regions, and the exploitation strategy is used to optimize the discovered regions continuously. The timing of the use of the two strategies is designed so that the SPO algorithm can converge faster while avoiding falling into local optima. The effectiveness of the SPO algorithm is extensively evaluated using seven test suites, including CEC2017, CEC2019, CEC2020, and CEC2022. It is also compared with two sets of 19 recent competitive algorithms. Statistical analyses are performed using five metrics such as the Wilcoxon test, the Friedman test, and variance. Finally, the practicality of the SPO algorithm is verified by four typical engineering problems and a real spacecraft trajectory optimization problem. The results show that the SPO algorithm can find superior results in 94.6% of the comparison tests and is a promising alternative for solving real-world problems.

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Integrated control‐structure co‐design for flexible manipulators

Bastos

2024

Optim Control Appl Methods

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This work aims to develop a methodology for the integrated control‐structure design of flexible multibody systems. Such an issue is linked to a generalization of the inverse dynamics problem, where both the feedforward control and mechanical parameters are designed to perform a desired trajectory optimally. The resulting constrained motion is aimed at improving the dynamic performance of the system, which is underactuated, with less power demand but possible elastic deformation. Stable inversion methods are required to deal with the internal dynamics related to underactuation. The proposed methodology is based on the optimal control theory. For illustrative purposes, we considered a fully actuated linear time‐invariant (LTI) system, establishing the integrated design results in a least‐squares homogeneous system and in an optimization problem. An additional formulation is proposed for the integrated design of the flexible multibody systems, where both a multi‐criterion optimization and a scalarized problem of a corresponding nonlinear programming problem are formulated to deal with the unstable zero‐dynamics related to non‐minimum phase systems and nonlinearity. The numerical simulation of an underactuated two‐masses‐spring‐damper system and a flexible robotic manipulator in planar motions are used for validation. Finally, the beneficial aspects of the integrated design are analyzed.

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A symplectic direct method for motion-driven optimal control of mechanical systems

Cited by 5 publications

References 36 publications

Stabilization Strategy of a Novel Car-Following Model with Time Delay and Memory Effect of the Driver

Stabilization Strategy of a Novel Car-Following Model with Time Delay and Memory Effect of the Driver

Symmetric projection optimizer: concise and efficient solving engineering problems using the fundamental wave of the Fourier series

Integrated control‐structure co‐design for flexible manipulators

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