优化输出同步欧勒-拉格朗日系统与不确定的时间变化的二次性成本函数
IEEE transactions on cybernetics
|March 4, 2025
概括
本研究解决了不确定的网络欧勒-拉格朗日系统的最佳输出同步问题. 研究人员开发了一个分布式自适应控制器,确保系统输出汇聚到时间变化的最佳解决方案,尽管存在不确定性.
科学领域:
- 控制系统工程 控制系统工程
- 网络化系统 网络化系统
- 优化理论 优化理论
背景情况:
- 网络系统经常面临不确定的参数和分布式控制目标的挑战.
- 最优输出同步问题 (OOSP) 要求系统输出跟踪一个动态的最佳解决方案.
- 现有的方法可能无法充分处理欧勒-拉格朗奇系统内的分布式优化问题的不确定性.
研究的目的:
- 为了研究不确定的网络欧勒-拉格朗日 (EL) 系统的最佳输出同步问题 (OOSP).
- 开发分布式自适应控制策略,以实现与时间变化的最佳解决方案同步.
- 在分布式二次优化问题的局部成本函数中处理不确定的参数.
主要方法:
- 一个具有适应性增益的集中控制器被设计为一个双集成器系统来跟踪最佳解决方案.
- 修改平均估计器被用来将集中设计扩展到EL系统的分布式实现.
- 使用矩阵痕迹特性和复合力普诺夫分析来证明趋同.
主要成果:
- 提出的分布式自适应控制器成功地引导系统输出向时间变化的最佳解决方案.
- 在不确定的条件下,系统输出在异常趋同到所需的时间变化的最佳解决方案.
- 用两个说明性示例进行了验证.
结论:
- 开发的分布式自适应控制方法有效地解决了不确定的网络EL系统的OOSP.
- 该方法在存在参数不确定性的情况下,确保了对动态最佳解决方案的稳健融合.
- 这些发现为复杂的网络控制系统中的同步任务提供了有价值的框架.
相关概念视频
01:21Linear Approximation in Time Domain
59
Nonlinear systems often require sophisticated approaches for accurate modeling and analysis, with state-space representation being particularly effective. This method is especially useful for systems where variables and parameters vary with time or operating conditions, such as in a simple pendulum or a translational mechanical system with nonlinear springs.
For a simple pendulum with a mass evenly distributed along its length and the center of mass located at half the pendulum's length,...
For a simple pendulum with a mass evenly distributed along its length and the center of mass located at half the pendulum's length,...
59
01:19Euler Equations of Motion
197
Imagine a rigid body that is rotating at an angular velocity of ω within an inertial frame of reference. Along with this, picture a second rotating frame that is attached to the body itself. This frame moves along with the body and possesses an angular velocity of Ω. The total moment about the center of mass is calculated by adding the rate of change of angular momentum about the center of mass in relation to the rotating frame and the cross-product of the body's angular velocity...
197
01:23Linear time-invariant Systems
202
A system is linear if it displays the characteristics of homogeneity and additivity, together termed the superposition property. This principle is fundamental in all linear systems. Linear time-invariant (LTI) systems include systems with linear elements and constant parameters.
The input-output behavior of an LTI system can be fully defined by its response to an impulsive excitation at its input. Once this impulse response is known, the system's reaction to any other input can be...
The input-output behavior of an LTI system can be fully defined by its response to an impulsive excitation at its input. Once this impulse response is known, the system's reaction to any other input can be...
202
01:13Stability of Equilibrium Configuration: Problem Solving
566
The stability of equilibrium configurations is an important concept in physics, engineering, and other related fields. In simple terms, it refers to the tendency of an object or system to return to its equilibrium position after being disturbed. The stability of an equilibrium configuration can be analyzed by considering the potential energy function of the system and examining its behavior near the equilibrium point.
Problem-solving in the context of the stability of equilibrium configuration...
Problem-solving in the context of the stability of equilibrium configuration...
566
01:15Kinematic Equations: Problem Solving
11.8K
When analyzing one-dimensional motion with constant acceleration, the problem-solving strategy involves identifying the known quantities and choosing the appropriate kinematic equations to solve for the unknowns. Either one or two kinematic equations are needed to solve for the unknowns, depending on the known and unknown quantities. Generally, the number of equations required is the same as the number of unknown quantities in the given example. Two-body pursuit problems always require two...
11.8K
01:28Euler's Equations of Motion
363
In fluid mechanics, shear stresses arise from viscosity, which represents a fluid's internal resistance to deformation. For low-viscosity fluids, like water, these stresses are minimal, simplifying flow analysis by allowing the fluid to be treated as inviscid, or frictionless. In an inviscid fluid, shear stresses are absent, leaving only normal stresses, which act perpendicularly to fluid elements. Notably, pressure — defined as the negative of the normal stress — remains...
363