This paper proposes a composite adaptive control architecture using dual adaptation scheme for dynamical systems comprising time-varying uncertain parameters. While majority of the adaptive control schemes in literature address the case of constant parameters, recent research has conceptualized improved adaptive control techniques for time-varying systems with rigorous stability proofs. The proposed work is an effort towards a similar direction, where a novel dual adaptation mechanism is introduced to efficiently tackle the time-varying nature of the parameters. Projection and σ\sigma-modification algorithms are strategically combined using congelation of variables to claim a global result for the tracking error space. While the classical adaptive systems demand a restrictive condition of persistence of excitation (PE) for accurate parameter estimation, the proposed work relies on a milder condition, called initial excitation (IE) for the same. A rigorous Lyapunov stability analysis is carried out to establish boundedness of the closed-loop system with a tighter ultimate bound compared to existing results. Further it is analytically shown that the proposed work can recover the performance of previously designed IE-based adaptive controller in case of time invariant systems.

中文翻译：

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双自适应时变系统的复合自适应控制


本文提出了一种针对包含时变不确定参数的动态系统使用双自适应方案的复合自适应控制架构。虽然文献中的大多数自适应控制方案都解决了参数恒定的情况，但最近的研究已经概念化了针对时变系统的改进的自适应控制技术，并具有严格的稳定性证明。所提出的工作是朝着类似的方向努力，其中引入了一种新颖的双重适应机制来有效地解决参数的时变性质。使用变量聚合来策略性地组合投影和 σ\sigma 修改算法，以获取跟踪误差空间的全局结果。虽然经典的自适应系统需要激励持续性（PE）的限制条件来进行精确的参数估计，但所提出的工作依赖于一个更温和的条件，称为初始激励（IE）。进行了严格的李亚普诺夫稳定性分析，以确定闭环系统的有界性，与现有结果相比，其最终界限更严格。此外，分析表明，在时不变系统的情况下，所提出的工作可以恢复先前设计的基于 IE 的自适应控制器的性能。