一类多变量系统的全形式无模型自适应控制
Full-Form Model-Free Adaptive Control for a Family of Multivariable System
摘要：
本文针对多变量非线性系统，提出了一种基于全形式等效动态线性化模型的无模型自适应控制。与现有的MFAC相比，i）该控制律没有分母，分母来源于逆矩阵的范数，并且不可避免地丢失了系统输入和输出（I/O）之间的耦合关系。（2）简化了对角占优矩阵的限制性假设，扩展了对角占优矩阵的应用范围。iii）基于全形式EDLM的MFAC比当前基于部分形式和紧凑形式EDLM的MFAC更通用。最后，证明了跟踪误差的收敛性和被控系统的BIBO稳定性，这是MFAC中的一个公开问题。
英文摘要：
This correspondence proposes a kind of model-free adaptive control (MFAC) on the basis of full-form equivalent-dynamic-linearization model (EDLM) for the multivariable nonlinear system. Compared with the current MFAC, i) this control law does not have denominator, which is stemmed from the norm of the inverse matrix and it inevitably misses the coupling relationships among the inputs and outputs (I/O) of systems. ii) the current restrictive assumption of a diagonally dominant matrix is reduced to extend its application. iii) the MFAC based on full-form EDLM is more general than the current MFAC based on partial-form and compact-form EDLM. At last, the convergence of tracking error and the BIBO stability of controlled system have been proved, which is one of the open questions in MFAC.
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