非线性参数化非线性耗散系统的间接自适应控制
Indirect Adaptive Control of Nonlinearly Parameterized Nonlinear Dissipative Systems
摘要：
本文研究了非线性输入仿射耗散系统的间接自适应控制问题。它是假设的供应率，存储和内部耗散函数可以表示为非线性参数化的回归方程的映射（取决于未知参数）满足单调性条件-这包括一个大类的物理系统，包括被动系统。我们建议使用“功率平衡”方程估计系统参数，这是经典耗散不等式的差分版本，具有新的估计，确保全局，指数，参数收敛的功率平衡方程回归的区间激励的非常弱的假设下。要设计的间接自适应控制器，我们的标准假设存在的渐近稳定控制器，依赖于-可能非线性-未知的植物参数，并应用一定的等效控制律。所提出的方法，相对于其他现有的解决方案的好处，用例子说明。
英文摘要：
In this note we address the problem of indirect adaptive (regulation or tracking) control of nonlinear, input affine dissipative systems. It is assumed that the supply rate, the storage and the internal dissipation functions may be expressed as nonlinearly parameterized regression equations where the mappings (depending on the unknown parameters) satisfy a monotonicity condition -- this encompasses a large class of physical systems, including passive systems. We propose to estimate the system parameters using the "power-balance" equation, which is the differential version of the classical dissipation inequality, with a new estimator that ensures global, exponential, parameter convergence under the very weak assumption of interval excitation of the power-balance equation regressor. To design the indirect adaptive controller we make the standard assumption of existence of an asymptotically stabilizing controller that depends -- possibly nonlinearly -- on the unknown plant parameters, and apply a certainty-equivalent control law. The benefits of the proposed approach, with respect to other existing solutions, are illustrated with examples.
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