Performance Analysis of Stochastic Adaptive Controllers

控制工程师经常面临这样的任务：为噪声系统设计控制器，这些系统的参数变化非常严重，以至于经典的或基于状态空间的控制器无法处理。这个问题为自适应控制理论的研究提供了材料。自适应控制理论有几个方面。首先是生成算法，实时估计不同的参数，然后使用这些估计来修改控制器设置。下一步是研究这些算法的行为和性能。这涉及到全局稳定性、对模型误差（寄生）的鲁棒性和性能（例如输出功率和控制信号功率）的问题。本研究的主要推力涉及自适应算法的性能分析相关问题，即；收敛、失调和过度滞后。后两者还有待于随机自适应控制的研究。要做到这一点，需要一些新的前提。参数收敛的前提不再相关，而是必须直接分析性能指标几乎确定的行为。最后，可以对自适应控制器进行近似灵敏度计算。期望本研究能对随机自适应控制有更好的理解，并最终产生更好的控制算法。

The control Engineer is often confronted with the task of designing controllers for noisy systems whose parameter variation is so severe that classical or state space based controllers cannot handle it. This problem provides the material of Adaptive Control Theory. There are several aspects to Adaptive Control Theory. The first is to produce algorithms that will estimate varying parameters in real time and then use these estimates to modify the controller settings. The next is to study the behavior and performance of such algorithms. This involves questions of global stability, robustness to model error (parasitics) and performance (e.g. output power and control signal power). The major thrust of this research concerns issues related to performance analysis of Adaptive algorithms, namely; convergence, misadjustment and excess lag. The latter two have yet to be investigated for Stochastic Adaptive Control. To do this, some new premises are needed. The premise of parameter convergence is no longer relevant, instead the almost sure behavior of performance indices must be directly analyzed. Finally, it is possible to do approximate sensitivity calculations for Adaptive Controllers. It is expected that this research will yield a better understanding of stochastic adaptive control and eventually to better control algorithms.