At the limits of adaptive systems: constrained adaptive control

自适应控制系统能够通过使用更新其参数的算法来自动适应其环境；简单地说，它们是自校正控制器。这是一个非常吸引人的特征，原则上，允许控制器进化以提高其性能或增加其对不确定性的容忍度。在利基应用领域(最明显的是在美国航空航天行业)，自适应控制器已被证明非常成功。同时，所有控制系统对它们应用于系统的“输入”都有限制(例如，电气系统中的电压和电流限制；机械系统中的力和扭矩限制)。众所周知，如果在控制器设计中没有正确考虑这些限制，它们会导致系统性能下降，甚至可能导致系统不稳定。在其他线性系统中，这些特征被很好地理解，并且已经设计了所谓的抗卷绕补偿器，它可以保护控制器免受这种灾难性的性能下降的影响。不幸的是，自适应控制器本质上是非线性的，要设计出能够处理自适应算法和控制约束的潜在有害混合的控制策略要困难得多。本研究旨在解决控制工程师工具箱中的上述空白，提出具有输入约束的自适应控制系统的抗卷绕补偿器。这些补偿器将作为现有自适应控制方案的反向匹配，只有在饱和发生时才会激活。当这种情况发生时，补偿器将帮助自适应控制器保持稳定性和性能，并通过一种我们称为“自适应冻结”的机制，防止自适应更新算法本身进入不稳定状态。该研究将提供可用于(I)设计自适应反饱和补偿器和(Ii)可用于分析受限输入自适应系统的数学算法。这项研究的第二部分将使人们能够将新的抗卷绕补偿器与已提出的解决自适应控制系统中输入约束的其他措施进行比较。本研究的目的是在自行开发的无人飞行器(UAV)上演示这些新型抗卷绕补偿器，以了解所提出的补偿器的优点和不足。莱斯特无人机需要一个自适应控制系统来获得最佳性能，但由于其体积小，发动机容量有限，在阵风飞行条件下非常容易受到饱和效应的影响。它将提供一个具有挑战性的应用程序来测试新的反发条算法。模拟研究和飞行测试都将进行。最终，希望这项研究将使控制工程师能够一瞥自适应控制迄今隐藏的一个方面，并希望开发的工具将使他/她更好地装备他/她处理自适应系统中的输入约束。

Adaptive control systems are able to adapt themselves to their environment automatically by using algorithms which update their parameters; simply put, they are self-tuning controllers. This is a very appealing feature and, in principle, allows a controller to evolve in order to enhance its performance or to increase its tolerance of uncertainty. In niche applications (most notably in the US aerospace industry) adaptive controllers have proven to be very successful. At the same time all control systems have limits on the "input" they apply to a system (e.g. limits on voltage and current in electrical systems; limits on force and torque in mechanical systems). It is well known if these limits are not accounted for properly in controller design, they can cause the system performance to degrade and may even drive it to instability.In otherwise linear systems these features are reasonably well understood and so-called "anti-windup" compensators have been devised which can protect a controller against this sort of catastrophic performance degradation. Unfortunately, adaptive controllers are, by their very nature, nonlinear and it is far more difficult to devise control strategies which can handle the potentially toxic mix of adaptation algorithms and control constraints. This research aims to address the above gap in the control engineer's toolbox by proposing anti-windup compensators for adaptive control systems subject to input constraints. These compensators will serve as retro-fits to existing adaptive control schemes and will only become active when saturation occurs. When this happens the compensators will assist the adaptive controller in maintaining stability and performance and also, via a mechanism we call an "adaptive freeze", prevent the adaptive update algorithms from entering instability themselves. The research will provide mathematical algorithms which can be used to (i) design the adaptive anti-windup compensators and (ii) can be used to analyse constrained input adaptive systems. This second part of the research will enable one to compare the new anti-windup compensators with other measures which have been proposed to tackle input constraints in adaptive control systems.The research aims to demonstrate these new anti-windup compensators on an in-house developed uninhabited aerial vehicle (UAV) in order to understand the merits and deficiencies of the proposed compensators. The Leicester UAV requires an adaptive control system to extract the best performance from it but, due to its small size and limited motor capacity, is very vulnerable to saturation effects during gusty flight conditions. It will provide a challenging application on which to test the new anti-windup algorithms. Both simulation studies and flight tests will be undertaken. Ultimately, it is hoped that the research will enable the control engineer to glimpse a hitherto hidden aspect of adaptive control and that the tools developed will better equip him/her for tackling input constraints in adaptive systems.