At the limits of adaptive systems: constrained adaptive control

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.

Beyond academics there are several groups who will stand to benefit from the proposed research

1. The UK/European Aerospace industry. The benefit to this group will be both direct and indirect. Adaptive control is of particular interest to branches of the aerospace industry because it, potentially, lessens the need for high-fidelity (and therefore time-consuming and costly) mathematical models of the system under control. However applied adaptive control has had considerable set-backs over the years. This research will develop adaptive control laws which may be applied more confidently in practice and hence help the industry to achieve similar levels of performance without the cost involved. Indirect benefit will also be felt by the research adding new impetus to the subject of adaptive aerospace control which has been forgotten in recent years. Together the direct and indirect benefits may, potentially, increase the competitiveness and agility of the UK aerospace industry over the medium to long term. An obvious beneficiary would be the Anglo-French company MBDA, with whom the investigators have recently worked on adaptive controller design.

2. In the longer term adaptive control has the potential to revolutionise the design of controllers for healthcare applications. Healthcare applications of control, such as insulin control, control of artificial organs and depth of anaesthesia control typically suffer from modelling problems: models are difficult to obtain, difficult to validate and have a large degree of variability. Adaptive control is an idea candidate design technique for such systems but, due to the extreme care with which such healthcare control systems must be implemented, these systems have very stringent constraints placed upon them and thus anti-windup-type controllers are vital to ensure their safe functionality. Therefore, overall society as a whole stands to benefit (longer term) from the research through improved and safe healthcare control systems.