Guaranteed Robustness with Fast Adaptation

S afety-critical systems appear in several application areas, such as transportation and air-traffi c control systems, nuclear plants, space systems, and operating rooms in hospitals. Reliable control of these systems requires not only meeting performance specifi ca-tions in the presence of multiple constraints, which together ensure predictable response of the overall system and safe operation , but also graceful performance degradation when the underlying assumptions are violated. Figure 1 explains this requirement for fl ight control applications. The green region for angle of attack and sideslip represents the normal fl ight envelope, where the airplane usually fl ies in the absence of abnormalities. The light blue area represents con-fi gurations for which high-fi delity nonlinear aerodynamic models of the aircraft are available from wind-tunnel data. Outside this wind-tunnel data envelope, the aerodynamic models available are typically obtained by extrapolating wind-tunnel test data and hence are highly uncertain. This fact suggests that pilots might not be adequately trained to fl y the aircraft in these regimes. Moreover, it is not reasonable to rely on a fl ight control system to compensate for the uncertainty in these fl ight conditions, since aircraft controllability is not guaranteed in such regimes. The main objective of the fl ight control system therefore, from safety considerations, is to ensure that an aircraft, suddenly experiencing an adverse fl ight regime or an unexpected failure, does not " escape " its a– b wind-tunnel data envelope, provided that enough control authority remains. This objective requires that the control system quickly adapt to the failure with guaranteed and uniform transient performance speci-fi cations to ensure the safety of the aircraft. Typical performance specifications in control applications include transient and steady-state performance, as well as robustness margins that the control engineer must be able to trade off in a systematic way subject to hardware constraints, such as CPU, sampling rates of sensors and actuators, and control channel bandwidth. This viewpoint has led to certification of flight control laws for commercial aviation, where the certification protocols rely on the gain and phase margins of the gain-scheduled controllers computed for all operating points [1]. This process is repeated for each aircraft, rendering the overall verification and validation (V&V) expensive. The price of this process increases with growing system complexity. L 1 adaptive-control theory is motivated by the emerging need to certify advanced adaptive flight critical systems with a more affordable V&V process. …