This dissertation extends the L1 adaptive control theory to sampled-data (SD) framework. Multi-input multi-output non-square (underactuated) systems are considered with different sampling rates for inputs and outputs. The sampled-data framework allows to address non-minimum phase systems, subject to less restrictive assumptions as compared to continuous time framework. It is shown that the closed-loop system can recover the response of a continuous-time reference system as the sampling time of the SD controller tends to zero. In this thesis, the L1 sampled data adaptive controller is integrated with the Simplex fault-tolerant architecture for resilient control of cyber-physical systems (CPSs). Detection and mitigation of zero-dynamics attacks are addressed and validated in flight tests of a quadrotor in Intelligent Robotics Laboratory of UIUC. The experiments show that the multirate L1 controller can e effectively detect stealthy zero-dynamics attacks and recover the stability of the perturbed system, where the single-rate conventional L1 adaptive controller fails.
From the perspective of applications, the dissertation considers navigation and control of autonomous vehicles and proposes a two-loop framework, in which the high-level reference commands are limited by a saturation function, while the low-level controller tracks the reference by compensating for disturbances and uncertainties. A class of nested, uncertain, multi-input multi-output (MIMO) systems subject to reference command saturation, possibly with non-minimum phase zeros, is considered. Robust stability and performance of the overall closed-loop system with command saturation and multirate L1 adaptive controller are analyzed.
Finally, a systematic analysis and synthesis method is proposed for the optimal design of filters in the L1 adaptive output-feedback structure, where the lowpass filter is the key to the trade-off between the performance and robustness of the closed-loop system. An optimization problem is formulated using the constraint on the input time-delay margin and a cost-function based on mixed L1/H2-norm performance measure. The optimization problem can be efficiently solved using linear/quadratic programming.
We note that the framework of this dissertation and the multi-loop problem formulation of navigation and control of autonomous systems provide suitable synthesis and analysis tools for autonomous cyber-physical systems (CPSs), including self-driving cars, unmanned aerial vehicles (UAVs), and industrial/medical robots, to name just a few. The SD design facilitates the implementation of control laws on digital computers in CPSs, where the input/output signals are available at discrete time instances with different sampling rates
