Design of Controllers and Observer-Based Controllers for Time-Delay Singularly Perturbed Systems via Composite Control

This paper presents a novel and general approach, which is based on the composite control method, to synthesize the controller and observer-based state feedback to stabilize the singularly perturbed time-delay systems. First, the equivalent models of the original systems and the subsystems reduced via singular perturbation techniques are derived. Through these equivalent models, approximation of the stabilization and observer design for the original systems can be achieved through separate analyses for the slow and fast subsystems via a transformation of block diagonalization

Full-State and Output Feedback Control of Uncertain Nonlinear Nonstandard Multiple-Time-Scale Systems

Nonlinear systems with dynamics evolving in distinct slow and fast time-scales are common in science and engineering. Geometric singular perturbation theory is a powerful tool for controller design for such systems over multiple-time-scales. Aerospace vehicles such as aircraft and spacecraft are examples of nonstandard multiple-time-scale systems, for which the control synthesis is more challenging than for standard systems. Most control methods for nonstandard systems assume deterministic model and full-state feedback. This dissertation extends the current capabilities of multiple-time-scale control for nonstandard systems by developing novel theories of control design for uncertain systems and using output feedback. Both of slow state tracking and simultaneous slow and fast state tracking for nonstandard systems are considered as control objectives. Using the time-scales of the slow states, slow actuators, fast states and fast actuators, the control laws developed over four-time-scales can account for multiplicative and additive uncertainties. The controller uses estimates of the unknown parameters and the unmeasured states, and ensures Lyapunov-stability of the lower-order reduced subsystems. The estimates are updated by an online parameter estimator and a nonlinear state observer respectively. They are designed using the composite Lyapunov analysis. This analysis also proves the boundedness of errors and establishes bounds of time-scale separation to accomplish the same. The theory is applied to perform attitude tracking for a generic spacecraft with uncertain inertias, and large-amplitude combined longitudinal and lateral/directional maneuvers of a nonlinear six-degree-of-freedom aircraft with uncertain inertias, control derivatives and engine time-constant