Regulation and tracking control of nonminimum phase systems

The dissertation focuses on the design of regulation and tracking controllers for a class of nonminimum phase systems using a combination of tools. Specifically, regulation control of nonminimum phase linear systems is first formulated and solved under the multi-objective optimization framework using linear matrix inequalities. Regulation and tracking control of a class of nonminimum phase nonlinear systems are then investigated using backstepping techniques and the property of input-to-state stability. The general adaptive robust control framework for minimum phase systems is extended to synthesize tracking controllers for a class of nonminimum phase nonlinear systems with unknown parameters and unstructured uncertainties. And a robust output feedback stabilization scheme is developed for a class of nonminimum phase nonlinear systems. The performance limitation associated with regulation and tracking control of linear time-invariant systems are well understood in the classical and modern control theories. Many physical applications need to satisfy performance requirement and robust stability simultaneously. This multi-objective problem has been formulated under the optimization framework and solved through the powerful computation tool of linear matrix inequality. In this dissertation, the multi-objective optimization using linear matrix inequality will firstly be applied to solve the tip regulation control problem of a flexible structure having nonminimum phase characteristics. Even though there exist many linear methodologies to analyze, design and synthesize feedback controllers, most of them can not be directly applied to nonlinear systems. For tracking control of nonlinear systems with structured and unstructured uncertainties, an adaptive robust control framework has been recently developed to design practical and performance oriented nonlinear controllers. It effectively integrates deterministic robust control and adaptive control to meet the high performance requirement. One assumption in the current adaptive robust control framework is that the internal dynamics of the nonlinear system is stable. This dissertation is to remove this assumption to extend the current adaptive robust control methodology to a class of nonminimum phase nonlinear systems transformable to semi-strict feedback forms. With the assumption that there exist feasible bounded trajectories for the internal states of the unstable internal dynamics, the proposed scheme assures that the output tracking error will converge to zero asymptotically with the bounded internal states when the system is subject to the structured uncertainties only. In addition, the proposed scheme also guarantees that the output tracking error will be bounded with known bounds even when the system has unstructured uncertainties as well. The proposed control schemes have been applied to a classical nonlinear system of an inverted pendulum with structured and unstructured uncertainties. Simulation results of inverted pendulum are presented to demonstrate the effectiveness of the proposed adaptive robust tracking control schemes. It is still one of the most challenging problems in the control communities to design output feedback stabilizing controllers for general nonminimum phase nonlinear systems. In this dissertation, an observer based robust control scheme will be developed to stabilize a class of nonminimum phase nonlinear systems transformable to a semi-strict feedback form. A reduced-order observer is designed to estimate the unknown states. Backstepping design techniques and the property of input-to-state stability are then used to synthesize a robust output feedback stabilizing controller for the nonminimum phase nonlinear system