Adaptive Control of Uncertain Constrained Nonlinear Systems

Abstract

This thesis investigates the use of Barrier Lyapunov Functions (BLFs) for the control of strict feedback nonlinear systems with constraints in the output and the states. A BLF has a value that grows to infinity whenever its arguments approach some limits. By ensuring boundedness of the BLF in the closed loop, we ensure that the constraints are never transgressed. The BLF-based framework accommodates the use of adaptive control techniques to handle parametric uncertainties. Based on adaptive backstepping with BLFs, stable output tracking is guaranteed without violation of constraints, and all closed loop signals are kept bounded, under certain restrictions on the initial conditions and the control parameters. A novel asymmetric BLF is also introduced as a generalized form that relaxes the restrictions on the initial conditions. As an application study, we consider electrostatic microactuators for trajectory tracking without electrode contact. Extensive simulation results illustrate the effectiveness of the proposed approach.