Constrained Adaptive Backstepping Control For Nonlinear Strict Feedback Systems And Its Applications

Constraints are ubiquitous in physical systems, and manifest themselves as physicalstoppages, saturation, as well as performance and safety specifications. Violation of theconstraints during operation may result in performance degradation, hazards or systemdamage. Driven by practical needs and theoretical challenges, the rigorous handling ofconstraints in control design has become an important research topic in recent decades.Motivated by this problem, this thesis investigates the use of Barrier Lyapunov Func-tions (BLFs) for the control of low-level nonlinear systems in strict feedback form withconstraints in the output and states. Unlike conventional Lyapunov functions, which arewell-defined over the entire domain, and radially unbounded for global stability, BLF-s possess the special property of finite escape whenever its arguments approach certainlimiting values. By ensuring boundedness of the BLFs along the system trajectories, weshow that transgression of constraints is prevented, and this embodies the key basis of ourcontrol design methodology.Starting with the simplest case where only the one state is constrained, and withknown control gain functions, we employ backstepping design with BLF in the first step,and quadratic functions in the remaining steps. It is shown that asymptotic state trackingis achieved without violation of constraint, and all closed-loop signals remain bounded,under a mild restriction on the initial state. Furthermore, we explore the use of asymmetricBLFs as a generalized approach that relaxes the restriction on the initial state. To tackleparametric uncertainties, adaptive versions of the controllers are presented. We provide acomparison study which shows that BLFs require less conservative initial conditions thanQuadratic Lyapunov Functions (QLFs) in preventing violation of constraints.The foregoing method is then extended to the case of full state constraints by em-ploying BLFs in every step of backstepping design. Besides the nominal case where fullknowledge of the plant is available, we also tackle scenarios wherein parametric uncer-tainties are present. It is shown that state constraints cannot be arbitrarily specified, butare subject to feasibility conditions on the initial states and control parameters, which,if satisfied, guarantee asymptotic output tracking without violation of state constraints.In the case of partial state constraints, the design procedure is modified such that BLFsare used in only some of the steps of backstepping, and the feasibility conditions can berelaxed. Finally, we consider, as an application study, a constrained adaptive backsteppingcontrol strategy has been proposed for vehicle active suspension systems in order toachieve multi-objective control. In addition to the improvement of ride comfort, thetime-domain constraints required in active suspension control have also been guaranteedwithin the whole time domain. The Barrier Lyapunov Function is employed to guaranteethe time-domain constraints with low conservatism. The efectiveness of the proposedapproach has been illustrated by a design example.