Control systems that are subject to constraints due to physical limitations, hardware
protection, or safety considerations have led to challenging control problems that have
piqued the interest of control practitioners and theoreticians for many decades. In
general, the design of constraint management schemes must meet several stringent
requirements, for example: low computational burden, performance, recovery mechanisms
from infeasibility conditions, robustness, and formulation simplicity. These
requirements have been particularly difficult to meet for the following three classes
of systems: stochastic systems, linear systems driven by unmodeled disturbances,
and nonlinear systems. Hence, in this work, we develop three constraint management
schemes, based on Reference Governor (RG), for these classes of systems. The
first scheme, which is referred to as Stochastic RG, leverages the ideas of chance
constraints to construct a Stochastic Robustly Invariant Maximal Output Admissible
set (SR-MAS) in order to enforce constraints on stochastic systems. The second
scheme, which is called Recovery RG (RRG), addresses the problem of recovery from
infeasibility conditions by implementing a disturbance observer to update the MAS,
and hence recover from constraint violations due to unmodeled disturbances. The
third method addresses the problem of constraint satisfaction on nonlinear systems
by decomposing the design of the constraint management strategy into two parts: enforcement
at steady-state, and during transient. The former is achieved by using the
forward and inverse steady-state characterization of the nonlinear system. The latter
is achieved by implementing an RG-based approach, which employs a novel Robust
Output Admissible Set (ROAS) that is computed using data obtained from the nonlinear
system. Added to this, this dissertation includes a detailed literature review
of existing constraint management schemes to compare and highlight advantages and
disadvantages between them. Finally, all this study is supported by a systematic
analysis, as well as numerical and experimental validation of the closed-loop systems
performance on vehicle roll-over avoidance, turbocharged engine control, and inverted
pendulum control problems
