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Robust Design of Constrained Dynamical Systems / von Diego Alejandro Muñoz Durango

In this work, the limited ability of actuators to manipulate physical quantities was analyzed considering how input saturation affects the closed-loop performance. The problem was solved progressively, starting with a general system class for which closed-loop stability in the presence of input saturation is assumed to be guaranteed and next considering two sub-classes of nonlinear systems for which theoretical results could be developed to account for these issues. The first subclass corresponds to input-output linearizable (IOL) systems with stable zero dynamics for which a control law based on control Lyapunov functions can be synthesized guaranteeing closed-loop stability in the presence of input bounds. Because many systems do not satisfy the input-output linearizable condition, novel results were proposed to expand the class of IOL systems. Thus, for the second subclass, stability boundaries based on contractive constraints were developed under some Lipschitz assumptions avoiding the input-output linearizable condition imposed initially.

The design problem was stated as an optimization problem in which input and state constraints for a class of uncertain nonlinear systems were systematically addressed to guarantee two properties despite parametric uncertainty, namely, closed-loop stability with bounded inputs and feasibility of the transient in the presence of state constraints. The resulting optimization problem proposed in this thesis for control design in the presence of input bounds, state constrains and uncertainty, is framed as a generalized semi-infinite optimization problem (GSIP) for which the local reduction approach was applied to compute a solution.