Robust Design of Closed-Loop Nonlinear Systems with Input and State Constraints

Abstract In this paper we address the task of finding a robust process and control design for nonlinear systems with uncertainties and disturbances such that bounds on inputs and outputs are not violated. The solution of this task is approached by Constructive Nonlinear Dynamics (CNLD), an optimization based method developed by the authors in recent years. CNLD guarantees robustness by backing off a nominal point of operation from critical manifolds. Critical manifolds are boundaries in the space of system and controller parameters that separate regions with qualitatively different system behavior, such as a region with stable operating points from a region with unstable system behavior. In this work, CNLD is adopted and extended to account for bounds and constraints on trajectories of inputs and states. Critical boundaries in the parameter space are presented that separate a region where all trajectories stay within the bounds from a region where trajectories violate the constraints. Constraints ensuring a minimal back off from this new type of critical manifold are derived. Application to an illustrative case study demonstrates the feasibility of the approach.

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