Summary Proportional Integral Derivative (PID) controllers still represent the core control method for achieving output regulation of either linear or nonlinear systems in the majority of industrial applications. However, conventional PID control cannot guarantee specific state constraint requirements for the plant, when the system introduces uncertainties. In this paper, a novel nonlinear PID control that achieves output regulation and guarantees a desired state limitation below a given value for a wide class of nonlinear systems with constant uncertainties is proposed. Using nonlinear ultimate boundedness theory, it is shown that the proposed state‐limiting PID (sl‐PID) control maintains a given bound for the desired system states at all times, ie, even during transients, whereas an analytic method for selecting the controller gains is also presented to ensure closed‐loop system stability and convergence at the desired equilibrium. Two nonlinear engineering examples that include an electric motor and a dc/dc converter are investigated using the conventional PID and the proposed sl‐PID to validate the superiority of the proposed controller in achieving the desired output regulation with a given bounded state requirement.

The use of available disturbance predictions within a nominal model predictive control formulation is studied. The main challenge that arises is the loss of recursive feasibility and stability guarantees when a persistent disturbance is present in the model and on the system. We show how standard stabilizing terminal conditions may be modified to account for the use of disturbances in the prediction model. Robust stability and feasibility are established under the assumption that the disturbance change across sampling instances is limited.

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