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The goal of this note is to highlight that the reformulation of saturation as constraints, typical of the computation of the maximal output admissible sets used in the reference governor literature, is not without loss of generality and may introduce a relevant amount of conservativeness. The note also proposes a modified reference governor able to overcome this limitation. [ABSTRACT FROM AUTHOR]

The explicit reference governor (ERG) is a simple and systematic approach that provides constraint handling capabilities to prestabilized systems. The basic idea behind this approach is to translate state and input constraints into an upper-bound on the value of the Lyapunov function, which is then enforced by suitably manipulating the derivative of the applied reference. When designing the ERG, one of the main challenges is the determination of an upper-bound on the value of the Lyapunov function that ensures constraints satisfaction. This paper proposes a systematic approach for estimating online the optimal upper-bound for systems subject to the intersection of concave constraints. To do this, the Barrier function method is used. The effect of the estimation error caused by the time-varying nature of the auxiliary reference on the constraint satisfaction capability of the ERG is studied analytically. A procedure is proposed to modify the estimated upper-bound to avoid constraints violation in the presence of estimation errors. The effectiveness of the proposed scheme is demonstrated through a simulation study on an overhead gantry crane system. [ABSTRACT FROM AUTHOR]

The systematic design of control laws for nonlinear systems subject to state and input constraints is one of the major challenges in the control of realworld systems. Depending on the application, the desired solution must achieve a satisfactory tradeoff between multiple and often contradicting requirements such as optimality, computational efficiency, robustness, reliability, tuning simplicity, and generality. This article proposes a novel framework for the closed-form control of nonlinear systems subject to constraints on the state and input variables. The proposed strategy differs from most existing methods because it systematically handles both state and input constraints without making use of online optimization. [ABSTRACT FROM AUTHOR]

This technical note introduces a novel control law that dynamically modifies the reference of a pre-compensated nonlinear system to ensure the satisfaction of constraints. This is done by translating the state space constraints into an upper bound on the value of the Lyapunov function and by manipulating the velocity of the applied reference to enforce this bound. The main advantage of this approach is that it systematically provides a closed-form control law able to enforce constraints. The theory is introduced for general nonlinear systems subject to constraints and is then specialized to the large and highly relevant class of nonlinear systems admitting a Lyapunov function lower-bounded by a quadratic form and subject to linear constraints. Numerical simulations show the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]