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The paper considers the application of feedback control to orbital transfer maneuvers subject to constraints on the spacecraft thrust and on avoiding the collision with the primary body. Incremental reference governor (IRG) strategies are developed to complement the nominal Lyapunov controller, derived based on Gauss variational equations, and enforce the constraints. Simulation results are reported that demonstrate the successful constrained orbital transfer maneuvers with the proposed approach. A Lyapunov function based IRG and a prediction‐based IRG are compared. While both implementation successfully enforce the constraints, a prediction‐based IRG is shown to result in faster maneuvers. [ABSTRACT FROM AUTHOR]

In this paper, the robust stability problem for uncertain linear continuous-time systems is faced making use of piecewise quadratic Lyapunov functions (PQLF). PQLF are obtained by partitioning the state space into polyhedral cones and by associating a quadratic form with each cone. The proposed formulation allows us to recover, as particular cases of PQLFs, not only the class of quadratic functions but also the class of polyhedral functions. In this way, we manage to show the universality of the class of PQLF for the robust stability problem. The main contribution of the paper is the formulation of a low-computational cost procedure for the stability analysis of uncertain linear systems. Several numerical examples are included in the paper, where the proposed approach is tested on some benchmark cases taken from the literature. Comparisons with existing methods show that the proposed method performs better under several aspects. Copyright © 2014 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper provides sufficient conditions to assess the stability and Input-to-State stability of a class of second-order systems by only looking at the structure of the dynamic equations. These results are proven by using the Variable Gradient Method to build suitable Lyapunov functions. The paper includes a number of relevant examples that highlight the value of the contribution. [ABSTRACT FROM AUTHOR]

This paper tackles the constrained control problem of unmanned aerial vehicles with planar multirotors. The proposed solution splits the constrained control problem into two separate tasks, i.e. stabilization and constraint enforcement. It is shown that the problems addressed by each individual layer is much simpler than the original combined problem. For the unconstrained control of UAVs we consider a control scheme based on a cascade structure. The Lyapunov function for the stabilized cascaded system is then derived. Using this Lyapunov function, we develop an Explicit Reference Governor for constraint enforcement. Numerical simulation shows the effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]

The goal of this paper is to present a systematic method to compute reference dependent positively invariant sets for systems subject to constraints. To this end, we first characterize these sets as level sets of reference dependent Lyapunov functions. Based on this characterization and using Sum of Squares theory, we provide a polynomial certificate for the existence of such sets. Subsequently, through some algebraic manipulations, we express this certificate in terms of a Semi-Definite Programming problem which maximizes the size of the resulting reference dependent invariant sets. We then present some results implementing the proposed method to an example and propose some variants that may help in reducing possible numerical issues. Finally, the proposed approach is employed in the Model Predictive Control for Tracking scheme to compute the terminal set, and in the Explicit Reference Governor framework to compute the so-called Dynamic Safety Margin. The effectiveness of the proposed method in each of the schemes is demonstrated through simulation studies. [ABSTRACT FROM AUTHOR]