Guaranteed set-point computation with application to the control of a sailboat

Abstract

The problem of characterizing in a guaranteed way the set of all feasible set-points of a control problem is known to be difficult. In the present work, the problem to be solved involves non-linear equality constraints with variables affected by logical quantifiers. This problem is not solvable by current symbolic methods like quantifier elimination, which is commonly used for solving this class of problems. We propose the utilization of guaranteed set-computation techniques based on interval analysis, in particular a solver referred to as Quantified Set Inversion (QSI). As an application example, the problem of simultaneously controlling the speed and the orientation of a sailboat is presented. For this purpose, the combination of QSI solver and feedback linearization techniques is employed.

An Interval Approach for Stability Analysis: Application to Sailboat Robotics

“…In the domain of robotics and automatic control, it has been used to study rigorously the stability of difficult linear [17] or nonlinear systems [26], to characterize capture domains [27] [16], to compute nonlinear controllers [10] and to build reliable observers [21][7] [1]. In this context, there exists also some point numerical techniques [23] which use some Lipschitz properties of the systems or ellipsoidal methods [22] when the system is linear.…”

Control Algorithms for a Sailboat Robot with a Sea Experiment

“…Theoretical methods have been published for sailboat regulation as Herrero et al [2010], but it is necessary to have a precise model. As mentioned in section 2, it is not realistic.…”

Interval-based projection method for under-constrained numerical systems

“…The problem taken from [6,11] models the behavior of a sailboat within its control domain: where the variables x 1 and x 2 represent the heading angle and the speed of the sailboat, respectively, and the variables y 1 and y 2 represent the input commands for the sailboat. Given a domain for the variables, the x projection of the solution set represents the speed diagram of the sailboat, i.e., its response to the input commands in terms of speed and direction.…”

“…The projection problem is difficult in general, and most existing interval methods were proposed to deal with specific subclasses: Linear systems [24]; Inequality systems [21]; Systems where the different constraints do not share any projected variables [11,12]. The first method able to deal with equality constraints that share projected variables is [5].…”