Model Reference Adaptive Control of Switched Dynamical Systems with Applications to Aerial Robotics
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Model Reference Adaptive Control of Switched Dynamical Systems with Applications to Aerial Robotics Robert B. Anderson1 · Julius A. Marshall1 · Andrea L’Afflitto1
· James M. Dotterweich2
Received: 1 January 2020 / Accepted: 4 September 2020 © Springer Nature B.V. 2020
Abstract This paper presents an adaptive control law for unknown nonlinear switched plants that must follow the trajectory of userdefined linear switched reference models. The effectiveness of the proposed control architecture is proven in two alternative frameworks, that is, analyzing Carath´eodory and Filippov solutions of discontinuous differential equations. Numerical and experimental data verify the applicability of the theoretical results to problems of practical interest. The proposed numerical simulation involves the design of a model reference adaptive control law to regulate the roll dynamics of a reconfigurable delta-wing aircraft. The proposed flight tests involve an aerial robot tasked with autonomously mounting a camera of unknown inertial properties to a vertical surface. Keywords Model reference adaptive control · Switched dynamical systems · Carath´eodory solutions · Filippov solutions · Aerial robots
1 Introduction The dynamics of numerous mechanical and electronic systems are subject to instantaneous changes and are best captured by switched dynamical systems, that is, differential equations with discontinuous right-hand sides. Examples of switched dynamical models involve mechanical systems subject to velocity jumps and force discontinuities [6, 45].
This work was supported in part by the US Army Research Lab (ARL), DARPA, and ONR under Grants no. 40304747, D18AP00069, and N000141912422, respectively. Andrea L’Afflitto
[email protected] Robert B. Anderson [email protected] Julius A. Marshall [email protected] James M. Dotterweich [email protected] 1
Grado Department of Industrial and Systems Engineering, Virginia Tech, Blacksburg, VA 24061, USA
2
CCDC Army Research Laboratory, Aberdeen Proving Ground, Adelphi, MD 21005, USA
Furthermore, the closed-loop dynamics of systems regulated by discontinuous control algorithms such as timeoptimal control laws [7, pp. 110-117], variable structure control laws [27, pp. 552-579], [14, 34, 52], and supervisory control architectures [29, 41, 42, 54] may be captured by switched models. Substantial complexity in the analysis and control synthesis of discontinuous dynamical systems is given by the fact that their solutions may not exist or may not be unique [27, Ch. 3]. Furthermore, the notion of solution of a switched differential equation is not univocal. Indeed, Carath´eodory [8], Filippov [16], Krasovskii [30], and Euler [12] solutions, to name a few, have been introduced to better capture the behavior of different classes of discontinuous dynamical systems; for additional details, see [13, 20, 23, 49] and the references therein. In this paper, we design an adaptive control law for unknown nonlinear switched plants so that their trajectories track the trajectories of user-d
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