Extended hybrid model reference adaptive control of piecewise affine systems

Abstract

We discuss an extension to the adaptive control strategy presented in di Bernardo et al. (2013) able to counter eventual instabilities due to disturbances at the input of an otherwise L2 stable closed-loop system. These disturbances are due to the presence of affine terms in the plant and reference model. The existence of a common Lyapunov function for the linear part of the PWA reference model is used to prove global convergence of the error system, even in the presence of sliding solutions, as well as boundedness of all the adaptive gains

A hierarchical Lyapunov-based cascade adaptive control scheme for lower-limb exoskeleton

“…where α 1 is defined in (56), and · is the Euclidean norm. In view of this and of the analysis in [12], with (48) and (49), one can write the derivative of V L,3 in the forṁ…”

Multiple model adaptive control for switched linear systems: A two‐layer switching strategy

“…Remark Under some assumptions, a switched system without canonical form can be transformed into system with control canonical form by the coordinate transformation and control design, which has been studied in the literature . In addition, in many cases, electromechanical systems modeled via a Lagrangian approach are structured already into the required canonical form . Our objective is to design a switched controller with the parameter resetting adaptive laws and construct a two‐layer switching strategy for system such that all the signals of the closed‐loop systems remain bounded and the state tracking error converges to a small ball whose radius can be made arbitrarily small by appropriately choosing the design parameter.…”

Direct data‐driven design of switching controllers

“…This limits the application of the method, especially when dealing with unknown nonlinear systems. Although the approaches presented in 41 have been further extended in 42 to overcome possible instabilities caused by disturbances on the input, the effect of uncertain/noisy state measurements has not been explored. Analogously, the hypothesis of exact state knowledge is shared by the approach proposed in 43 for asynchronous adaptive tracking control for switched system, where the authors further assume prior knowledge on the lower and upper bounds on the controller parameters.…”