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Abstract: In this paper, a design of a stabilizing state-dependent switching law is presented. First, it is based on a new reformulation of this control problem into a class of BMI (Bilinear Matrix Inequality) problem. The originality of this reformulation is that it will be used, in a second part, by an algorithm dedicated to solve this class of BMI without loss of generality. The construction of this algorithm is then specified, and the proof of its convergence is given for the two-subsystem case. The last part of the work consists in presenting the problem for a polytopic switching system, and how the previous algorithm can be extended. The proposed scheme is illustrated by an academical example. [Copyright &y& Elsevier]

Abstract: This work deals with relaxed conditions for stability and stabilization of discrete-time Takagi–Sugeno (TS) models. It recalls classical results found in the literature which use quadratic Lyapunov functions leading to very conservative conditions, and various extensions based on piecewise and non-quadratic Lyapunov functions. Afterwards, a new and powerful way to enhance the previous results is depicted. The basic idea is that waiting long enough a stable model will converge towards its equilibrium and, therefore, the Lyapunov functions under consideration are not necessarily decreasing at every sample, but are allowed to decrease every k samples. Whatever it is k >1, the results are proved to include the standard one-sample case. The potential of this approach is shown through several examples in the paper. [Copyright &y& Elsevier]

We propose a generic nonlinear reduced-order tracking control method for elastic soft robots. To this end, a new linear parameter varying (LPV) control framework is developed using the data collected from the soft robots. Specifically, for LPV modeling we first derive a nonlinear robot model, which is large-scale by nature, using finite element methods (FEM). Then, a proper orthogonal decomposition (POD) algorithm is used to generate a set of linearized reduced-order models, representing the local behaviors of the soft robot at different operating points within the workspace. Via a unified POD projector, not only the order of these linearized models can be significantly reduced but also their mechanical structure and stability properties can be preserved for LPV modeling and control design. Next, using radial basis function (RBF) networks, we propose an iterative training method to build the LPV robot model by interpolating a subset of selected linearized models with a specified interpolation error. For LPV control design, the equivalent-input-disturbance (EID) concept is exploited to develop a dynamic tracking control scheme, which is composed of three core components: feedforward control, disturbance-estimator control and feedback control. The feedforward control is designed to account for the effects of the trajectory reference and the time-varying affine term, issued from the FEM-based model linearization. The disturbance-estimator control is obtained from a generalized proportional integral LPV observer, which also provides the estimated reduced-order states for feedback control. The observer-based feedback control design is reformulated as a convex optimization problem under linear matrix inequality (LMI) constraints. The globally uniformly ℓ ∞ stability of the closed-loop LPV robot model is guaranteed by means of Lyapunov stability theory. Experimental tests are conducted with a soft Trunk robot, inspired by the elephant trunk, under several scenarios with small and large deformations to show the effectiveness of the proposed LPV tracking control framework. A comparative study is also performed with a recent linear EID-based controller and an iterative learning controller to emphasize the interests this nonlinear control method for soft elastic robots. This paper is complemented with a series of demonstration videos: https://bit.ly/3D8C4Vd. [ABSTRACT FROM AUTHOR]