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Register a new userSliding-mode theory under feedback constraints and the problem of epidemic control
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One of the most important branches of nonlinear control theory is the so-called sliding-mode. Its aim is the design of a (nonlinear) feedback law that brings and maintains the state trajectory of a dynamic system on a given sliding surface. Here, dynamics becomes completely independent of the model parameters and can be tuned accordingly to the desired target. In this paper we study this problem when the feedback law is subject to strong structural constraints. In particular, we assume that the control input may take values only over two bounded and disjoint sets. Such sets could be also non perfectly known a priori. An example is a control input allowed to switch only between two values. Under these peculiarities, we derive the necessary and sufficient conditions that guarantee sliding-mode control effectiveness for a class of time-varying continuous-time linear systems that includes all the stationary state-space linear models. Our analysis covers several scientific fields. It is only apparently confined to the linear setting and allows also to study an important set of nonlinear models. We describe fundamental examples related to epidemiology where the control input is the level of contact rate among people and the sliding surface permits to control the number of infected. For popular epidemiological models we prove the global convergence of control schemes based on the introduction of severe restrictions, like lockdowns, to contain epidemic. This greatly generalizes previous results obtained in the literature by casting them within a general sliding-mode theory.
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In adaptive sliding mode control methods, an updating gain strategy associated with finite-time convergence to the sliding set is essential to deal with matched bounded perturbations with unknown upper-bound. However, the estimation of the finite time of any adaptive design is a complicated task since it depends not only on the upper-bound of unknown perturbation but also on the size of initial conditions. This brief proposes a uniform adaptive reaching phase strategy (ARPS) within a predefined reaching-time. Moreover, as a case of study, the barrier function approach is extended for perturbed MIMO systems with uncertain control matrix. The usage of proposed ARPS in the MIMO case solves simultaneously two issues: giving a uniform reaching phase with a predefined reaching-time and adapting to the perturbation norm while in a predefined vicinity of the sliding manifold.
The paper considers autonomous rendezvous maneuver and proximity operations of two spacecraft in presence of obstacles. A strategy that combines guidance and control algorithms is analyzed. The proposed closed-loop system is able to guarantee a safe path in a real environment, as well as robustness with respect to external disturbances and dynamic obstacles. The guidance strategy exploits a suitably designed Artificial Potential Field (APF), while the controller relies on Sliding Mode Control (SMC), for both position and attitude tracking of the spacecraft. As for the position control, two different first order SMC methods are considered, namely the component-wise and the simplex-based control techniques. The proposed integrated guidance and control strategy is validated by extensive simulations performed with a six degree-of-freedom (DOF) orbital simulator and appears suitable for real-time control with minimal on-board computational effort. Fuel consumption and control effort are evaluated, including different update frequencies of the closed-loop software.
Conventional Sliding mode control and observation techniques are widely used in aerospace applications, including aircrafts, UAVs, launch vehicles, missile interceptors, and hypersonic missiles. This work is dedicated to creating a MATLAB-based sliding mode controller design and simulation software toolbox that aims to support aerospace vehicle applications. An architecture of the aerospace sliding mode control toolbox (SMC Aero) using the relative degree approach is proposed. The SMC Aero libraries include 1st order sliding mode control (1-SMC), second order sliding mode control (2-SMC), higher order sliding mode (HOSM) control (either fixed gain or adaptive), as well as higher order sliding mode differentiators. The efficacy of the SMC Aero toolbox is confirmed in two case studies: controlling and simulating resource prospector lander (RPL) soft landing on the Moon and launch vehicle (LV) attitude control in ascent mode.
This paper studies epidemic processes over discrete-time periodic time-varying networks. We focus on the susceptible-infected-susceptible (SIS) model that accounts for a (possibly) mutating virus. We say that an agent is in the disease-free state if it is not infected by the virus. Our objective is to devise a control strategy which ensures that all agents in a network exponentially (resp. asymptotically) converge to the disease-free equilibrium (DFE). Towards this end, we first provide a) sufficient conditions for exponential (resp. asymptotic) convergence to the DFE; and b) a necessary and sufficient condition for asymptotic convergence to the DFE. The sufficient condition for global exponential stability (GES) (resp. global asymptotic stability (GAS)) of the DFE is in terms of the joint spectral radius of a set of suitably-defined matrices, whereas the necessary and sufficient condition for GAS of the DFE involves the spectral radius of an appropriately-defined product of matrices. Subsequently, we leverage the stability results in order to design a distributed control strategy for eradicating the epidemic.
The fundamental problem of stabilizing a general non-affine continuous-time nonlinear system is investigated via piecewise affine linear models (PALMs) in this paper. A novel integral sliding-mode parallel control (ISMPC) approach is developed, where an uncertain piecewise affine system (PWA) is constructed to model a non-affine continuous-time nonlinear system equivalently on a compact region containing the origin. A piecewise integral sliding-mode parallel controller is designed to globally stabilize the uncertain PWA and, consequently, to semi-globally stabilize the original nonlinear system. The proposed scheme enjoys two favorable features: i) some restrictions on the system input channel are eliminated, thus the developed method is more relaxed compared with the published approaches; and ii) it is convenient to be used to deal with both matched and unmatched uncertainties of the system. Moreover, we provide discussions about the universality analysis of the developed control strategy for two kinds of typical nonlinear systems. Simulation results from two numerical examples further demonstrate the performance of the developed control approach.
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