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It has been proven that model predictive control (MPC) is an efficient method for closed-loop insulin delivery in clinical studies. This paper aims to design an observer-based fractional-order nonlinear MPC for type 1 diabetes mellitus (T1DM) patients. It is assumed that the proposed model is nonlinear and contains parametric uncertainty. To estimate unknown states, optimal non-fragile H∞ observer is designed for Lipschitz nonlinear fractional-order systems including parametric uncertainty and the existence of input disturbance. The min–max optimization-based robust fractional model predictive control (RFMPC) has been presented in the following for insulin delivery. Since sensor noise of continuous monitoring of interstitial glucose concentration is considered non-Gaussian, the performance of the proposed controller is improved under non-Gaussian measurement noise by selecting a proper cost function based on generalized correntropy, and as a contrast, the performance of the mean square error (MSE)-based controller is simulated. According to the results, not only is the performance of the proposed controller better under non-Gaussian situations but also effectively reaches the set point in the case of disturbance and uncertainty and provides higher control accuracy and robustness compared with the MSE-based MPC.

This article introduces a new technique for stabilizing autonomous underwater vehicles in the descriptor model. Autonomous underwater vehicle stabilization is limited by several constraints, including time-variable uncertainty, time delay, and disturbances. The interaction of descriptor system requirements and the issues mentioned above adds complexities. This study outlines the delay-dependent [Formula: see text] robust stability achieved through memory-less and memory state feedback. Furthermore, a less conservative sufficient condition is obtained for admissibility using a new delay-dependent linear matrices inequality. Autonomous underwater vehicle is regular, impulse-free, and stable under all permissible conditions and satisfies prescribed [Formula: see text] performance conditions via a Lyapunov functional approach. The method applies to neutral and retarded dynamics with discrete and distributed time delays.

This article proposes an event-triggered control framework to satisfy the tracking formation performance for a group of uncertain non-linear n-link robotic manipulators. The robotic manipulators are configured as a multi-agent system and they communicate over a directed graph (digraph). Furthermore, the non-linear robotic manipulator-multi-agent systems are subject to stochastic environmental loads. By introducing extra virtual controllers in the final step of the backstepping design, a total number of n event-triggering mechanisms are introduced independently for each link of all the robotic manipulator agents to update the control inputs in a fully distributed manner. More precisely, the actuator of each link of a particular agent is capable of being updated independent of other link actuator updates. A rigorous proof of the convergence of all the closed-loop signals in probability is then given and the Zeno phenomenon is excluded for the control event-triggered architectures. The simulation experiments finally quantify the effectiveness of proposed approach in terms of reducing the number of control updates and handling the stochastic environmental loads.

This paper focuses on autonomous underwater vehicle (AUV) stabilization in the nonlinear descriptor model, as well as some AUV limitations such as model uncertainty, singularity, saturation constraint, and time delay. The capability of the descriptor model to show the real model is more reasonable than the standard state-space model. Based on the constructed Lyapunov function method and applying the bilinear matrix inequalities technique, all of the constraints are handled by introducing the new theorem. This theorem aims to design a state feedback with the intent that the closed-loop system be admissible. Here, the results are less conservative than other approaches. This issue has not yet been fully addressed in the literature, especially on AUVs. Theorem achievement is implemented on new AUV descriptor model that is obtained and introduced here. This method covers both neutral and descriptor systems. Also, it can be generalized and applied to conventional AUVs or similar dynamics. Examples and simulation results illustrate the effectiveness of the proposed approach.

This article investigates an enhanced optimal robust time-delay stabilizer for an autonomous underwater vehicle in the descriptor model. Time-delay, model uncertainty, and actuator saturation constraint are some practical challenges in autonomous underwater vehicle controller design. In this regard, an appropriate autonomous underwater vehicle descriptor model is obtained, and sufficient stabilization conditions are determined in the terms of linear matrix inequality. The obtained criterion guarantees the system to be regular, impulse-free, and stable. Meanwhile, the delay-dependent and rate-dependent conditions are taken into account. Furthermore, uncertainty and time-delay are time-variant. This method includes a tuning factor for practical design aspects and tradeoff among desired requirements. Also, as an essential general requirement in non-linear systems, the maximal estimate of the attraction domain is proposed as an optimization problem. Numerical examples and simulations illustrate that the proposed methods are effective and useful in less conservative results. The technique can be generalized and applied to the most conventional autonomous underwater vehicles.

The main purpose of this paper is to introduce a hybrid controller for global attitude tracking of a quadrotor. This controller globally exponentially stabilizes the desired attitude, a task that is impossible to accomplish with memoryless discontinuous or continuous state feedback owing to topological obstruction. Thereafter, this paper presents a new centrally synergistic potential function to construct hybrid feedback that defeats the topological obstruction. This function induces a gradient vector field to globally asymptotically stabilize the reference attitude and produces the synergy gap to generate a switching control law. The proposed control structure is consisting of two major parts. In the first part, a synergetic controller is designed to cooperate with the hybrid controller, whereas it exponentially stabilizes the origin of the error dynamics. In the second part, a hybrid controller is introduced to globally stabilize the attitude of the quadrotor, where an average dwell constraint is considered with the switching control law to guarantee the exponential stability of the switched system. Finally, the effectiveness and superiority of the proposed control technique are validated by a comparative analysis in simulations.

This study investigates a novel fractional-order nonsingular terminal sliding mode controller via a finite-time disturbance observer for a class of mismatched uncertain nonlinear systems. For this purpose, a finite-time disturbance observer–based fractional-order nonsingular terminal sliding surface is proposed, and the corresponding control law is designed using the Lyapunov stability theory to satisfy the sliding condition in finite time. The proposed fractional-order nonsingular terminal sliding mode control based on a finite-time disturbance observer exhibits better control performance; guarantees finite-time convergence, robust stability of the closed-loop system, and mismatched disturbance rejection; and alleviates the chattering problem. Finally, the effectiveness of the proposed fractional-order robust controller is illustrated via simulation results of both the numerical and application examples which are compared with the fractional-order nonsingular terminal sliding mode controller, sliding mode controller based on a disturbance observer, and integral sliding mode controller methods.

The consensus control with the leader of delayed linear multi-agent systems under the relative state saturations is investigated in this article. Using an incidence matrix, the consensus problem of delayed multi-agent systems (time-varying input delays) with relative state saturation is converted into the stability problem of edge dynamics on the closed sets. Then, a new linear control protocol is designed using a saturation function that guarantees stability for all agents under relative state saturation constraints. With the appropriate Lyapunov–Krasovskii functional definition, sufficient conditions are created for the consensus of the agents. Meanwhile, the relative state saturations do not happen. Also, the agents track the leader’s path well, while bounded delays can be time-varying and arbitrarily fast. This consensus and stability are achieved by maintaining graph connectivity. Finally, the correctness of the above content is confirmed by simulating a practical example.

This paper deals with the fuzzy control design for nonlinear impulsive switched systems modeled by a novel nonlinear Takagi-Sugeno (T-S) fuzzy structure. To model, this structure only uses some of the nonlinearities as premise variables. So, the derived model has fewer rules compared with the traditional T-S fuzzy models that utilize standard local sector nonlinearity; and accordingly, the number of stability/stabilization conditions is sharply reduced. In our structure, considering only a part of nonlinearities as premise variables causes that some of the local models in the consequent part of the fuzzy rules be nonlinear but with less complexity than the original nonlinear system. As a result, the feasibility of our model’s stability criteria is more than those that one can directly establish for the original nonlinear system. Besides, unlike the existing methods in the literature of impulsive switched systems that aim to permanently reduce the value of Lyapunov function candidates, this paper takes into account this process until trajectories reach a sufficient small region containing the origin. Then, within this region, the size of Lyapunov functions is just controlled at impulse instants. This strategy is useful when there are non-vanishing impulses and/or uncertainties, and it is more relaxed when the goal is ultimate bound stability. Finally, to achieve the stabilizing control signal that ensures practical control issues along with smallest ultimate bound and widest region of attraction, this paper also proposes an optimization problem with linear and bilinear constraints. The simulation results represent the performance of the proposed method.

This paper aims to investigate an efficient numerical scheme for the optimal control of fractional-order dynamic systems. By using the Grünwald–Letnikov approximation for the fractional derivatives and introducing a new transformation in the calculus of variations, the fractional optimal control problem under consideration is converted into a linear programming problem. Then, the internal model principle is employed in order to extend the new scheme for the fractional dynamic systems affected by the external persistent disturbances. Numerical examples and comparative results verify the validity and applicability of the new technique.

In this paper, the state estimation problem for fractional-order nonlinear discrete-time stochastic systems is considered. A new method for the state estimation of fractional nonlinear systems using the statistically linearized method and cubature transform is presented. The fractional extended Kalman filter suffers from two problems. Firstly, the dynamic and measurement models must be differentiable and, secondly, nonlinearity is approximated by neglecting the higher order terms in the Taylor series expansion; by the proposed method in this paper, these problems can be solved using a statistically linearized algorithm for the linearization of fractional nonlinear dynamics and cubature transform for calculating the expected values of the nonlinear functions. The effectiveness of this proposed method is demonstrated through simulation results and its superiority is shown by comparing our method with some other present methods, such as the fractional extended Kalman filter.