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In this study, control and fault detection are examined for Takagi–Sugeno (T–S) fuzzy continuous-time systems with conic-type nonlinearity. In a conic-type dynamic system, Takagi–Sugeno fuzzy models are applied. A conic-type non-linearity must lie in an n-dimensional hyper-sphere with an uncertain centre to satisfy the restrictive condition. A combined error system of estimation and control error is obtained by combining the observations and the controller. Our main goal is to design an observer and controller for fault detection that minimizes the impact of unknown inputs and faults on the system in terms of the $ H_{\infty } $ H ∞ performance. The Lyapunov function is used to construct the residual signal using an observer and a controller. Using Linear Matrix Inequalities (LMIs), we can express the performance conditions for $ H_{\infty } $ H ∞ . The scheme's effectiveness is demonstrated with numerical examples. [ABSTRACT FROM AUTHOR]

The effectiveness of this paper lies in presenting a new solution for the singular fractional two-dimensional linear continuous-time systems using the conformable derivative and Sumudu transform. The proposed technique combines the new advantageous features of conformal derivative and double-delta-Kronecker, which efficiently handles singularities and Sumudu transform, and provides an efficient solution for 2D singular Fornasini–Marchesini fractional models. Applying these approaches, we then derive new explicit expressions for the fundamental matrices of the considered model. The applicability and usefulness of our proposed methods are validated and evaluated by numerical simulations in order to show the accuracy of the obtained results. [ABSTRACT FROM AUTHOR]

In this article, a delayed complex network model with non-identical nodes is established, where the mismatched uncertain parameters are involved in each node. The concept of approximate synchronization is proposed. A linear feedback controller is designed and a sufficient condition for boundedness of the synchronous error is presented in terms of linear matrix inequalities. A pseudoconvex optimization problem for minimizing the upper bound of the synchronous error is proposed. Furthermore, an iterative algorithm involving convex problem is designed to solve this pseudoconvex optimization problem and obtain the globally optimal solution, by which the approximate synchronization is achieved. At last, two numerical examples are given to show the effectiveness of the proposed criterion. [ABSTRACT FROM AUTHOR]

This paper investigates the robust H∞ control of synchronization for uncertain singular complex delayed networks with stochastic switched coupling. The switched coupling is dependent on a continuous time Markovian process. Based on Lyapunov-Krasovskii stability theory, sufficient conditions for the existence of the H∞ control laws are given in terms of linear matrix inequalities, which ensure robustly global mean-square synchronization and a prescribed H∞ disturbance attenuation level for the resulting closed-loop complex networks. Numerical examples are given to illustrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

Robust H∞ consensus control for second-order multi-agent systems is addressed. Considering the delayed directed networks with disturbances and uncertainty parameters on dynamic topologies, the consensus protocols are proposed and analysed. By constructing the common Lyapunov-Krasovkii functional, applying the Lyapunov-Krasovkii theory and integral inequality approach, the sufficient condition of consensus protocol convergence is derived, guaranteeing robust H∞ consensus for given second-order multi-agent systems. Finally, numerical examples are provided to demonstrate the effectiveness of the main results. [ABSTRACT FROM AUTHOR]

Optimal control theory is applied to a mathematical model that describes the interaction of the immune system with the human immunodeficiency virus (HIV) and that permits the administration of triple HIV drug therapy. The optimal control represents a percentage effect the chemotherapy consisting of fusion inhibitors (FIs), reverse transcriptase inhibitors (RTIs), and protease inhibitors (PIs) has on the interaction of CD4+T-cells with the virus. First, we maximize the benefit based on the T-cell count and minimize the systemic cost based on the percentage of chemotherapies given and then build an objective functional to minimize the viral replication and treatment systemic costs. Our results indicate that highly toxic drugs and small dosage sizes have the potential for improving the quality of life and reducing economic costs of therapy. An optimal control strategy that seeks to maximize CD4+ T-cells has the potential to provide better treatment results over the optimal treatmet strategy that seeks to minimize the viral production. The addition of FIs to the current HIV treatment strategy of RTIs and PIs improves to relax both concentration and dose sizes of RTIs and PIs. [ABSTRACT FROM AUTHOR]

This paper investigates numerical methods for direct decoupled sensitivity and discrete adjoint sensitivity analysis of stiff systems based on implicit Runge-Kutta schemes. Efficient implementations of tangent linear and adjoint schemes are discussed for two families of methods: fully implicit three-stage Runge-Kutta and singly diagonally-implicit Runge-Kutta. High computational efficiency is attained by exploiting the sparsity patterns of the Jacobian and Hessian. Numerical experiments with a large chemical system used in atmospheric chemistry illustrate the power of the stiff Runge-Kutta integrators and their tangent linear and discrete adjoint models. Through the integration with the Kinetic PreProcessor KPP-2.2 these numerical techniques become readily available to a wide community interested in the simulation of chemical kinetic systems. [ABSTRACT FROM AUTHOR]

Chaos control and synchronization problem of a three-species food chain model with Holling I-type functional response is investigated. By the linearization approach, a feedback control law is developed to stabilize the model system to equilibrium points. Based on the bidirectional coupled method, chaos synchronization of the model system is studied. Numerical simulations show that the feedback control law can suppress chaos to unstable equilibrium points successfully. Further, the numeric results show that when the coupling strength 0

In this paper, time-delayed optimal control problems governed by delayed differential equation are solved. Two different techniques based on integration and differentiation matrices are considered. The time-delayed term of the problem has been approximated by Chebyshev interpolating polynomials. On this basis, the optimal control problem can be solved as a mathematical programming problem. The example illustrates the robustness, accuracy and efficiency of the proposed numerical techniques. [ABSTRACT FROM AUTHOR]

By applying local feedback injections to a small fraction of network vertices, a dynamical network can be stabilized on a homogeneous equilibrium. However, different pinning strategies may lead to different performances. This paper develops a novel pinning scheme based on ControlRank (CR), which is a vertex centrality index exploring the link structure of the directed networks. Simulation study is given on a scale-free directed dynamical network, which demonstrates that it is much more effective to pin the vertex with largest CR than pin the vertex with largest out-degree. [ABSTRACT FROM AUTHOR]