Bipartite consensus for multi-agent networks of fractional diffusion PDEs via aperiodically intermittent boundary control

In this paper, the exponential bipartite consensus issue is investigated for multi-agent networks, whose dynamic is characterized by fractional diffusion partial differential equations (PDEs). The main contribution is that a novel exponential convergence principle is proposed for networks of fractional PDEs via aperiodically intermittent control scheme. First, under the aperiodically intermittent control strategy, an exponential convergence principle is developed for continuously differentiable function. Second, on the basis of the proposed convergence principle and the designed intermittent boundary control protocol, the exponential bipartite consensus condition is addressed in the form of linear matrix inequalities (LMIs). Compared with the existing works, the result of the exponential intermittent consensus presented in this paper is applied to the networks of PDEs. Finally, the high-speed aerospace vehicle model is applied to verify the effectiveness of the control protocol

Optimal Control and Approximate controllability of fractional semilinear differential inclusion involving ψ\psi- Hilfer fractional derivatives

The current paper initially studies the optimal control of linear $\psi$-Hilfer fractional derivatives with state-dependent control constraints and optimal control for a particular type of cost functional. Then, we investigate the approximate controllability of the abstract fractional semilinear differential inclusion involving $\psi$-Hilfer fractional derivative in reflexive Banach spaces. It is known that the existence, uniqueness, optimal control, and approximate controllability of fractional differential equations or inclusions have been demonstrated for a similar type of fractional differential equations or inclusions with different fractional order derivative operators. Hence it has to research fractional differential equations with more general fractional operators which incorporate all the specific fractional derivative operators. This motivates us to consider the $\psi$-Hilfer fractional differential inclusion. We assume the compactness of the corresponding semigroup and the approximate controllability of the associated linear control system and define the control with the help of duality mapping. We observe that convexity is essential in determining the controllability property of semilinear differential inclusion. In the case of Hilbert spaces, there is no issue of convexity as the duality map becomes simply the identity map. In contrast to Hilbert spaces, if we consider reflexive Banach spaces, there is an issue of convexity due to the nonlinear nature of duality mapping. The novelty of this paper is that we overcome this convexity issue and establish our main result. Finally, we test our outcomes through an example.Comment: 39 page

Finite-time adaptive synchronization of fractional-order delayed quaternion-valued fuzzy neural networks

Based on direct quaternion method, this paper explores the finite-time adaptive synchronization (FAS) of fractional-order delayed quaternion-valued fuzzy neural networks (FODQVFNNs). Firstly, a useful fractional differential inequality is created, which offers an effective way to investigate FAS. Then two novel quaternion-valued adaptive control strategies are designed. By means of our newly proposed inequality, the basic knowledge about fractional calculus, reduction to absurdity as well as several inequality techniques of quaternion and fuzzy logic, several sufficient FAS criteria are derived for FODQVFNNs. Moreover, the settling time of FAS is estimated, which is in connection with the order and initial values of considered systems as well as the controller parameters. Ultimately, the validity of obtained FAS criteria is corroborated by numerical simulations

Evaluation of macroeconomic models for financial stability analysis

As financial stability has gained focus in economic policymaking, the demand for analyses of financial stability and the consequences of economic policy has increased. Alternative macroeconomic models are available for policy analyses, and this paper evaluates the usefulness of some models from the perspective of financial stability. Financial stability analyses are complicated by the lack of a clear and consensus definition of ‘financial stability’, and the paper concludes that operational definitions of this term must be expected to vary across alternative models. Furthermore, since assessment of financial stability in general is based on a wide range of risk factors, one can not expect one single model to satisfactorily capture all the risk factors. Rather, a suite of models is needed. This is in particular true for the evaluation of risk factors originating and developing inside and outside the financial system respectively.Financial stability; Banks; Default; Macroeconomic models; Policy

Evaluation of macroeconomic models for financial stability analysis

As financial stability has gained focus in economic policymaking, the demand for analyses of financial stability and the consequences of economic policy has increased. Alternative macroeconomic models are available for policy analyses, and this paper evaluates the usefulness of some models from the perspective of financial stability. Financial stability analyses are complicated by the lack of a clear and consensus definition of ‘financial stability’, and the paper concludes that operational definitions of this term must be expected to vary across alternative models. Furthermore, since assessment of financial stability in general is based on a wide range of risk factors, one can not expect one single model to satisfactorily capture all the risk factors. Rather, a suite of models is needed. This is in particular true for the evaluation of risk factors originating and developing inside and outside the financial system respectively.Financial stability; Banks; Default; Macroeconomic models; Policy

On the Robust Control and Optimization Strategies for Islanded Inverter-Based Microgrids

In recent years, the concept of Microgrids (MGs) has become more popular due to a significant integration of renewable energy sources (RESs) into electric power systems. Microgrids are small-scale power grids consisting of localized grouping of heterogeneous Distributed Generators (DGs), storage systems, and loads. MGs may operate either in autonomous islanded mode or connected to the main power system. Despite the significant benefits of increasing RESs, many new challenges raise in controlling MGs. Hence, a three layered hierarchical architecture consisting of three control loops closed on the DGs dynamics has been introduced for MGs. The inner loop is called Primary Control (PC), and it provides the references for the DG’s DC-AC power converters. In general, the PC is implemented in a decentralized way with the aim to establish, by means of a droop control term, the desired sharing of power among DGs while preserving the MG stability. Then, because of inverterbased DGs have no inertia, a Secondary Control (SC) layer is needed to compensate the frequency and voltage deviations introduced by the PC’s droop control terms. Finally, an operation control is designed to optimize the operation of the MGs by providing power setpoints to the lower control layers. This thesis is mainly devoted to the design of robust distributed secondary frequency and voltage restoration control strategies for AC MGs to avoid central controllers and complexity of communication networks. Different distributed strategies are proposed in this work: (i) Robust Adaptive Distributed SC with Communication delays (ii) Robust Optimal Distributed Voltage SC with Communication Delays and (iii) Distributed Finite-Time SC by Coupled Sliding-Mode Technique. In all three proposed approaches, the problem is addressed in a multi-agent fashion where the generator plays the role of cooperative agents communicating over a network and physically coupled through the power system. The first approach provides an exponentially converging voltage and frequency restoration rate in the presence of both, model uncertainties, and multiple time-varying delays in the DGs’s communications. This approach consist of two terms: 1) a decentralized Integral Sliding Mode Control (ISMC) aimed to enforce each agent (DG) to behaves as reference unperturbed dynamic; 2) an ad-hoc designed distributed protocol aimed to globally, exponentially, achieves the frequency and voltage restoration while fulfilling the power-sharing constraints in spite of the communication delays. The second approach extends the first one by including an optimization algorithm to find the optimal control gains and estimate the corresponding maximum delay tolerated by the controlled system. In the third approach, the problem of voltage and frequency restoration as well as active power sharing are solved in finite-time by exploiting delay-free communications among DGs and considering model uncertainties. In this approach, for DGs with no direct access to their reference values, a finite-time distributed sliding mode estimator is implemented for both secondary frequency and voltage schemes. The estimator determines local estimates of the global reference values of the voltage and frequency for DGs in a finite time and provides this information for the distributed SC schemes. This dissertation also proposes a novel certainty Model Predictive Control (MPC) approach for the operation of islanded MG with very high share of renewable energy sources. To this aim, the conversion losses of storage units are formulated by quadratic functions to reduce the error in storage units state of charge prediction