Robust mixed H2/H∞ fuzzy tracking control of photovoltaic system subject to asymmetric actuator saturation

This paper focuses on mixed [Formula: see text] fuzzy maximum power point tracking (MPPT) of photovoltaic (PV) system under asymmetric saturation and variations in climatic conditions. To maximize the power from the PV panel array, the DC–DC boost converter is controlled by its duty ratio which is practically saturated between 0 and 1. MPPT based on conventional control presents the problems of oscillations around maximum power point (MPP) and divergence under rapid climatic changes. In order to attenuate the effect of atmospheric condition variation and take into account asymmetric saturation of the duty ratio, we propose a novel robust saturated controller based on both [Formula: see text] performances and Takagi-Sugeno (T-S) representation of PV-boost nonlinear system. Within this approach, the nonlinear PV-boost system and its reference are first described by T-S fuzzy models. Second, the saturation effect is represented by a polytopic model. Then, a fuzzy integral state feedback controller is designed to achieve stable MPPT control. Based on Lyapunov function, the mixed [Formula: see text] stabilization conditions are derived in terms of linear matrix inequalities (LMIs). The optimization of the attraction domain of closed-loop system is solved as a convex optimization problem in LMI terms. Finally, the efficiency of the proposed controller under irradiance and temperature variations is demonstrated through the simulation results. The comparison with some existing controllers shows an improvement of MPPT control performance in terms of power extraction.

A Chaotic Krill Herd Optimization Algorithm for Global Numerical Estimation of the Attraction Domain for Nonlinear Systems

Nowadays, solving constrained engineering problems related to optimization approaches is an attractive research topic. The chaotic krill herd approach is considered as one of most advanced optimization techniques. An advanced hybrid technique is exploited in this paper to solve the challenging problem of estimating the largest domain of attraction for nonlinear systems. Indeed, an intelligent methodology for the estimation of the largest stable equilibrium domain of attraction established on quadratic Lyapunov functions is developed. The designed technique aims at computing and characterizing a largest level set of a Lyapunov function that is included in a particular region, satisfying some hard and delicate algebraic constraints. The formulated optimization problem searches to solve a tangency constraint between the LF derivative sign and constraints on the level sets. Such formulation avoids possible dummy solutions for the nonlinear optimization solver. The analytical development of the solution exploits the Chebyshev chaotic map function that ensures high search space capabilities. The accuracy and efficiency of the chaotic krill herd technique has been evaluated by benchmark models of nonlinear systems. The optimization solution shows that the chaotic krill herd approach is effective in determining the largest estimate of the attraction domain. Moreover, since global optimality is needed for proper estimation, a bound type meta-heuristic optimization solver is implemented. In contrast to existing strategies, the synthesized technique can be exploited for both rational and polynomial Lyapunov functions. Moreover, it permits the exploitation of a chaotic operative optimization algorithm which guarantees converging to an expanded domain of attraction in an essentially restricted running time. The synthesized methodology is discussed, with several examples to illustrate the advantageous aspects of the designed approach.

Admissibility analysis for autonomous underwater vehicle based on descriptor model with time-varying delay

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.

Breaking of the Similarity Principle in Markov Generators of Low Density Limit Type and the Role of Degeneracies in the Landscape of Invariant States

The similarity principle is an extension of the principle of thermal relaxation that naturally arises in the stochastic limit of quantum theory. We construct examples of Low Density Limit (LDL) generators, associated to an environment state in equilibrium at inverse temperature β, which admit non-(β, HS)-equilibrium states. We prove that in some cases, the attraction domain of the (β, HS)-equilibrium state is empty. This means that the similarity principle, in its original thermodynamical formulation, can be broken in the LDL limit. This result is obtained as a consequence of a more general phenomenon: the role of degeneracies in the spectrum of the Liouvillian of the system Hamiltonian associated to the generator. We start from the definition of LDL type generators given in [5] and we introduce a finer classification of these generators based on the above degeneracies. The simplest subclass, called 2-generic, is a nontrivial extension of the generators associated to the so-called Λ and V configurations, widely used in quantum optics and involving 2 levels of the system Hamiltonian. Since each 2-generic block involves 3 or 4 levels of the system Hamiltonian we expect that they can reveal some interesting new physical phenomenon, as it happened in the 2-level case. In the last section, we restrict our attention to a 3-level system with a Hamiltonian that is associated to a class of 2-generic LDL generators. Finally, we prove that, for some LDL generators in this class the statement formulated at the beginning holds true.

Lyapunov-based Methods for Maximizing the Domain of Attraction

This paper investigates Lyapunov approaches to expand the domain of attraction (DA) of nonlinear autonomous models. These techniques had been examined for creating generic numerical procedures centred on the search of rational and quadratic Lyapunov functions. The outcomes are derived from all investigated methods: the method of estimation via Threshold Accepted Algorithm (TAA), the method of estimation via a Zubov technique and the method of estimation via a linear matrix inequality (LMI) optimization and genetic algorithms (GA). These methods are effective for a large group of nonlinear models, they have a significant ability of improvement of the attraction domain area and they are distinguished by an apparent propriety of direct application for compact and nonlinear models of high degree. The validity and the effectiveness of the examined techniques are established based on a simulation case analysis. The effectiveness of the presented methods is evaluated and discussed through the study of the renowned Van der Pol model.

Dynamic Investigation in Green Supply Chain considering Channel Service

Considering firm’s innovation input of green products and channel service, this paper, in dynamic environment, studies a dynamic price game model in a dual-channel green supply chain and focuses on the effect of parameter changing on the pricing strategies and complexity of the dynamic system. Using dynamic theory, the complex behaviors of the dynamic system are discussed; besides, the parameter adaptation method is adopted to restrain the chaos phenomenon. The conclusions are as follows: the stable scope of the green supply chain system enlarges with decision makers’ risk-aversion level increasing and decreases with service value increasing; excessive adjustment of price parameters will make the green supply chain system fall into chaos with a large entropy value; the attraction domain of initial prices shrinks with price adjustment speed increasing and enlarges with the channel service values raising. As the dynamic game model system is in a chaotic state, the profit of the manufacturer will be damaged, while the efficiency of the retailer will be improved. The system would be kept at a stable state and casts off chaos by the parameter adaptation method. Results are significant for the manager to make reasonable price decision.

Research on a Cournot–Bertrand Game Model with Relative Profit Maximization

This paper considers a Cournot–Bertrand game model based on the relative profit maximization with bounded rational players. The existence and stability of the Nash equilibrium of the dynamic model are investigated. The influence of product differentiation degree and the adjustment speed on the stability of the dynamic system is discussed. Furthermore, some complex properties and global stability of the dynamic system are explored. The results find that the higher degree of product differentiation enlarges the stable range of the dynamic system, while the higher unit product cost decreases the stable range of price adjustment and increases the one of output adjustment; period cycles and aperiodic oscillation (quasi-period and chaos) occur via period-doubling or Neimark–Sacker bifurcation, and the attraction domain shrinks with the increase of adjustment speed values. By selecting appropriate control parameters, the chaotic system can return to the stable state. The research of this paper is of great significance to the decision-makers’ price decision and quantity decision.

Research on the Complexity of Game Model about Recovery Pricing in Reverse Supply Chain considering Fairness Concerns

A reverse recycling supply chain consisting of two recyclers is established in this paper, which takes into account the fact that the recyclers will consider the issue of fair concern in pricing. The paper discusses the local stability of the Nash equilibrium point in this price game model showing that the fair concern factors will reduce the stable area of the system. The paper also discusses the impacts of the sensitivity of the recovery price and the price cross coefficient on the stable area of the system. Through the method of system simulation and use of some indicators, such as the singular attractor, bifurcation diagram, attraction domain, power spectrum, and maximum Lyapunov exponent, the characteristics of the system at different times will be illustrated.