Results in Control and Optimization最新文献

Reinforcement learning has been used extensively to learn the low-level tactical choices during gameplay; however, less effort is invested in the strategic decisions governing the effective engagement of a diverse set of opponents. In this paper, a two-tier reinforcement learning model is created to play competitive games and effectively engage in matches with different opponents to maximize earnings. The multi-agent environment has four types of learners, which vary in their ability to learn gameplay directly (tactics) and their ability to learn to bet or withdraw from gameplay (strategy). The players are tested in three different competitive games: Connect 4, Dots and Boxes, and Tic-Tac-Toe. Analyzing the behavior of players as they progress from naivety to game mastery reveals some interesting features: (1) learners who optimize strategy and tactics outperform all learners, (2) learners who initially optimize their strategy to engage in matches outperform those who focus on optimizing tactical gameplay, and (3) the advantage of strategy optimization versus tactical gameplay optimization diminishes as more games are played. A reinforcement learning model with a dual learning scheme presents possible applications in adversarial scenarios where both strategic and tactical learning are critical. We present detailed results in a systematic manner, providing strong support for our claim.

Melioidosis is a significant health problem in tropical and subtropical regions, especially in Southeast Asia and Northern Australia. Recurrent melioidosis is a major obstacle to eliminating the disease from the community in these nations. This work aims to propose and analyze a human melioidosis model with recurrent phenomena and an optimal control model by incorporating time-dependent control functions. The basic reproduction number ($R_0$) of the uncontrolled model is derived using the method of the next-generation matrix. Using the construction of a Lyapunov functional, we present the global asymptotic dynamics of the autonomous model in the presence of recurrent for both disease-free and endemic equilibria. The global asymptotic stability of the model’s equilibria shows the absence of a backward bifurcation for the model in both cases, whether in the absence or presence of relapse. The sensitivity analysis aims to identify the parameters that have the most significant impact on the model’s dynamics. Furthermore, qualitative analysis of the model’s global dynamics and the changing effect of the most influential parameters on $R_0$ are supported by numerical experiments, with the results being illustrated graphically. The model with time-dependent controls is analyzed using optimal control theory to assess the impact of various intervention strategies on the spread of the epidemic. The numerical results of the optimality system are carried out using the Forward–Backward Sweep method in Matlab. We also conducted a cost-effectiveness analysis using two approaches: the average cost-effectiveness ratio and the incremental cost-effectiveness ratio.

This paper resolves around relative controllability of $\psi -$fractional delayed differential equations in finite dimensional space. The Mittag Leffler type of $\psi -$delayed perturbation matrix function with two parameters exhibits the Grammian matrix of fractional delay system. Based on this Grammian matrix we derived the necessary and sufficient conditions for the linear system which is relatively controllable. The fixed point approach is applied for obtaining a controllability result for semilinear system. This concept can be applied to some examples in order to illustrate the efficacy of our results.

Using the Caputo operator, a model for a fractional-order epidemic is developed to investigate the fear effect in a pathogenic environment and vaccination procedure. First, we examine if the proposed model is positive. Next, based on the value of the control reproduction number $R_c$, we compute both the control reproduction and strength numbers and derive the stability criteria of the disease-free equilibrium. In fact, we use the comparison theorem to show that the disease-free equilibrium point is globally asymptotically stable whenever $R_c<1$. Next, we prove that the solutions of the fractional model exist and are unique. Finally, several numerical simulations are conducted to verify our theoretical results.

Black-box optimization plays a pivotal role in addressing complex real-world problems where the underlying mathematical model is unknown or expensive to evaluate. In this context, this work presents a method to enhance the performance of derivative-free optimization algorithms by integrating an adaptive sampling process. The proposed methodology aims to overcome the limitations of traditional methods by intelligently guiding the search towards promising regions of the search space. To achieve this, we utilize machine learning models, which effectively substitute first principles models. Furthermore, we employ the error maximization approach to steer the exploration towards areas where the surrogate model deviates significantly from the true model. Moreover, we involve a heuristic method, an adaptive sampling procedure, that repeats calls to a widely-used derivative-free optimization algorithm, SNOBFIT, allowing for the creation of new and improved surrogate models. To evaluate the efficiency of the proposed method, we conduct a comparative analysis across a benchmark set of 776 continuous problems. Our findings indicate that our approach successfully solved 93% of the problems. Notably, for larger problems, our method outperformed the standard SNOBFIT algorithm by achieving a 19% increase in problem-solving rate, and when, we introduced an additional termination criterion to enhance computational efficiency, the proposed method achieved a 31% time reduction compared to SNOBFIT.

The dynamical behaviors of an epidemic model based on the susceptible–infected–susceptible (SIS) model are investigated. The Beddington–DeAngelis functional response is used for the infection rate to present the dependence of the transmission of the infection on the ratio of both susceptible and infected populations. A Caputo fractional derivative is applied to show the existence of memory in nature affects population dynamics. The disease-free and endemic equilibrium points are obtained as the equilibrium points that describe the condition when the population is free from the disease or the disease exists in the population throughout time. The existence, uniqueness, non-negativity, and boundedness are proven which state the biological validity of the mathematical model. The local and global stability of each equilibrium point is studied including the basic reproduction number and its influence on the dynamical behaviors. Some numerical simulations are portrayed to explore more about the dynamics of the model which are relevant to the analytical findings. The partial rank correlation coefficient is presented to investigate the dominant parameter with respect to the basic reproduction number and the density of susceptible and infected populations. The parameter continuations are demonstrated to show the impact of infection rate and the inhibitory effect which lead to the occurrence of forward bifurcations. The memory effect is also demonstrated numerically to show the changes in convergence rate due to the changes in memory strength.

While Unmanned Aerial Vehicles (UAVs) have found applications across numerous industries, they still remain vulnerable to various cybersecurity challenges. Different types of cyberattacks target UAVs. Early detection of these cyberattacks is considered the most important step in ensuring the cybersecurity of UAVs. In this article, an artificial intelligence method based on machine learning was developed for detecting different types of Denial of Service (DoS) attacks targeting the UAV network. Initially in this work, feature selection methods are implemented to select the most important features. Then, machine learning methods are used to classify attacks. According to the conducted experiments, the proposed method outperformed others with an accuracy of 99.51 % and a prediction time of 0.1 s. Additionally, a novel dataset is used in this work, which offers several advantages. The dataset was created within a real-world environment rather than a simulated one. Furthermore, the data were collected within a 5G network.

In this study, we developed and analyzed a compartmental epidemic model and a system model that incorporate vaccination, elimination, and quarantine techniques, with a saturated incidence rate, by theoretical and numerical means. The model is described by a system of four nonlinear differential equations. Our analysis included determining the reproduction number $R_q$ and examining equilibrium solutions. The outcomes of the disease are identified through the threshold $R_q$. When $R_q<1$, the disease-free equilibrium is globally asymptotically stable, as proved by the LaSalle invariance principle and disease extinction analysis. However, using the Routh–Hurwitz criterion, we have proved that the disease-free equilibrium is not stable, and when $R_q>1$, the unique endemic equilibrium is asymptotically stable locally. The stability of the endemic and disease-free equilibria globally has been examined using the Routh–Hurwitz and Dulac criteria. Subsequently, numerical simulations were utilized to illustrate the theoretical findings effectively.

This paper examines the analysis of some rational-type contractions within the context of extended b-metric spaces, establishes a theoretical foundation for rational-type contractions and demonstrates their application in Volterra integral inclusions and Urysohn integral equations. Some examples are provided for the authenticity of the findings.

Sufficient conditions for controllability of impulsive nonlinear integro-differential equations with $\psi$-Hilfer fractional derivative are established. The result are obtained by using fractional calculus and Schaefer’s fixed point theorem. Finally, a numerical examples are then provided to demonstrate the outcomes.