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Nowadays, environmental issues have received increasing attention from experts. The main cause is the increase of carbon emissions in the atmosphere, so it is urgent to reduce carbon emissions. In order to establish the optimal pricing strategy as well as the emission reduction effort strategy for companies who produce and sell low carbon products, this paper proposes an optimal control model for low carbon products. The reduction of the carbon emission for the product is described dynamically by a differential equation, and the analytical expressions of the optimal pricing and the emission abatement strategies are derived using the Pontryagin's maximum principle. Finally, the numerical experiments are used to explain the results obtained. The results show that companies producing and selling low-carbon products must pay more attention to the amount of carbon emission reduction in their products, and make more efforts to reduce emissions in order to make more profits. Additionally, the parametric analysis shows that expanding market size and reducing inventory depletion can be equally helpful in shortening the sales cycle and boosting profits. [ABSTRACT FROM AUTHOR]

In the context of constrained control-systems, the Set of Sustainable Thresholds plays in a sense the role of a dual object to the so-called Viability Kernel, because it describes all the thresholds that must be satisfied by the state of the system along a time interval, for a prescribed initial condition. This work aims at analyzing the sensitivity of the Set of Sustainable Thresholds, when it is seen as a set-valued map that depends on the initial position. In this regard, we investigate semicontinuity and Lipschitz continuity properties of this mapping, and we also study several contexts when the Set of Sustainable Thresholds is convex-valued. [ABSTRACT FROM AUTHOR]

In epidemiological modelling, efficiency and economic analyses have become important metrics for identifying efficient and cost-effective intervention strategies that avert highest number of infection cases at cheapest implementation cost. This study examines an optimal control model for malaria dynamics which incorporates all the three categories of recurrent malaria such as, relapse, re-infection and recrudescence with four interventions including, personal protection using insecticide-treated bed nets, anti-relapse strategy using anti-hypnozoites drug, treatment control using anti-malaria drug, and vector control using insecticide spraying. Detailed efficiency and economic methodologies are employed to analyse the model by considering different combinations of interventions which are classified into four distinct groups, namely single control, double control, triple control, and quadruple control interventions. In each of the groups, most efficient intervention is obtained by calculating efficiency indices of each intervention, while most cost-effective intervention is determined using average cost-effectiveness ratio (ACER) and incremental cost-effectiveness ratio (ICER) methods. Furthermore, overall groups, it is shown that quadruple control which combines all the four interventions is the most efficient, while personal protection using insecticide-treated bed nets from the single control group is found to be the most cost-effective intervention. Hence, intervention strategies capable of bringing down the menace of recurrent malaria in the population are provided based on availability of resources. [ABSTRACT FROM AUTHOR]

Numerical continuation tools are nowadays standard methods for the bifurcation analysis of dynamical systems. Unfortunately, the full power of these methods is still unavailable in experiments, in particular, if no underlying mathematical model is at hand. We here aim to narrow this gap by providing control based continuation of periodic states which can be ultimately implemented in real-world experimental set-ups. Taking inspiration from atomic force microscopy, we develop experimentally relevant control and tracking tools for time periodic solutions in driven nonlinear oscillator systems based on stroboscopic maps. [ABSTRACT FROM AUTHOR]

This article is concerned with the stability and dynamics for the weak damped Lamé system with nonlinear time-varying delay in a bounded domain. Under some appropriate assumptions, the global well-posedness and asymptotic stability are shown in the case where the delay coefficient is upper dominated by the damping one. Moreover, the finite dimensional global and exponential attractors have also been presented by relying on quasi-stability arguments. The results in this article is an extension of Ma, Mesquita, and Seminario-Huertas’s recent work [Smooth dynamics of weakly damped Lamé systems with delay, SIAM J. Math. Anal. 53 (2021), no. 4, 3759–3771].

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]

By considering the idea and the notion of observers of dynamical systems, it is shown that relative semidynamical systems can be a suitable model for inserting an observer as a realistic fact to systems theory. Multi-dimensional observers and their affect on semidynamical systems are considered. Locally distinguishable semidynamical systems are introduced, and it is proved that this property preserves under relative conjugate relations which preserves observers. For an application of the role of observer relative topological entropy for relative semidynamical systems on compact relative topological spaces are considered. [ABSTRACT FROM AUTHOR]

This paper addresses the equivalence problem of conic submanifolds in the tangent bundle of a smooth 2-dimensional manifold. Those are given by a quadratic relation between the velocities and are treated as nonholonomic constraints whose admissible curves are trajectories of the corresponding control systems, called quadratic systems. We deal with the problem of characterising and classifying conic submanifolds under the prism of feedback equivalence of control systems, both control-affine and fully nonlinear. The first main result of this work is a complete description of non-degenerate conic submanifolds via a characterisation under feedback transformations of the novel class of quadratic control-affine systems. This characterisation can explicitly be tested on structure functions defined for any control-affine system and gives a normal form of quadratisable systems and of conic submanifolds. Then, we consider the classification problem of regular conic submanifolds (ellipses, hyperbolas, and parabolas), which is treated via feedback classification of quadratic control-nonlinear systems. Our classification includes several normal forms of quadratic systems (in particular, normal forms not containing functional parameters as well as those containing neither functional nor real parameters) and, as a consequence, gives a classification of regular conic submanifolds. [ABSTRACT FROM AUTHOR]

In this paper, we are interested in designing a suitable boundary control to suppress axial vibration in a varying-length mining cable. The existence of a solution to the closed loop system is proved using the Faedo-Galerkin method. And by using Lyapunov's method, we have shown that the closed-loop system with the boundary control is exponentially stable, these result are confirmed by simulation. [ABSTRACT FROM AUTHOR]

The second-order ILC algorithm is studied for a class of linear discrete-time switched systems with model uncertainties, external noises and the time-delay for tracking reference trajectory by taking advantage of super-vector representation. This study is based on the assumption that the systems operate under finite intervals. A sufficient condition for convergence of the algorithms is deduced when the model uncertainties and external noises are absent. Then the convergence is analysed, when the model uncertainties are present but the external noises are absent and the robustness against the bounded external noises is discussed. The analysis manifests that the second-order ILC algorithm is feasible and effective when it is imposed on the linear switched systems specified by the arbitrarily present switching rules when they are imposed on the system. We have presented a simulation example to illustrate effectiveness of the proposed second-order ILC algorithm in the study of robustness of the considered SISO linear discrete time-invariant time delay switched system. [ABSTRACT FROM AUTHOR]

This paper deals with the exact boundary controllability and the exact boundary synchronization for a 1-D system of wave equations coupled with velocities. These problems can not be solved directly by the usual HUM method for wave equations, however, by transforming the system into a first order hyperbolic system, the HUM method for 1-D first order hyperbolic systems, established by Li-Lu (2022) and Lu-Li (2022), can be applied to get the corresponding results. [ABSTRACT FROM AUTHOR]

In this paper, we propose a new system called an alternate control system with double impulses. The present system is a cyclic control system, composed of four parts in a circle: to the first and last halves of each period of the system we add different continuous controls, and at the half-period time and the end of each period of the system we add different impulses. We then investigate the exponential stability of the considered system. An example based on Chua's circuit is provided to confirm the effectiveness of the theoretical result. [ABSTRACT FROM AUTHOR]

In the present work we formally extend the theory of port-Hamiltonian systems to include random perturbations. In particular, suitably choosing the space of flow and effort variables we will show how several elements coming from possibly different physical domains can be interconnected in order to describe a dynamic system perturbed by general continuous semimartingale. Relevant enough, the noise does not enter into the system solely as an external random perturbation, since each port is itself intrinsically stochastic. Coherently to the classical deterministic setting, we will show how such an approach extends existing literature of stochastic Hamiltonian systems on pseudo-Poisson and pre-symplectic manifolds. Moreover, we will prove that a power-preserving interconnection of stochastic port-Hamiltonian systems is a stochastic port-Hamiltonian system as well. [ABSTRACT FROM AUTHOR]

In this work, we model the movement of a figure skater gliding on ice by the Chaplygin sleigh, a classic pedagogical example of a nonholonomic mechanical system. The Chaplygin sleigh is controlled by a movable added mass, modeling the movable center of mass of the figure skater. The position and velocity of the added mass act as controls that can be used to steer the skater in order to produce prescribed patterns. Our control method is based on the observation that any piecewise smooth curve can be approximated by a collection of circular arcs. We impose a steering constraint stating that the contact point is moving locally along a circular arc. Then, the accuracy of the method depends solely on the accuracy of approximation of a trajectory by circular arcs. To reproduce the individual elements of a pattern, we employ a control mechanism based on minimization of the square of the velocity of control mass relative to the sleigh subject to the trajectory being locally a circular arc. We conclude by reproducing a classical "double flower" figure skating pattern and compute the resulting controls. [ABSTRACT FROM AUTHOR]

A countermeasure against sediment depletion in rivers is sand replenishment. The cost-efficient sizing of its capacity is critical for sustainable environmental management. However, only temporally discrete replenishment is possible, and sediment transport is intermittent and uncertain. In this paper, we approach this new design problem using a robust ergodic control. First, a stochastic differential equation driven by a (tempered) stable subordinator describes the sediment storage dynamics. Sand replenishment is considered an impulse control, wherein observation/replenishment chances arrive at Poisson jump times. The subordinator is ambiguous since the decision-maker does not precisely know its Lévy measure. Using a dynamic risk measure that balances replenishment cost, disutility triggered by sediment depletion, and penalization of ambiguity, we derived the Hamilton–Jacobi–Bellman–Isaacs (HJBI) equation to determine the optimal storage capacity. We obtained that the HJBI equation has an analytical solution when a stable subordinator is used. Furthermore, we prove it admits a unique continuous viscosity solution and that it is optimal and applied the proposed model to real data. [ABSTRACT FROM AUTHOR]

Due to the significant role of discrete chaos and sensitivity to initial conditions, various discrete difference maps have found a dominant place in the study of nonlinear dynamics and are widely used for different scientific applications like secure communication, cryptography, weather forecasting, and discrete traffic flow models. Under this article, it is proposed to study the dynamical properties such as period-doubling, fixed-orbit evolution, time-series evolution, and Lyapunov exponent of one such discrete difference map using Mann orbit. The results are demonstrated through analytical as well as experimental analysis followed by different theorems, counterexamples, functional plots, and a few concluding remarks. Because of the presence of an additional parameter μ , the proposed orbit offers an extra degree of freedom in control parameters α and β , which renders better dynamical properties as compared to the traditional orbit and hence improves the stability performance of the system. Furthermore, in comparison with the existing discrete systems, the proposed system displays more remarkable dynamical characteristics such as better stability range, improved sensitivity, and appropriate lower maximum Lyapunov exponent value [ABSTRACT FROM AUTHOR]

In this paper, we propose new approaches to the construction of extremely multistable systems containing one-, two-, and three-dimensional lattices of identical hidden chaotic attractors possessing the same Lyapunov exponents. In particular, we prove that for multidimensional models of automatic control systems in the Lurie form, it is always possible to pass from an interactive system to a cascade system; this substantially simplifies the procedure for constructing multidimensional lattices of identical chaotic attractors. [ABSTRACT FROM AUTHOR]

The prime aim of this paper is to synthesize a novel disturbance observer based on a cascade structure for a class of Lipschitz nonlinear systems with model uncertainties and output measurements corrupted by external disturbances and multiple time-varying delays. The proposed observation scheme is comprised of a cascade of state observers, where everyone is tasked to estimate the state over a short time interval, while the initial item provides the undelayed estimation. Each item of the cascade disturbance observer contains a dynamical proportional-integral term which allows to reduce effects of the time-delay and the unknown signals. An originality of the proposed approach is that it involves less-restrictive Lipschitz inequalities for function describing the nonlinear system. The convergence analysis is based on a Lyapunov–Krasovskii functional approach to demonstrate that the observation error is decaying to zero. The proposed disturbance observer can appropriately estimate the state variables by attenuating the effect of model uncertainties and external disturbances. An example considering a Chua's chaotic system illustrates the effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]

Symptomatic and asymptomatic individuals play a significant role in the transmission dynamics of novel Coronaviruses. By considering the dynamical behaviour of symptomatic and asymptomatic individuals, this study examines the temporal dynamics and optimal control of Coronavirus disease propagation using an epidemiological model. Biologically and mathematically, the well-posed epidemic problem is examined, as well as the threshold quantity with parameter sensitivity. Model parameters are quantified and their relative impact on the disease is evaluated. Additionally, the steady states are investigated to determine the model's stability and bifurcation. Using the dynamics and parameters sensitivity, we then introduce optimal control strategies for the elimination of the disease. Using real disease data, numerical simulations and model validation are performed to support theoretical findings and show the effects of control strategies.

Unlimited access to a motorway network can, in overloaded conditions, cause a loss of throughput. Ramp metering, by controlling access to the motorway at onramps, can help avoid this loss of throughput. The queues that form at onramps are dependent on the metering rates chosen at the onramps, and these choices affect how the capacities of different motorway sections are shared amongst competing flows. In this paper we perform an analytical study of a fluid, or differential equation, model of a linear network topology with onramp queues. The model allows for adaptive arrivals, in the sense that the rate at which external traffic enters the queue at an onramp can depend on the current perceived delay in that queue. The model also includes a ramp metering policy which uses global onramp queue length information to determine the rate at which traffic enters the motorway from each onramp. This ramp metering policy minimizes the maximum delay over all onramps and produces equal delay times over many onramps. The paper characterizes both the dynamics and the equilibrium behavior of the system under this policy. While we consider an idealized model that leaves out many practical details, an aim of the paper is to develop analytical methods that yield interesting qualitative insights and might be adapted to more general contexts. The paper can be considered as a step in developing an analytical approach towards studying more complex network topologies and incorporating other model features. [ABSTRACT FROM AUTHOR]

In this paper we focus our attention on the design of the feedback-based feed-forward controller asymptotically stabilizing the double-pendulum-type (D-P-T) crane system with the time-varying rope length in the desired end position of payload (the origin of the coordinate system). In principle, two cases are considered, in the first case, the sway angle of payload is uncontrolled and second case, when the sway angle of payload is controlled by an external force. Precise mathematical modeling in the framework of Lagrange formalism without the traditional neglect of the important structural parameters of the D-P-T crane system and numerical simulation in the Matlab environment indicate the substantial reduction of the transportation time to the desired end position. [ABSTRACT FROM AUTHOR]

Abstract In this paper, we investigate a hybrid projective combination–combination synchronization scheme among four non-identical hyperchaotic systems via adaptive control method. Based on Lyapunov stability theory, the considered approach identifies the unknown parameters and determines the asymptotic stability globally. It is observed that various synchronization techniques, for instance, chaos control problem, combination synchronization, projective synchronization, etc. turn into particular cases of combination–combination synchronization. The proposed scheme is applicable to secure communication and information processing. Finally, numerical simulations are performed to demonstrate the effectivity and correctness of the considered technique by using MATLAB.

In this paper, we formulate and analyze a new fractional-order Logistic model with feedback control, which is different from a recognized mathematical model proposed in our very recent work. Asymptotic stability of the proposed model and its numerical solutions are studied rigorously. By using the Lyapunov direct method for fractional dynamical systems and a suitable Lyapunov function, we show that a unique positive equilibrium point of the new model is asymptotically stable. As an important consequence of this, we obtain a new mathematical model in which the feedback control variables only change the position of the unique positive equilibrium point of the original model but retain its asymptotic stability. Furthermore, we construct unconditionally positive nonstandard finite difference (NSFD) schemes for the proposed model using the Mickens' methodology. It is worth noting that the constructed NSFD schemes not only preserve the positivity but also provide reliable numerical solutions that correctly reflect the dynamics of the new fractional-order model. Finally, we report some numerical examples to support and illustrate the theoretical results. The results indicate that there is a good agreement between the theoretical results and numerical ones. [ABSTRACT FROM AUTHOR]

We present a computational study of a simple finite-dimensional feedbackcontrol algorithm for stabilizing solutions of infinite-dimensional dissipativeevolution equations such as reaction-diffusion systems, the Navier-Stokesequations and the Kuramoto-Sivashinsky equation. This feedback control schemetakes advantage of the fact that such systems possess finite number ofdetermining parameters or degrees of freedom, namely, finite number ofdetermining Fourier modes, determining nodes, and determining interpolants andprojections. In particular, the feedback control scheme uses finitely many ofsuch observables and controllers that are acting on the coarse spatial scales.We demonstrate our numerical results for the stabilization of the unstable zerosolution of the 1D Chafee-Infante equation and 1D Kuramoto-Sivashinkskyequation. We give rigorous stability analysis for the feedback controlalgorithm and derive sufficient conditions relating the control parameters andmodel parameter values to attune to the control objective.

We introduce here a simple finite-dimensional feedback control scheme for stabilizing solutions of infinite-dimensional dissipative evolution equations, such as reaction-diffusion systems, the Navier-Stokes equations and the Kuramoto-Sivashinsky equation. The designed feedback control scheme takes advantage of the fact that such systems possess finite number of determining parameters (degrees of freedom), namely, finite number of determining Fourier modes, determining nodes, and determining interpolants and projections. In particular, the feedback control scheme uses finitely many of such observables and controllers. This observation is of a particular interest since it implies that our approach has far more reaching applications, in particular, in data assimilation. Moreover, we emphasize that our scheme treats all kinds of the determining projections, as well as, the various dissipative equations with one unified approach. However, for the sake of simplicity we demonstrate our approach in this paper to a one-dimensional reaction-diffusion equation paradigm.

We introduce here a simple finite-dimensional feedback control scheme for stabilizing solutions of infinite-dimensional dissipative evolution equations, such as reaction-diffusion systems, the Navier-Stokes equations and the Kuramoto-Sivashinsky equation. The designed feedback control scheme takes advantage of the fact that such systems possess finite number of determining parameters (degrees of freedom), namely, finite number of determining Fourier modes, determining nodes, and determining interpolants and projections. In particular, the feedback control scheme uses finitely many of such observables and controllers. This observation is of a particular interest since it implies that our approach has far more reaching applications, in particular, in data assimilation. Moreover, we emphasize that our scheme treats all kinds of the determining projections, as well as, the various dissipative equations with one unified approach. However, for the sake of simplicity we demonstrate our approach in this paper to a one-dimensional reaction-diffusion equation paradigm.

In the manuscript, fractional order neural network under electromagnetic radiation is introduced and its dynamics studied using Lyapunov exponents, stagnation points, symmetry, bifurcation diagrams etc. The dynamics for variable fractional order between 0.8 to 1 is also observed. The neural network model shows high sensitivity to external stimuli. The neural functioning shows improvement when exposed to the right amount of electromagnetic radiations. The chaos in the studied dynamical system is controlled about its unique stagnation point using SMC controllers in presence of uncertainties and disturbances, which are also estimated in this method. These results could bring vision into the occurrence of neuron related problems.

In this paper, we investigate a hybrid projective combination–combination synchronization scheme among four non-identical hyperchaotic systems via adaptive control method. Based on Lyapunov stability theory, the considered approach identifies the unknown parameters and determines the asymptotic stability globally. It is observed that various synchronization techniques, for instance, chaos control problem, combination synchronization, projective synchronization, etc. turn into particular cases of combination–combination synchronization. The proposed scheme is applicable to secure communication and information processing. Finally, numerical simulations are performed to demonstrate the effectivity and correctness of the considered technique by using MATLAB. [ABSTRACT FROM AUTHOR]

In the paper, we consider the problem of robust approximation of transfer Koopman and Perron–Frobenius (P–F) operators from noisy time-series data. In most applications, the time-series data obtained from simulation or experiment are corrupted with either measurement or process noise or both. The existing results show the applicability of algorithms developed for the finite-dimensional approximation of the deterministic system to a random uncertain case. However, these results hold only in asymptotic and under the assumption of infinite data set. In practice, the data set is finite, and hence it is important to develop algorithms that explicitly account for the presence of uncertainty in data set. We propose a robust optimization-based framework for the robust approximation of the transfer operators, where the uncertainty in data set is treated as deterministic norm bounded uncertainty. The robust optimization leads to a min–max type optimization problem for the approximation of transfer operators. This robust optimization problem is shown to be equivalent to regularized least-square problem. This equivalence between robust optimization problem and regularized least-square problem allows us to comment on various interesting properties of the obtained solution using robust optimization. In particular, the robust optimization formulation captures inherent trade-offs between the quality of approximation and complexity of approximation. These trade-offs are necessary to balance for the proposed application of transfer operators, for the design of optimal predictor. Simulation results demonstrate that our proposed robust approximation algorithm performs better than some of the existing algorithms like extended dynamic mode decomposition (EDMD), subspace DMD, noise-corrected DMD, and total DMD for systems with process and measurement noise. [ABSTRACT FROM AUTHOR]

Switched server systems are mathematical models of manufacturing, traffic and queueing systems that have being studied since the early 1990s. In particular, it is known that typically the dynamics of such systems is asymptotically periodic: each orbit of the system converges to one of its finitely many limit cycles. In this article, we provide an explicit example of a switched server system with exotic behaviour: each orbit of the system converges to the same Cantor attractor. To accomplish this goal, we bring together recent advances in the understanding of the topological dynamics of piecewise contractions and interval exchange transformations (IETs) with flips. The ultimate result is a switched server system whose Poincaré map is semiconjugate to a minimal and uniquely ergodic IET with flips. [ABSTRACT FROM AUTHOR]

We propose an extension of the Loewner framework to descriptor linear systems that preserves the DAE (differential algebraic equation) structure of the underlying system. More precisely, by means of post-processing the data, the behavior at infinity is matched. As it turns out, the conventional procedure constructs a reduced model by directly compressing the data and hence losing information at infinity. By transforming the matrix pencil composed of the E and A matrices into a generalized block diagonal form, we can separate the descriptor system into two subsystems; one corresponding to the polynomial part and the other to the strictly proper part of the transfer function. Different algorithms are implemented to transform the matrix pencil into block diagonal form. Furthermore, a data-driven splitting of the descriptor system can be achieved in the Loewner framework. Hence, the coefficients of the polynomial part can be estimated directly from data. Several numerical examples are presented to illustrate the theoretical discussion. [ABSTRACT FROM AUTHOR]

This study proposes a non-linear mathematical model for analysing the effect of COVID-19 dynamics on the student population in higher education institutions. The theory of positivity and boundedness of solution is used to investigate the well-posedness of the model. The disease-free equilibrium solution is examined analytically. The next-generation operator method calculates the basic reproduction number ( R 0 ) . Sensitivity analyses are carried out to determine the relative importance of the model parameters in spreading COVID-19. In light of the sensitivity analysis results, the model is further extended to an optimal control problem by introducing four time-dependent control variables: personal protective measures, quarantine (or self-isolation), treatment, and management measures to mitigate the community spread of COVID-19 in the population. Simulations evaluate the effects of different combinations of the control variables in minimizing COVID-19 infection. Moreover, a cost-effectiveness analysis is conducted to ascertain the most effective and least expensive strategy for preventing and controlling the spread of COVID-19 with limited resources in the student population., Competing Interests: The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (© 2023 The Author(s).)