First-order System Research Articles

A Method for Robust Partial Quadratic Eigenvalue Assignment with Repeated Eigenvalues

Abstract A new method is proposed for robust partial quadratic eigenvalue assignment problem (RPQEAP) with repeated prescribed eigenvalues. We first derive a result on the solution of partial quadratic eigenvalue assignment problem, which leads to the partial Schur form of the close-loop system. Then by minimizing the normality departure of the partial Schur form of the close-loop system, we assign the prescribed eigenvalues step by step such that the close-loop system is as robust as possible. Our method allows the prescribed eigenvalues are repeated. Moreover, the proposed method does not use the unchanged eigenpairs of the open-loop system and avoids transforming the second-order control system to the first-order system. Numerical experiments show that the proposed method is efficient for solving the RPQEAP with repeated eigenvalues.

Drive-Response Synchronization for Second-Order Memristor-Based Delayed Neural Networks with Settling Time Estimation via Discontinuous Feedback Control

In this paper, the settling time estimation of synchronization issues for inertial memristive neural networks (IMNNs) with mixed time-varying delays is investigated. First, by using a new reduced order approach and introducing free-weighted coefficients η i and ξ i into variable transformation, the original second-order derivative system is transformed into a first-order differential system. Second, appropriate controllers are designed for IMNNs to guarantee the system synchronization in a settling time. In addition, the settling time is explicitly estimated and dependent on time delays and the initial values of the coupled system. Finally, two numerical examples are presented to demonstrate the effectiveness of the theoretical results.

Linear Quadratic Regulator for Delayed Systems Using the Hamiltonian Approach and Exact Closed-Loop Poles for First-Order Systems

Abstract We consider the linear quadratic regulator (LQR) for linear constant-coefficient delay differential equations (DDEs) with multiple delays. The Hamiltonian approach is used instead of an algebraic Riccati partial differential equation. Two coupled DDEs governing the state and control input are derived using the calculus of variations. This coupled system, with infinitely many roots in both left and right half-planes, defines a boundary value problem. Its left half-plane roots are the exact closed-loop poles of the controlled system. These closed-loop poles have not been used to compute the optimal feedback before. Here, the distributed delay kernel that yields exactly those poles is first computed using an eigenfunction expansion. Increasing the number of terms in the truncated expansion yields a highly oscillatory kernel. However, the oscillatory kernel's antiderivative converges to a piecewise smooth function on the delay interval plus a Dirac delta function at zero. Discontinuities in the kernel coincide with discrete delay values in the original DDE. Using this insight, a fitted piecewise polynomial kernel matches the exact closed-loop poles very well. The twofold contribution of the Hamiltonian approach is thus clarity on the form of the feedback kernel as well as the exact closed-loop poles. Subsequently, the fitted piecewise polynomial kernel can be used for a much simpler control calculation. The polynomial coefficients can be fitted by solving a few simultaneous linear equations. Two detailed numerical examples of the LQR for DDEs, one with two delays and one with three delays, show excellent results.

A Novel First-Order Fuzzy Rules-Based Forecasting System Using Distance Measures Approach for Financial Market Forecasting

The precise estimates about finance, atmospheric science, power sector, industries, agriculture, and other science help governments and institutions economically in making the relevant policies regarding import-export, demand, consumption, storage, and local industries. Due to the uncertainty and nondeterministic behavior of data series with respect to time, the foremost challenge is to develop and identify the practical method to handle the above stated complex issues. As an illustration, this study presented an analysis of a new fuzzy time-series (FTS) approach and comparison with traditional forecasting models for prediction of gram pulse production. Taking into consideration the theory of fuzzy sets, FTS, fuzzy rules, triangular membership functions, distance measures, and modified weighted average method, a robust and effective fuzzy rules-based methodology was developed for the prediction of time-series data regarding crop production and share prices. Conventional statistical forecasting methods such as Holt’s linear trend, Holt’s exponential trend, and Holt’s damped exponential trend models were also applied on time-series data for comparison. To identify the primacy of modeling and forecasting, the techniques of root mean squared error (RMSE) and mean absolute error (MAE) were used as a criterion. The numerical values of RMSE and MAE such as 106.51 and 74.8897 clearly demonstrated that the proposed fuzzy rules-based method is robust for forecasting of production and market share prices in the environment of uncertainty.

On the Jacobi Stability of Two SIR Epidemic Patterns with Demography

In the present work, two SIR patterns with demography will be considered: the classical pattern and a modified pattern with a linear coefficient of the infection transmission. By reformulating of each first-order differential systems as a system with two second-order differential equations, we will examine the nonlinear dynamics of the system from the Jacobi stability perspective through the Kosambi–Cartan–Chern (KCC) geometric theory. The intrinsic geometric properties of the systems will be studied by determining the associated geometric objects, i.e., the zero-connection curvature tensor, the nonlinear connection, the Berwald connection, and the five KCC invariants: the external force εi—the first invariant; the deviation curvature tensor Pji—the second invariant; the torsion tensor Pjki—the third invariant; the Riemann–Christoffel curvature tensor Pjkli—the fourth invariant; the Douglas tensor Djkli—the fifth invariant. In order to obtain necessary and sufficient conditions for the Jacobi stability near each equilibrium point, the deviation curvature tensor will be determined at each equilibrium point. Furthermore, we will compare the Jacobi stability with the classical linear stability, inclusive by diagrams related to the values of parameters of the system.

Bidirectional formation-involved consensus for uncertain multi-Lagrange systems under directed signed topology networks

Regarding complex behaviors of multi-agent systems (MAS), this paper proposes control protocols to reach a bidirectional formation-involved (FI) consensus for MAS. It primarily considers the multiple Lagrange systems (MLS) with uncertain parameters. And bipartite topology communication networks. Then, the validity of control protocols and the stability of the MLS are confirmed by determining the consistency convergence of the Lyapunov functions. With the stabilized MLS, the first-order linear system is adopted as a leader to provide trajectory guidance. With bipartite topology, MLS performs the FI complex behavior with pairwise tracking motion. The experiment part provides sufficient simulation examples that are selected to be consistent with the systems in the theoretical part.

On a Mixed FEM and a FOSLS with 𝐻−1 Loads

Abstract We study variants of the mixed finite element method (mixed FEM) and the first-order system least-squares finite element (FOSLS) for the Poisson problem where we replace the load by a suitable regularization which permits to use H − 1 H^{-1} loads. We prove that any bounded H − 1 H^{-1} projector onto piecewise constants can be used to define the regularization and yields quasi-optimality of the lowest-order mixed FEM resp. FOSLS in weaker norms. Examples for the construction of such projectors are given. One is based on the adjoint of a weighted Clément quasi-interpolator. We prove that this Clément operator has second-order approximation properties. For the modified mixed method, we show optimal convergence rates of a postprocessed solution under minimal regularity assumptions—a result not valid for the lowest-order mixed FEM without regularization. Numerical examples conclude this work.

A rate-of-injection model for predicting single and double injection with or without fusion.

Models used to predict the instantaneous injected fuel mass are of varied interest in automotive applications, including for providing inputs to CFD calculations or for engine control. While multiple injection strategies are now commonly used in diesel engines, the overall approach may be susceptible to injection fusion, which is defined as two successive injections that are partly or totally coupled due to the short time interval between each event. In this work, a new model to predict the instantaneous mass flow rate from a diesel injector is proposed based on the analytical solution of a first-order linear dynamic system exposed to an impulsion. Experiments are also conducted to quantify the main injection characteristics of a solenoid indirect-action injector under different injection pressures, backpressures and injection durations, representing a total of 33 different conditions. From these results, a model is proposed and validated against experimental data using a single injection strategy. Then, the model is enhanced to predict split injection with and without injection fusion. Successful comparisons are realized between the model and the experiment. The model is then used to successfully simulate a piezoelectric injector experiencing different levels of fusion available in the literature so as to illustrate the universality of the proposed approach.

Effects of adding arcs on the consensus convergence rate of leader-follower multi-agent systems

For a first-order leader-follower multi-agent system (MAS) with a directed graph as its interaction topology, the consensus convergence rate is determined by the algebraic connectivity (the smallest real part of the nonzero eigenvalues of the Laplacian matrix). Adding arcs to the followers is an effective approach to improve the consensus convergence rate of a leader-follower MAS. In this paper, the effects of adding arcs to the followers on the algebraic connectivity are investigated, when the followers’ interaction topology is a strongly connected directed graph. Our results include: (1) If arcs are added to the followers, then the algebraic connectivity increases if and only if the sum of entries of the Fiedler vector, corresponding to all the tails, is smaller than that of the heads; (2) For the case when a fixed number of arcs with a common head are added, the smaller the sum of entries of the Fiedler vector is, corresponding to all the tails, the larger the algebraic connectivity will be; (3) Each entry of the Fiedler vector, corresponding to the informed agents, is greater than that of the other types of followers; (4) If the Laplacian matrix of a leader-follower interaction topology can be divided into equal row sum blocks by layers, then the entries of the Fiedler vector in each layer are the same and the entries increase by layers. Thus the effects of adding arcs on algebraic connectivity can be determined by the layers of heads and tails of the arcs. Finally, the theoretical results are illustrated by numerical experiments.

Hygro-Elastic Coupling in a 3D Exact Shell Model for Bending Analysis of Layered Composite Structures

In this work, a 3D fully coupled hygro-elastic model is proposed. The moisture content profile is a primary variable of the model’s displacements. This generic fully coupled 3D exact shell model allows the investigations into the consequences arising from moisture content and elastic fields in terms of stresses and deformations on different plate and shell configurations embedded in composite and laminated layers. Cylinders, plates, cylindrical and spherical shells are analyzed in the orthogonal mixed curvilinear reference system. The 3D equilibrium equations and the 3D Fick diffusion equation for spherical shells are fully coupled in a dedicated system. The main advantage of the orthogonal mixed curvilinear coordinates is related to the degeneration of the equations for spherical shells to simpler geometries thanks to basic considerations of the radii of curvature. The exponential matrix method is used to solve this fully coupled model based on partial differential equations in the thickness direction. The closed-form solution is related to simply supported sides and harmonic forms for displacements and the moisture content. The moisture content amplitudes are directly applied at the top and bottom outer faces through steady-state hypotheses. The final system is based on a set of coupled homogeneous second-order differential equations. A first-order differential equation system is obtained by redoubling the number of variables. The moisture field implications are evaluated for the static analysis of the plates and shells in terms of displacement and stress components. After preliminary validations, new benchmarks are proposed for several thickness ratios, geometrical and material data, lamination sequences and moisture values imposed at the external surfaces. In the proposed results, there is clearly accordance between the uncoupled hygro-elastic model (where the 3D Fick diffusion law is separately solved) and this new fully coupled hygro-elastic model: the differences between the investigated variables (displacements, moisture contents, stresses and strains) are always less than 0.3%. The main advantages of the 3D coupled hygro-elastic model are a more compact mathematical formulation and lower computational costs. Both effects connected with the thickness layer and the embedded materials are included in the conducted hygro-elastic analyses.

Global asymptotic synchronization of inertial memristive Cohen–Grossberg neural networks with proportional delays

In this article, the global asymptotic synchronization (GAS) using inertial memristive Cohen-Grossberg neural networks (IMCGNNs) with proportional delays (PDs) as drive–response systems is studied. By utilizing differential inclusion theory (DIT) and appropriate variable transformation, the studied systems can be converted to first-order differential systems. Both the feedback controller and the adaptive controller are designed, which are easy to implement in hardware. By constructing Lyapunov functionals and using mean value inequality analysis skills, two GAS criteria of the studied systems are gained, which are embodied in the form of algebraic inequalities and are easy to verify. Ultimately, the numerical examples with simulations are applied to sustain the obtained consequences.

On One Representation of a Generalized Holomorphic Vector Via the Derivatives of Harmonic Functions

We study the theory of first-order elliptic systems and generalized holomorphic vectors. By using the Moisil–Teodorescu system, we construct a representation of generalized holomorphic vector via the derivatives of two harmonic functions of three independent variables.

Influences of the Order of Derivative on the Dynamical Behavior of Fractional-Order Antisymmetric Lotka–Volterra Systems

This paper studies the dynamic behavior of a class of fractional-order antisymmetric Lotka–Volterra systems. The influences of the order of derivative on the boundedness and stability are characterized by analyzing the first-order and 0<α<1-order antisymmetric Lotka–Volterra systems separately. We show that the order does not affect the boundedness but affects the stability. All solutions of the first-order system are periodic, while the 0<α<1-order system has no non-trivial periodic solution. Furthermore, the 0<α<1-order system can be reduced on a two-dimensional space and the reduced system is asymptotically stable, regardless of how close to zero the order of the derivative used is. Some numerical simulations are presented to better verify the theoretical analysis.

Heat transfer on non-Newtonian nanofluid flow with bioconvection aspects over rotating thin needle by variable viscosity

Microorganisms have been widely employed in the production of industrial and commercial goods like ethanol, waste-derived biofuels, etc. These bacteria create biodiesel, a possible sustainable source of energy. As a result, we must investigate flow dimensions and microorganisms’ transfer of mass properties to make their applications more successful, economical, and widespread for the benefit of humanity. Researching the impacts of bio-convection through the thin needle on Casson nanofluid is the purpose of that work. For the present issue, a variable magnetic field and temperature-dependent viscosity are assumed. Furthermore, nonlinear thermal radiation and activation energy aspects are considered. Nanofluid is referred to as the concentrated solution of antireflective coating nanoparticles and base fluid. Typically, nanoparticles are made of non-metals (carbon nanotubes, graphite) or metals (Al, Ag, Cu). for example, regular fluid is a permeable fluid, such as oil, ethylene glycol, water, etc. After replacing a unique optimum shooting method, multiple-order ordinary ones are reduced into a first-order system of ODEs. The conclusions are measured and organized in the form of tables and graphs by making use of the MATLAB bvp4c tool. The velocity of nanomaterials rises when the velocity ratio constant is increased.

Recursively Contextual Identity: A Variant Formulation of First- and Second-Order

The core cybernetics concept of first- and second-order has been interpreted in various ways, including as the cybernetics of cybernetics, as systems observed and observing, as epistemic and ethical modes, and as historical phases. In this paper, I describe an approach in which first-order systems are distinguished as contexts and second-order systems are distinguished by the self-reflective awareness of contextual participants. Seeking to analyze first- and second-order as a relational unity, I adopt Francisco Varela’s notation for complementarities, specifying their dialectics in the format: first/second. I use a performative exercise to constrain and enable the development of a variant formulation and then compare this variant with textual ones by Heinz von Foerster and Gordon Pask and with visual depictions by Gregory Bateson and Margaret Mead and by Ray Ison. Interpretively, first/second approaches that I examine might be distinguished in several respects, including by their relational domains and associated modes (observers of objects versus organisms in contexts), diagrammatics (1-in-2 versus 2-in-1), and challenges of a second-order stance (e.g., resisting objectification versus maintaining awareness of one’s coupled, transcontextual, and situated relations). This enquiry emphasizes an object-context distinction while also imbricating or making a complementarity of the first/second distinction, such that both modes—observers of objects and organisms in contexts—are discussed in terms of self-reference.

Research on stability of deepwater drilling riser system in freestanding mode

If a floating drilling platform encounters sudden bad sea conditions during deepwater operation, it is necessary to disconnect the drilling riser and the floating platform in an emergency. A buoyancy can structure is required to be installed at the top of the riser to ensure that the disconnected drilling riser can stand alone without instability accidents. According to the main structural characteristics and environmental conditions of the freestanding riser and the buoyancy can at the top of the riser, the compressive buckling stability of deepwater drilling riser in freestanding mode under the condition of insufficient top tension is studied in this paper, and the main problem is simplified to the buckling problem of an equal section beam under uniformly distributed axial load and top concentrated force. Firstly, the elastic stability control equation of the riser is established according to the mechanical balance, geometry and constitutive relationship of the riser's micro-element, and the equation as well as the corresponding top and bottom boundary conditions are made dimensionless. Secondly, the elastic stability equation of the micro-bending riser is linearized, the power series solution is obtained according to the perturbation theory, and the influence of different parameters on linear buckling is analyzed. Finally, we convert the elastic stability equation with large deflection into a two-point boundary value problem of the first-order differential equation system under the boundary conditions and two other given conditions. The shooting method program of the two-point boundary value problem including the changes of the top concentrated load and the distributed axial load parameters is developed by using MATLAB, and the calculation analysis is carried out, which reveals the rules of the buckling load and buckling shape after the buckling. The research results of this paper can provide scientific basis and technical guidance for the structure and size design of drilling riser and buoyancy can.

Optimal frequency control for wind power-integrated power system based on parameter identification

Frequency control based on wind power is required by the grid code for maintaining system inertia level as well as frequency stability. However, synchronous generator (SG)-emulated frequency control of wind power will result in a nadir and second dip of frequency trajectory after a disturbance, which may threaten system safety. Optimizing the frequency trajectory of system to improve the nadir and avoid second dip usually relies on grid-wide information. But the information is hardly perfectly acquired in advance for real power system since it may change anytime. To address these problems, an optimal frequency control method for wind power-integrated power system based on parameter identification is proposed. Frequency characteristics of wind power-integrated are firstly analyzed based on the common frequency theory. Then the control framework of proposed method to eliminate the nadir and second dip of frequency trajectory is introduced. To realize this framework, system equivalent parameters like inertia and damp coefficient are identified by the extended Kalman smoother algorithm after each disturbance. These parameters are furtherly utilized to shape the transfer function of wind power-integrated power system as a first-order system. Finally, the implementation steps of proposed method are presented. The effectiveness of proposed method is verified by case studies.

An Efficient Reinforcement Learning Approach to Optimal Control with Application to Biodiesel Production

Optimal control problems are one of the most challenging problems in optimization. This paper presents a new and efficient Reinforcement Learning approach to optimal control problems based on the Batch Q-learning algorithm. To improve the convergence of the RL algorithm, we use k-dimensional uniformity of advanced sampling procedures, namely employing Hamersley sequences (HSS). HSS is used to randomly sample the state variables and discrete controls from the action space for the RL optimal control problem. The Neural-fitted Q-iterative algorithm is applied to solve an optimal control problem for a first-order state dynamical system. A real-world application of optimal temperature profile determination for biodiesel production in a batch reactor is presented. We present the comparison of our HSS-RL algorithm with that of the maximum principle.

Estimation of dislocated phases and tunable orbital angular momentum using two cylindrical lenses.

A first-order optical system consisting of two cylindrical lenses separated by a distance is considered. It is found to be non-conserving of orbital angular momentum of the incoming paraxial light field. The first-order optical system is effectively demonstrated to estimate phases with dislocations using a Gerchberg-Saxton-type phase retrieval algorithm by making use of measured intensities. Tunable orbital angular momentum in the outgoing light field is experimentally demonstrated using the considered first-order optical system by varying the distance of separation between the two cylindrical lenses.

Dynamic Compensation of a Piezoelectric Accelerometer Obtained through a General Probabilistic Approach.

Dynamic compensation is the (partial) correction of the measurement signals for the effects due to bandwidth limitations of measurement systems and constitutes a research topic in dynamic measurement. The dynamic compensation of an accelerometer is here considered, as obtained by a method that directly comes from a general probabilistic model of the measurement process. Although the application of the method is simple, the analytical development of the corresponding compensation filter is quite complex and had been previously developed only for first-order systems, whilst here a second-order system is considered, thus moving from a scalar to a vector problem. The effectiveness of the method has been tested both through simulation and by a dedicated experiment. Both tests have shown the capability of the method of significantly improve the performance of the measurement system when dynamic effects are more prevalent than additive observation noise.