Showing papers on "Linearization published in 2023"

Enhanced P-Type Control: Indirect Adaptive Learning From Set-Point Updates

Abstract: In this article, an indirect adaptive iterative learning control (iAILC) scheme is proposed for both linear and nonlinear systems to enhance the P-type controller by learning from set points. An adaptive mechanism is included in the iAILC method to regulate the learning gain using input–output measurements in real time. An iAILC method is first designed for linear systems to improve control performance by fully utilizing model information if such a linear model is known exactly. Then, an iterative dynamic linearization (IDL)-based iAILC is proposed for a nonlinear nonaffine system, whose model is completely unknown. The IDL technique is employed to deal with the strong nonlinearity and nonaffine structure of the systems such that a linear data model can be attained consequently for the algorithm design and performance analysis. The convergence of the developed iAILC schemes is proved rigorously, where contraction mapping, two-dimensional (2-D) Roesser’s system theory, and mathematical induction are employed as the basic analysis tools. Simulation studies are provided to verify the developed theoretical results.

Observer-Based Backstepping Sliding Mode Control Design for Microgrids Feeding a Constant Power Load

Abstract: This article deals with the problem of controller design for dc microgrids that feed constant power loads. To design the proposed controller, first by the use of the exact feedback linearization approach, the linear model of Brunovsky's canonical representation of the system has been obtained to address the nonlinearity problem of the system. Then, the desired control technique is developed by a combination of sliding mode and backstepping control approaches in which a nonlinear disturbance observer is utilized to estimate the disturbance. The overall stability of the system is analyzed based on the Lyapunov approach. A suitable and practical sliding surface is one of the controller strengths that allow the bus voltage to track the reference voltage with high accuracy and fast transient response. Finally, to prove the mentioned claims, an experimental setup has been constructed and the proposed controller is implemented. The experimental results have been analyzed and error analysis is performed. The results confirm the superiority of the proposed controller compared to state-of-the-art controllers.

Event-Triggered Control for Markov Jump Systems Subject to Mismatched Modes and Strict Dissipativity

Abstract: In order to save network resources of discrete-time Markov jump systems, an event-triggered control framework is employed in this article. The threshold parameter in the event-triggered mechanism is designed as a diagonal matrix in which all elements can be adjusted according to system performance requirements. The hidden Markov model is introduced to characterize the asynchronization between the controller and controlled system. The effect of randomly occurring gain fluctuations is taken into account during the controller design. For the purpose of guaranteeing that the closed-loop system is stochastically stable and satisfies the strictly $(\mathcal {D}_{1},\mathcal {D}_{2},\mathcal {D}_{3})-\gamma -$ dissipative performance, sufficient conditions are constructed by employing the Lyapunov function and stochastic analysis. After linearization, the proposed controller gains are obtained by solving the linear matrix inequalities. Ultimately, a practical example of the dc motor device is used to illustrate the effectiveness of the proposed new design technique.

Data-Driven Bipartite Formation for a Class of Nonlinear MIMO Multiagent Systems

Abstract: The bipartite formation control for the nonlinear discrete-time multiagent systems with signed digraph is considered in this article, in which the dynamics of the agents are completely unknown and multi-input multi-output (MIMO). First, the unknown nonlinear dynamic is converted into the compact-form dynamic linearization (CFDL) data model with a pseudo-Jacobian matrix (PJM). Based on the structurally balanced signed graph, a distance-based formation term is constructed and a bipartite formation model-free adaptive control (MFAC) protocol is designed. By employing the measured input and output data of the agents, the theoretical analysis is developed to prove the bounded-input bounded-output stability and the asymptotic convergence of the formation tracking error. Finally, the effectiveness of the proposed protocol is verified by two numerical examples.

Physical-Model-Aided Data-Driven Linear Power Flow Model: An Approach to Address Missing Training Data

Abstract: Data-driven linear power flow (D-LPF) models are prevalent due to their excellent accuracy. Typically, D-LPF models rely on sufficient training data. However, in practice, the training data may be insufficient due to recording errors or limited measurement conditions. To address this practical and important issue, this letter presents a physical-model-aided data-driven linear power flow (PD-LPF) model, in which, physical model parameters are introduced to assist the data-driven training process, thereby avoiding unreasonable training results, and guaranteeing linearization accuracy for critical operating points with the maximum probability. The proposed method is applicable for both transmission and distribution systems. Compared to current LPF models, the PD-LPF model exhibits excellent accuracy and robustness under severe missing-data conditions.

Distributed Event-Triggered Bipartite Consensus for Multiagent Systems Against Injection Attacks

Abstract: This article studies fully distributed data-driven problems for nonlinear discrete-time multiagent systems (MASs) with fixed and switching topologies preventing injection attacks. We first develop an enhanced compact form dynamic linearization model by applying the designed distributed bipartite combined measurement error function of the MASs. Then, a fully distributed event-triggered bipartite consensus (DETBC) framework is designed, where the dynamics information of MASs is no longer needed. Meanwhile, the restriction of the topology of the proposed DETBC method is further relieved. To prevent the MASs from injection attacks, neural network based detection and compensation schemes are developed. Rigorous convergence proof that the bipartite consensus error is ultimately bounded is presented. Finally, the effectiveness of the designed method is verified through simulations and experiments.

Learning‐based model predictive control for improved mobile robot path following using Gaussian processes and feedback linearization

Abstract: This paper proposes a high‐performance path following algorithm that combines Gaussian processes (GP) based learning and feedback linearization (FBL) with model predictive control (MPC) for ground mobile robots operating in off‐road terrains, referred to as GP‐FBLMPC. The algorithm uses a nominal kinematic model and learns unmodeled dynamics as GP models by using observation data collected during field experiments. Extensive outdoor experiments using a Clearpath Husky A200 mobile robot show that the proposed GP‐FBLMPC algorithm's performance is comparable to existing GP learning‐based nonlinear MPC (GP‐NMPC) methods with respect to the path following errors. The advantage of GP‐FBLMPC is that it is generalizable in reducing path following errors for different paths that are not included in the GP models training process, while GP‐NMPC methods only work well on exactly the same path on which GP models are trained. GP‐FBLMPC is also computationally more efficient than the GP‐NMPC because it does not conduct iterative optimization and requires fewer GP models to make predictions over the MPC prediction horizon loop at every time step. Field tests show the effectiveness and generalization of reducing path following errors of the GP‐FBLMPC algorithm. It requires little training data to perform GP modeling before it can be used to reduce path‐following errors for new, more complex paths on the same terrain (see video at https://youtu.be/tC09jJQ0OXM).

Distributed and Collective Intelligence for Computation Offloading in Aerial Edge Networks

Abstract: Unmanned aerial vehicles (UAVs) with integrated computing platforms can be used to provide computing offloading services for ground user equipments (UEs) with limited local computing capabilities, especially in remote areas. In this paper, we focus on the task offloading in an aerial edge network (AEN) assisted by a UAV. We aim at minimizing the sum energy consumption of all UEs by the joint optimization of the task offloading decisions and the UAV position under the constraints of the latency and the total energy of UAV. The formulated optimization problem is a mixed-integer nonconvex problem and involves coupling of many optimization variables. To address this challenge, we first transform the original optimization problem into a linear convex optimization problem via reformulation linearization technology, and then the alternating direction method of multipliers (ADMM) algorithm is proposed to achieve the approximate optimal solution. Numerical results confirm that the proposed ADMM algorithm can effectively reduce the total of energy consumption of UEs and ensure the continuous operation of the UEs.

PI-Based Security Control Against Joint Sensor and Controller Attacks and Applications in Load Frequency Control

Abstract: This article addresses the proportional-integral (PI)-based security control issue of large-scale systems subject to randomly occurring joint attacks. Specifically, the considered cyber-attacks could happen in both sensor-to-observer and controller-to-actuator, and only partial data of sensors and controllers are randomly tampered with by malicious attacks due to energy limits. For the addressed problem, an observer-based PI controller is constructed by resorting to the compensation of randomly occurring joint attacks, which are modeled by two diagonal matrices combined with a set of stochastic variables. A sufficient condition only dependent on the local system dynamics as well as the local interconnected matrices is derived in the framework of the input-to-state stability (ISS) theory, and the desired gains of both the controller and the observer are obtained by the cone complementarity linearization (CCL) algorithm. Benefiting from the element matrix inequality, the developed design scheme satisfies the scalability requirement. In the end, the simulation test based on IEEE 39-bus power systems is seriously used to demonstrate the validity of the proposed control scheme.

Barycentric rational interpolation method for solving KPP equation

Abstract: In this paper, we seek to solve the Kolmogorov-Petrovskii-Piskunov (KPP) equation by the linear barycentric rational interpolation method (LBRIM). As there are non-linear parts in the KPP equation, three kinds of linearization schemes, direct linearization, partial linearization, Newton linearization, are presented to change the KPP equation into linear equations. With the help of barycentric rational interpolation basis function, matrix equations of three kinds of linearization schemes are obtained from the discrete KPP equation. Convergence rate of LBRIM for solving the KPP equation is also proved. At last, two examples are given to prove the theoretical analysis.

A Sufficient Condition for the Super-Linearization of Polynomial Systems

Abstract: We provide in this paper a sufficient condition for a polynomial dynamical system ˙ x ( t ) = f ( x ( t )) to be super-linearizable, i.e

A Linear Programming Method Based Optimal Power Flow Problem for Iraqi Extra High Voltage Grid (EHV)

Abstract: The objective of an Optimal Power Flow (OPF) algorithm is to find steady state operation point which minimizes generation cost, loss etc. while maintaining an acceptable system performance in terms of limits on generators real and reactive powers, line flow limits etc. The OPF solution includes an objective function. A common objective function concerns the active power generation cost. A Linear programming method is proposed to solve the OPF problem. The Linear Programming (LP) approach transforms the nonlinear optimization problem into an iterative algorithm that in each iteration solves a linear optimization problem resulting from linearization both the objective function and constrains. A computer program, written in MATLAB environment, is developed to represent the proposed method. The adopted program is applied for the first time on Iraqi 24 bus Extra High Voltage (EHV) network (400 kV). The required are data taken from the operation and control office, which belongs to the ministry of electricity.

A Novel Multi-Agent Model-Free Adaptive Control Algorithm for a Class of Multivehicle Systems with Constraints

Abstract: To solve the problem of longitudinal cooperative formation driving control of multiple vehicles, a model-free adaptive control algorithm with constraints (cMFAC) is proposed in this paper. In the cMFAC algorithm, a dynamic linearization technique with a time-varying parameter pseudo-gradient (PG) is used to linearize the multivehicle collaborative system. Then, a cMFAC controller is designed. The algorithm sets the input and output constraints at the same time to prevent the vehicle speed and other parameters from exceeding the specified range. The main advantage of the cMFAC algorithm is that the entire control process only needs the input and output data of each vehicle and can effectively handle the input and output constraints. In addition, the stability of the cMFAC method is verified through strict mathematical analysis, and its effectiveness is verified with semi-physical experiments based on a MATLAB/Simulink module and CarSim platform connection environment. It is worth noting that the proposed cMFAC controller is symmetric because the input cost function and PG cost function have symmetric and similar structures, and the forms of the two cost functions are the same.

Discontinuous Galerkin Approximation of the Fully Coupled Thermo-poroelastic Problem

Abstract: We present and analyze a discontinuous Galerkin method for the numerical modeling of the nonlinear fully coupled thermo-poroelastic problem. For the spatial discretization, we design a high-order discontinuous Galerkin method on polygonal and polyhedral grids based on a novel four-field formulation of the problem. To handle the nonlinear convective transport term in the energy conservation equation we adopt a fixed-point linearization strategy. We perform a robust stability analysis for the linearized semidiscrete problem under mild requirements on the problem’s physical parameters. A priori hp-version error estimates in suitable energy norms are also derived. A complete set of numerical simulations is presented in order to validate the theoretical analysis, to inspect numerically the robustness properties, and to test the capability of the proposed method in a practical scenario inspired by a geothermal problem.

A second-order modular grad-div stabilized scheme for the Darcy–Brinkman model

Abstract: Abstract In this article, a fully discrete modular grad-div stabilized finite element scheme for the Darcy–Brinkman equations are considered. This fully discrete scheme includes two steps: the first step is a combination of a mixed finite element approximation for space discretization, the second-order backward differentiation formula for temporal discretization, and extrapolated treatments in linearization for the nonlinear terms. Then, in the second step, a modular grad-div stabilized technique is applied, which can improve solution accuracy without increasing computational time for large stabilized parameters. Moreover, we show that the scheme is unconditionally stable and convergent with second-order accuracy with respect to time step. Finally, several numerical examples are provided to support the derived theoretical results, and demonstrate the efficiency of the presented scheme.

Linearizing Bilinear Products of Shadow Prices and Dispatch Variables in Bilevel Problems for Optimal Power System Planning and Operations

Abstract: This work presents a method for linearizing bilinear terms in the upper level of bilevel optimization problems when the bilinear terms are products of the primal and dual variables of the lower level. Bilinear terms of this form often appear in energy market optimization models where the dual variable represents the market price of energy and the primal variable represents a generator dispatch decision. Prior works have linearized such bilinear terms for specific problems. This work is the first to demonstrate how to linearize these terms in the most general case and the conditions required to perform the linearization for bilevel problems with integer or continuous variable in the upper level. The method is provided in an open source Julia module that allows researchers to write their bilevel programs in an intuitive fashion.

Guided Deep Learning Manifold Linearization of Porous Media Flow Equations

Abstract: Integrated reservoir studies for performance prediction and decision-making processes are computationally expensive. In this paper, we develop a novel linearization approach to reduce the computational burden of intensive reservoir simulation execution. We achieve this by introducing two novel components: (1) augment the state-space to yield a bi-linear system, and (2) an autoencoder based on a deep neural network to linearize physics reservoir equations in a reduced manifold employing a Koopman operator. Recognizing that reservoir simulators execute expensive Newton-Raphson iterations after each timestep to solve the nonlinearities of the physical model, we propose "lifting" the physics to a more amenable manifold where the model behaves close to a linear system, similar to the Koopman theory, thus avoiding the iteration step. We use autoencoder deep neural networks with specific loss functions and structure to transform the nonlinear equation and frame it as a bilinear system with constant matrices over time. In such a way, it forces the states (pressures and saturations) to evolve in time by simple matrix multiplications in the lifted manifold. We also adopt a "guided" training approach: our training process is performed in three steps: we initially train the autoencoder, then we use a "conventional" MOR (Dynamic Mode Decomposition) as an initializer for the final full training when we use reservoir knowledge to improve and to lead the results to physically meaningful output. Many simulation studies exhibit extremely nonlinear and multi-scale behavior, which can be difficult to model and control. Koopman operators can be shown to represent any dynamical system through linear dynamics. We applied this new framework to a two-dimensional two-phase (oil and water) reservoir subject to a waterflooding plan with three wells (one injector and two producers) with speed ups around 100 times faster and accuracy in the order of 1-3 percent on the pressure and saturations predictions. It is worthwhile noting that this method is a non-intrusive data-driven method since it does not need access to the reservoir simulation internal structure; thus, it is easily applied to commercial reservoir simulators and is also extendable to other studies. In addition, an extra benefit of this framework is to enable the plethora of well-developed tools for MOR of linear systems. This is the first work that utilizes the Koopman operator for linearizing the system with controls to the author's knowledge. As with any ROM method, this can be directly applied to a well-control optimization problem and well-placement studies with low computational cost in the prediction step and good accuracy.

Distributed Model-Free Adaptive Control for MIMO Nonlinear Multiagent Systems Under Deception Attacks

Abstract: The consensus tracking and containment control problems of multiple-input and multiple-output (MIMO) nonaffine nonlinear multiagent systems (MASs) are studied in this article under deception attacks using the distributed model-free adaptive control (DMFAC) method. An equivalent dynamic linearized data model of MIMO MASs’s distributed output vector containing deception signals is established using dynamic linearization technology. Then, a fully data-driven DMFAC strategy is designed just using I/O information instead of the knowledge of mathematical model. Furthermore, the boundedness of distributed output vector of MIMO-MASs under deception attacks is proved through the contraction mapping principle without employing global topology graph information. Finally, the validity of the proposed DMFAC scheme is verified through detailed simulations.

A higher order Galerkin time discretization scheme for the novel mathematical model of COVID-19

Abstract: In the present period, a new fast-spreading pandemic disease, officially recognised Coronavirus disease 2019 (COVID-19), has emerged as a serious international threat. We establish a novel mathematical model consists of a system of differential equations representing the population dynamics of susceptible, healthy, infected, quarantined, and recovered individuals. Applying the next generation technique, examine the boundedness, local and global behavior of equilibria, and the threshold quantity. Find the basic reproduction number $R_0$ and discuss the stability analysis of the model. The findings indicate that disease fee equilibria (DFE) are locally asymptotically stable when $R_0 < 1$ and unstable in case $R_0 > 1$. The partial rank correlation coefficient approach (PRCC) is used for sensitivity analysis of the basic reproduction number in order to determine the most important parameter for controlling the threshold values of the model. The linearization and Lyapunov function theories are utilized to identify the conditions for stability analysis. Moreover, solve the model numerically using the well known continuous Galerkin Petrov time discretization scheme. This method is of order 3 in the whole-time interval and shows super convergence of order 4 in the discrete time point. To examine the validity and reliability of the mentioned scheme, solve the model using the classical fourth-order Runge-Kutta technique. The comparison demonstrates the substantial consistency and agreement between the Galerkin-scheme and RK4-scheme outcomes throughout the time interval. Discuss the computational cost of the schemes in terms of time. The investigation emphasizes the precision and potency of the suggested schemes as compared to the other traditional schemes.

Numerical Simulation for Generalized Time-Fractional Burgers' Equation with Three Distinct Linearization Schemes

Abstract: In the present study, we examined the effectiveness of three linearization approaches for solving the time-fractional generalized Burgers' equation using a modified version of the fractional derivative by adopting the Atangana-Baleanu Caputo derivative. A stability analysis of the linearized time-fractional Burgers' difference equation was also presented. All linearization strategies used to solve the proposed non-linear problem are unconditionally stable. To support the theory, two numerical examples are considered. Furthermore, numerical results demonstrate the comparison of linearization strategies and manifest the effectiveness of the proposed numerical scheme in three distinct ways.

Feedback Linearization of a Grid-Tied Synchronverter

Abstract: One of the main limitations of the classic control of the syncronverter is that there are not enough degrees of freedom to allow the designer to set the desired dynamics of the injected active and reactive powers ( $p$ and $q$ , respectively). Moreover, the classic control also results in great coupling between $p$ and $q$ . To solve these issues, a controller based on the feedback linearization technique is presented in this article. The proposed strategy allows the designer to set the dynamics of $p$ and $q$ , and also reduces the coupling between them to negligible levels. This controller also reproduces the behavior of the classic controller in steady state, modifying both $p$ and $q$ to changes in the grid frequency and point of common coupling voltage, respectively.

Propagating input uncertainties into parameter uncertainties and model prediction uncertainties—A review

Abstract: A review of uncertainty quantification techniques is provided for a variety of situations involving uncertainties in model inputs (independent variables). The situations of interest are divided into three categories: (i) when model prediction uncertainties are quantified based on uncertainties in uncertain inputs, (ii) when parameter estimate uncertainties are calculated by propagation of uncertainties from measured inputs and outputs, and (iii) when model prediction uncertainties are quantified based on corresponding uncertainties in measured inputs and uncertain parameter estimates. For all three situations, linearization-based and Monte Carlo-based techniques are reviewed and details for their corresponding algorithms are presented. Recommendations are provided on which uncertainty quantification techniques are best for different types of chemical engineering models based on the amount of input uncertainty and nonlinearity over the range of plausible input and parameter values.

Exact Feedback Linearization Control of Three-Level Boost Converters

Abstract: Three-level boost dc–dc converters present several advantages in comparison with conventional boost converters, such as reduced switching losses, lower voltage ratings for the diodes and switches, and smaller size of reactive components. The topology requires three voltage levels at the output, therefore, replacing the output capacitor of the traditional boost converter with two capacitors and a midpoint. However, due to component tolerances and/or current flowing through the midpoint, output capacitors voltages become unbalanced, leading to converter malfunctioning or destruction. To overcome this issue, an exact feedback linearization control strategy is proposed, for which an implementation with minimum sensors is obtained. Analyses of its performance at different input voltages and of its robustness against component variations are included. Simulation results are provided, showing a comparison of the proposal with a conventional control strategy and its steady-state performance with nonlinear loads. The proposed control strategy was implemented in a low-cost microcontroller unit and, experimental verification is included.