Nonlinear Systems Research Articles

NON-ANALYTICAL DESIGN OF THE PI CONTROLLER OPTIMAL PARAMETERS FOR A CONTINUOUS LINE

The multiple motor drives are complex and coupled MIMO nonlinear systems. Due to the complexity of their mathematical models the development of effective control systems is quite complicated task. This paper presents the design of optimal control based on the quadratic optimality criterion for the central section of the continuous production line using soft computer methods when fuzzy model of the controlled system has been used. In this case, the proposed method demonstrates non-analytical design of the optimal parameters of PI controller with emphasis on minimal knowledge on the controlled system. The realized experimental measurements on a continuous line laboratory model confirmed the effectiveness and the good dynamic properties of the optimal continuous line controller and also its applicability to others MIMO nonlinear dynamic systems.

Impact of wind flow and global warming in the dynamics of prey-predator model

Prey-predator interaction is among the most crucial aspects of ecology. In this paper, the dynamics of a prey-predator system in which the prey and predator populations experience a birth rate reduction due to global warming and the wind flow effect on them are investigated. The system’s well-posedness before presenting findings about the existence of potential equilibrium points is studied. Conditions under which a different number of interior equilibria exist are also derived here. It is very important to know that when the positive equilibrium point is stable, this reflects positively on the ecosystem, its continuity and persistence. The conditions that have been identified are conditions that preserve the ecosystem from extinction when environmental influences such as global warming and wind speed are present. In addition, the local stability study around all equilibrium points and established the transversality criteria for the occurrence of transcritical bifurcations and Hopf bifurcations is conducted. The existence of different equilibrium points numerically by altering the prey’s global warming effect is illustrated , also showcasing the model’s dynamic character from a mathematical perspective. For significant amounts of global warming, its notice that the system exhibits periodic behavior. Thus, ecologists can approximate the parameters necessary to investigate and obtain such crucial findings regarding nonlinear systems with the aid of the current study.

Reduced Order Observer Based Synchronization and Secure Communication for a Class of Nonlinear Chaotic Systems

Reduced Order Observer Based Synchronization and Secure Communication for a Class of Nonlinear Chaotic Systems

Cases of PD-CFPID selector for frequency adjustment of integrated power grid

In current article an improved salp swarm algorithm (SSA) has been suggested. Likewise, the adjustable scaling-component is locked in to manage salp’s situation in time of the hunt system to limit arbitrary development salps. The upgraded salp swarm method combines random objection-based learning, multiple management, and simulated hardening in swarm brilliant-based metaheuristic salp swarm method, which rises the exploration and exploitation of the primary salp swarm method. To exhibit viability of the improved SSA, a bunch of multichannel test capabilities are locked in. A partially decentralized combined fuzzy proportional integral derivative (PD-CFPID) regulator is planned for integrated grid. A partially decentralized robust control plan is introduced to deal with a class of multi-inputs multi outputs (MIMO) non-square, linear framework different systems. Partially decentralized command is a control composition that lies between a completely decentralized structure and a wholly centralized one, and has the primacy of achieving comparable performance as an entirely centralized regulator but with simpler shape. The proposed flexible partially decoupled command scheme works in a straightforward and systematic way. Simulations show that the proposed partially decentralized control performs well for the nonlinear system, nearly equivalent to the multivariable control, and they achieve better performance indexes. Simulation outcomes appear that the stated method is simple and can reach better performance. The results of the PD-CFPID regulator are compare among CFPID and PID as many circumstances of the presented control outlook.

Autonomous vehicle tracking control for a curved trajectory

Recently, research about trajectory tracking of autonomous vehicles has significantly contributed to the development of autonomous vehicle technology, particularly with novel control methods. However, tracking a curved trajectory is still a challenge for autonomous vehicles. This research proposes a state feedback linearization with observer feedback to overcome some difficulties arising from such a path. This approach suits a complex nonlinear system such as an autonomous vehicle. This method also has been compared with the linear-quadratic regulator (LQR) method. So, the goal of this research is to improve the control system performance of autonomous vehicles that are stable enough to navigate a curved path. Moreover, the study shows that the developed control law can track the curved path and solve existing problems. However, improvements are still necessary for the vehicle's performance and robustness.

Adaptive synchronous sliding control for a robot manipulator based on neural networks and fuzzy logic

Robot manipulators have become important equipment in production lines, medical fields, and transportation. Improving the quality of trajectory tracking for robot hands is always an attractive topic in the research community. This is a challenging problem because robot manipulators are complex nonlinear systems and are often subject to fluctuations in loads and external disturbances. This article proposes an adaptive synchronous sliding control scheme to improve trajectory tracking performance for a robot manipulator. The proposed controller ensures that the positions of the joints track the desired trajectory, synchronize the errors, and significantly reduces chattering. First, the synchronous tracking errors and synchronous sliding surfaces are presented. Second, the synchronous tracking error dynamics are determined. Third, a robust adaptive control law is designed, the unknown components of the model are estimated online by the neural network, and the parameters of the switching elements are selected by fuzzy logic. The built algorithm ensures that the tracking and approximation errors are ultimately uniformly bounded (UUB). Finally, the effectiveness of the constructed algorithm is demonstrated through simulation and experimental results. Simulation and experimental results show that the proposed controller is effective with small synchronous tracking errors, and the chattering phenomenon is significantly reduced.

Modified Newton-NDSS Method for Solving Nonlinear System with Complex Symmetric Jacobian Matrices

Modified Newton-NDSS Method for Solving Nonlinear System with Complex Symmetric Jacobian Matrices

Particle swarm optimization based sliding mode control for maximum power point tracking in solar PV systems

One of the most significant renewable energies is photovoltaic (PV) energy, however it has a low efficiency due to its variable maximum power point that depends on weather conditions. In order to guarantee the system's best performance, intelligent algorithms can effectively track this point in real-time utilizing the maximum power point tracking (MPPT) method. Consequently, it is crucial to maximize the use of the solar energy that has been captured as well as the PV system's generated electricity. Variations in solar irradiance affects the amount of electric energy obtained from solar arrays. For efficient extraction of electricity from solar PV systems, MPPT algorithms are required. Sliding mode control (SMC) can be used in the control of nonlinear systems. However, the effectiveness of SMC can be improved by the choice of the sliding coefficients. In this paper, optimal search using particle swarm optimization (PSO) is used in the design of the sliding manifold. Results obtained via simulations showed that MPPT tracking efficiencies obtained for the PSO based SMC and the conventional SMC are 99.65% and 96.79% respectively. That means, PSO based SMC is 2.86% better than conventional SMC.

Life-span of solutions for a nonlinear parabolic system

Life-span of solutions for a nonlinear parabolic system

The switching dynamics of self-defocusing nonlinear coupled system with PT-symmetric Scarf II barrier potential

The switching dynamics of self-defocusing nonlinear coupled system with PT-symmetric Scarf II barrier potential

Backstepping synchronization control for four-dimensional chaotic system based on DNA strand displacement

Backstepping control is an important nonlinear control design method, which realizes the control of complex systems by constructing control law step by step, and has significant advantages for dealing with complex nonlinear systems. This article proposes a synchronization technique for four-dimensional chaotic systems using a combination of backstepping control method and DNA strand displacement technology. By relying on theoretical knowledge of DNA molecules, five basic chemical reaction modules such as trigger reaction, reference reaction, catalytic reaction, annihilation reaction and degradation reaction are given to construct a four-dimensional DNA chaotic system. On the basis of the relevant theory of chaotic dynamics, the constructed system is analyzed by Lyapunov exponent diagram and spectral entropy complexity algorithm, and the results come to the conclusion that the system reveals extremely complex and varied dynamic behaviors. Combining DNA strand displacement technology with backstepping control method, four controllers are developed to ensure that the trajectories of two homogeneous chaotic systems are synchronized. The numerical simulation results validate the feasibility and applicability of the proposed method. The method proposed in this paper may provide some references in the field of DNA molecular chaos synchronization control.

Discrete-Time Impedance Control for Dynamic Response Regulation of Parallel Soft Robots

Accurately controlling the dynamic response and suppression of undesirable dynamics such as overshoots and vibrations is a vital requirement for soft robots operating in industrial environments. Pneumatically actuated soft robots usually undergo large overshoots and significant vibrations when deactuated because of their highly flexible bodies. These large vibrations not only decrease the reliability and accuracy of the soft robot but also introduce undesirable characteristics in the system. For example, it increases the settling time and damages the body of the soft robot, compromising its structural integrity. The dynamic behavior of the soft robots on deactuation needs to be accurately controlled to increase their utility in real-world applications. The literature on pneumatic soft robots still does not sufficiently address the issue of suppressing undesirable vibrations. To address this issue, we propose the use of impedance control to regulate the dynamic response of pneumatic soft robots since the superiority of impedance control is already established for rigid robots. The soft robots are highly nonlinear systems; therefore, we formulated a nonlinear discrete sliding mode impedance controller to control the pneumatic soft robots. The formulation of the controller in discrete-time allows efficient implementation for a high-order system model without the need for state-observers. The simplification and efficiency of the proposed controller enable fast implementation of an embedded system. Unlike other works on pneumatic soft robots, the proposed controller does not require manual tuning of the controller parameters and automatically calculates the parameters based on the impedance value. To demonstrate the efficacy of the proposed controller, we used a 6-chambered parallel soft robot as an experimental platform. We presented the comparative results with an existing state-of-the-art controller in SMC control of pneumatic soft robots. The experiment results indicate that the proposed controller can effectively limit the amplitude of the undesirable vibrations.

Regularization based reweighted estimation algorithms for nonlinear systems in presence of outliers

Regularization based reweighted estimation algorithms for nonlinear systems in presence of outliers

Reliability for music-induced heart rate synchronization

Common inputs synchronize various biological systems, including human physical and cognitive processes. This mechanism potentially explains collective human emotions in theater as unintentional behavioral synchronization. However, the inter-subject correlation of physiological signals among individuals is small. Based on findings on the common-input synchronization of nonlinear systems, we hypothesized that individual differences in perceptual and cognitive systems reduce the reliability of physiological responses to aesthetic stimuli and, thus, disturb synchronization. We tested this by comparing the inter- and intra-subject Pearson’s correlation coefficients and nonlinear phase synchronization, calculated using instantaneous heart rate data measured while appreciating music. The results demonstrated that inter-subject correlations were consistently lower than intra-subject correlations, regardless of participants’ music preferences and daily moods. Further, music-induced heart rate synchronization depends on the reliability of physiological responses to musical pieces rather than mood or motivation. This study lays the foundation for future empirical research on collective emotions in theater.

Asymptotic tracking control for a class of uncertain nonlinear systems with output constraint

In this paper, we investigate the asymptotic tracking control for a class of strict-feedback nonlinear systems with unknown nonlinear functions and output constraint. The nonlinear transformation function-based system transformation approach is employed to convert the initial constrained system into an unconstrained one. To achieve the objective of asymptotic tracking, the tracking error is scaled by an exponential proportional function. Furthermore, to address the challenge of repetitive derivation of virtual control laws that occurs in the traditional design process of high-order backstepping methods, a first-order filter is applied. The designed control scheme guarantees that the system output will asymptotically track a predefined reference tracking trajectory while ensuring that the output constraint is not violated. Moreover, it is shown that the filter error will converge asymptotically to the origin. The effectiveness of the developed control strategy is verified through simulation results.

Event‐triggered practical tracking control via switching for a class of uncertain high‐order nonlinear systems with unknown input powers and control directions

AbstractThis article is devoted to the event‐triggered practical tracking control for a class of high‐order nonlinear systems with serious uncertainties. Remarkably, the serious uncertainties are greatly reflected from the unknown control directions and input powers which give rise to essential obstacles in control design and hence lead to incapability of the traditional control methods on this topic. To solve the control problem, a novel switching event‐triggered control scheme is proposed by a skillful incorporation of logic‐based switching mechanism into the event‐triggered one. Specifically, two pivotal events are smartly chosen to give the event‐triggered mechanism for the determination of the sampling times. In particular, one of the events is used to give the switching varying mechanism, by which the controller parameters are respectively switched in two groups of sequences which are carefully chosen for the compensation of serious uncertainties. Under the proposed switching event‐triggered mechanism, a state‐feedback controller is designed which guarantees that all the signals of the closed‐loop system are bounded while system output practically tracks the reference signal, along with a finite number of switching of controller parameters as well as the exclusion of the Zeno phenomenon. Finally, simulation examples are provided to validate the effectiveness of the proposed theoretical results.

Observer-based fault-tolerant control design for a class of sampled-data nonlinear systems with bounded disturbances

Observer-based fault-tolerant control design for a class of sampled-data nonlinear systems with bounded disturbances

Whole Body Control of Mobile Manipulators With Series Elastic Actuators for Cart Pushing Tasks.

Human-centered environments provide affordance for the use of two-handed mobile manipulators. Yet robots designed to function in and physically interact with such environments are not yet capable of meeting human users' requirements. This work proposes a whole body control framework of a two-handed mobile manipulator driven by series elastic actuators (SEAs) for cart pushing tasks. A whole body dynamic model for an integrated mobile platform and on-board arms is revealed, which takes into account the interaction forces with the cart. Then, the explicit force/position control of the mobile manipulator is performed. It enables the robot to interact dynamically with the environment while providing motion, i.e., the manipulators provide both output force control and motion control for pushing a cart. To cope with the highly nonlinear system dynamics and parameter variation of a SEA-driven mobile manipulator, this work proposes an adaptive robust controller based on a novel integral barrier Lyapunov function for cart pushing tasks by considering model uncertainty. The proposed controller enables the mobile manipulator to complete cart pushing tasks by regulating the position and output force of the mobile base and arms. The experimental results show the effectiveness of this approach in cart pushing tasks.

Zero‐sum game‐based H∞ optimal finite‐time prescribed performance control for nonlinear multiagent systems with actuator faults

AbstractThis article proposes an optimal leader‐follower consensus control protocol with finite‐time prescribed performance for nonlinear multiagent systems suffering from the actuator fault based on the zero‐sum game framework. First, to guarantee the specified performance of the system within a finite time frame, a novel error transformation function (ETF) is constructed. The ETF proposed in this paper can adjust the mapping range of error transformation to achieve better error convergence performance, thereby enhancing the flexibility of the controller design. Then, to compensate for the negative impact of actuator fault, an error‐related item is separated from the optimal performance index function to design an online fault estimator, which can obtain a better error estimation accuracy. Furthermore, to lessen the need for difficult‐to‐verify persistent excitation signal in adaptive dynamic programming algorithm, both historical and real‐time data are applied to adjust the updating law of neural network weight. Moreover, it demonstrates that the signals within the closed‐loop system are bounded and the expected finite‐time prescribed performance can be ensured in the presence of faults. Finally, a numerical example of multiple single‐link robots manipulator system is executed to validate the efficacy of the developed scheme.

The use of Hermite wavelet collocation method for fractional cancer dynamical system

Tumour is a very serious and dangerous health risk, which is defined as a mass or lump of tissue formalized by the aggregation of abnormal cells. In this paper, we have presented a comparative and chaotic investigation of tumour and effector cells using non-integer order tumour immune dynamical model. Also, we have looked at the interactions between different tumour cell populations and immunological composition using a model of a real-world medical research problem. Additionally, stability analysis of the proposed model is established with the help of fixed-point iteration. Further bifurcation diagrams, as well as phase portraits, have been used to study the proposed system numerically and to analyse its behaviour. For numerical simulations, we have used the Hermite wavelet operational matrix and Taufik-Atangana methods using Caputo fractional derivatives. models. The main objective of the paper is to convert nonlinear fractional systems into algebraic equations. Our findings will be valuable to biologists in cancer treatment.