Nonlinear Control Research Articles

A nonlinear control in αβ reference frame for single-stage three-phase grid-connected photovoltaic systems with an LCL-filter

A nonlinear control in αβ reference frame for single-stage three-phase grid-connected photovoltaic systems with an LCL-filter

A Novel Approach for Trajectory Tracking Control of an Under-Actuated Quad-Rotor UAV

A novel Udwadia-Kalaba approach for the trajectory tracking control of an under-actuated quad-rotor unmanned aerial vehicle (UAV) is presented. Compared to standard control approaches, the desired trajectories are treated as constraints called trajectory tracking constraints in this approach. Neither making any approximations or linearization of the nonlinear system nor imposing any a priori structure on the nature of the nonlinear controller, this methodology provides closedform nonlinear control. The control inputs satisfying the desired trajectory requirements can be obtained explicitly in compact closed form by solving Udwadia-Kalaba equation. Nonlinear dynamics modeling of a quad-rotor UAV is processed and a desired trajectory is given in this paper to illustrate this approach. The theoretical analysis and MATLAB simulation results verify the validity and efficiency of this approach. The real-time servo constraint forces are obtained conveniently and the quad-rotor UAV's movement meets the designed trajectory precisely.

Asynchronous Quantizer-Dependent Event-Triggered Control for Nonlinear Networked Control System With Observer-Based Controller

Asynchronous Quantizer-Dependent Event-Triggered Control for Nonlinear Networked Control System With Observer-Based Controller

Data-Driven Nonlinear Model Predictive Control for Power Sharing of Inverter-Based Resources

Data-Driven Nonlinear Model Predictive Control for Power Sharing of Inverter-Based Resources

Optimal nonlinear Fractional-Order Proportional-Integral-Derivative controller design using a novel hybrid atom search optimization for nonlinear Continuously stirred Tank reactor

Atom search optimization (ASO) algorithm derived from physics molecular dynamics. Lennard-Jones(L-J) and bond length potential of molecules are used to derive the model for optimization. In this paper, ASO is used for developing a nonlinear Fractional Order Proportional Integral Derivative controller (NL-FOPID) for Continuously Stirred Tank Reactor (CSTR). The convergence characteristics of ASO was improved by proposing a novel hybridization approach. The proposed hybridization approach called Hybrid ASO(HASO) guides the Atom search algorithm to optimally replace the atoms that goes out of the boundary of the search space. The designed algorithm is implemented to optimize various unimodal and multi model standard benchmark functions. From results obtained from this extensive simulation, it is indicated that proposed approach increased the convergence rate and also improved the optimization effort of conventional ASO. The proposed algorithm also tested with controller design for nonlinear CSTR. The NLPID and NL FOPID designed by HASO was better than conventional controllers found in the literature.

Cooperative learning‐based practical formation‐containment control with prescribed performance for heterogeneous clusters of UAV/USV

SummaryIn this paper, a new approach for formation‐containment control with prescribed performances is introduced for heterogeneous autonomous vehicles involving a cluster of leader unmanned aerial vehicles (UAVs) and follower unmanned surface vessels (USVs). We introduce a two‐layer distributed control system: The upper layer focuses on guiding the UAVs to form a scalable lattice while synchronizing their movement along a predefined path, and the second layer guides the USVs to enter the convex hull formed by the UAVs, ensuring collision‐free operation with static/dynamic objects. To prevent collisions and ensure lattice formation, a set of well‐defined bump functions are utilized in the design of the backstepping control algorithm. Managing virtual controls, we incorporate a nonlinear dynamic surface control (NDSC), while a universal barrier function enhances the convergence of formation tracking errors. Furthermore, each USV employs a cooperative adaptive learning neural network to handle uncertainties in heterogeneous vehicle models. Utilizing the Lyapunov theorem, the stability of the formation‐containment of UAV/USV is achieved, and all signals in the formation‐containment systems are semiglobal uniform ultimate bounded (SGUUB). A simulation example showcases the effectiveness of our proposed approach, highlighting contributions in collision avoidance, synchronization speed, and adaptive learning. Our work advances the heterogeneous formation‐containment literature towards more realistic scenarios with safety‐critical considerations amidst multiple layers of uncertainties and unknown parameters.

Complete Controllability of Nonlinear Neural Network Control Systems

Complete Controllability of Nonlinear Neural Network Control Systems

Time-delay feedback control of nonlinear forced vibration of graphene/piezoelectric sandwich nanoplates under a mechanical shock

In this study, the nonlinear forced vibration of graphene/piezoelectric sandwich nanosheets under mechanical impact was investigated. For the first time, linear (displacement and velocity) and nonlinear (displacement) time-delay proportional derivative (PD) controllers were applied to graphene/piezoelectric sandwich nanosheets, and the primary/secondary resonance under different time-delay parameters were analyzed. An approximate analytical solution for the nonlinear forced vibration control equation was obtained using the multiple scale perturbation method, and the stability of graphene/piezoelectric sandwich nanosheets under primary/secondary resonance conditions was discussed using the Ross Herwitz theorem. Finally, the results of this study were compared with those of other studies. The feasibility of the research methodology was demonstrated. On this basis, the research results indicate that linear displacement delay, nonlinear displacement delay, and velocity delay parameters can suppress the unsteady vibration characteristics of the main system. And comparing the linear and nonlinear displacement time-delay, it is found that the nonlinear displacement time-delay has a greater effect on the system. Specifically, the presence of nonlinear displacement time-delay changes the vibration characteristics of the curve from hard spring characteristics to soft spring characteristics. Comparison of displacement time-delay and velocity time-delay reveals that velocity time-delay gives better control over the system. In addition, the results show that the excitation amplitude, nonlocal parameters, and external voltage enhance the nonlinear characteristics of the system under the main and superharmonic resonance conditions before the time-delay control. Subharmonic resonance conditions, the system parameters make the vibration range wider. After the time-delay control, the influence of these three factors on the system vibration is significantly reduced for the three resonance conditions, especially for the non-local parameters. The results of the study can provide guidance for active control of time delay in different types of nanodevices for engineering applications.

Dynamic Nonlinear Droop Control (DNDC): A Novel Primary Control Method for DC Microgrids

Dynamic Nonlinear Droop Control (DNDC): A Novel Primary Control Method for DC Microgrids

Reservoir Computing for Drone Trajectory Intent Prediction: A Physics Informed Approach.

The design of accurate trajectory prediction algorithms is crucial to implement adequate countermeasures against drones with anomalous performances. Wrong predictions may cause high-false-positives that compromise safety in national infrastructures. In this article, a physics informed reservoir computing (PIRC) scheme for drone trajectory prediction is proposed. The approach is comprised of two main complementary learning algorithms that enhance the prediction and generalization capabilities: 1) a standard reservoir computing scheme for high-dimensional encoding exploitation and 2) a nonlinear control scheme that gives a physical feedback to the reservoir weights to ensure the prediction error is minimized. The nonlinear control scheme is modeled by the prediction error dynamics and a feedback linearization controller. Two different PIRC schemes are proposed which preserve the reservoir properties and enhance the prediction robustness. Lyapunov stability theory is used to verify the boundedness and convergence of the proposed algorithms. Simulation studies and comparisons are given to verify the proposed approach.

Efficient and robust nonlinear control MPPT based on artificial neural network for PV system

Efficient and robust nonlinear control MPPT based on artificial neural network for PV system

A novel nonlinear controller design of three-phase grid-tied photovoltaic system

A novel nonlinear controller design of three-phase grid-tied photovoltaic system

Computationally efficient trajectory tracking control of AUVs with nonlinear model predictive control using neural-based dynamics modeling

Computationally efficient trajectory tracking control of AUVs with nonlinear model predictive control using neural-based dynamics modeling

Nonlinear attitude tracking control for four-wheel-leg-vehicle with series active suspension

This study proposes the active disturbance rejection control (ADRC) algorithm to decouple the attitudes of the nonlinear active suspension system of a four-wheel-leg-vehicle (FWLV) system and solve its attitude-tracking problem. Current technologies control the attitude state variables of the vehicle typically at 0° to maintain the car body at a horizontal inclination. However, in complex terrains, the centre of gravity needs to be elevated to improve passability or reduce the centre of gravity to increase driving stability. During steering or braking, the pitch or roll angle of the body needs to be actively changed to improve the gripping force and reduce the possibility of rollover. This study considered the non-linear characteristics of shock absorbers and exploited the advantages of the active disturbance rejection technology, such as high tracking efficiency and small overshoot, to achieve stable tracking. The stability of the tracking attitude angle is analysed within the Lyapunov framework. Simultaneously, a linear suspension attitude-tracking control algorithm is designed as a linear quadratic regulator (LQR) for verifying the tracking control performance of the FWLV. The accuracies of the two algorithms were compared under stationary state, single-side sinusoidal, and random pavement conditions through simulations and vehicular tests. The results indicate that the stability of the attitude-tracking values by ADRC is better than that by the LQR. In addition, comparisons between the simulations and tests illustrated the validity of the active attitude-tracking system.

Hopf bifurcation control for the traffic flow model considering the tail light effect

The research on traffic congestion control has seen rapid development in recent years. Investigating the bifurcation characteristics of traffic flow and designing control schemes for unstable bifurcation points can offer new methods for alleviating traffic congestion. This paper focuses on studying the bifurcation characteristics and nonlinear control of traffic flow based on the continuous model and the taillight effect. Firstly, the traffic flow model is transformed into a stability model suitable for branching analysis through the use of the traveling wave transform. This transformation facilitates the analysis of stability that reflects unstable traffic characteristics such as congestion. Based on this stability model, the existence condition of Hopf bifurcation is proved and some bifurcation points of the traffic system are identified. Secondly, the congestion and stability mutation behaviors near equilibrium and branching points are studied to understand the formation mechanism of traffic congestion. Finally, control schemes are designed using Chebyshev polynomial approximation and stochastic feedback control to delay or eliminate unstable bifurcation points and relieve traffic congestion. This improved traffic flow model helps explain changes in system stability through bifurcation analysis and identify unstable bifurcation points. It can also effectively manage these points by designing a feedback controller. It is beneficial for controlling sudden changes in traffic system stability behavior and mitigating traffic congestion, with important theoretical significance and practical application value.

Robust Nonlinear Control with Estimation of Disturbances and Parameter Uncertainties for UAVs and Integrated Brushless DC Motors

Robust Nonlinear Control with Estimation of Disturbances and Parameter Uncertainties for UAVs and Integrated Brushless DC Motors

Mainardi smoothing homotopy method for solving nonlinear optimal control problems

This paper proposes a new type of smoothing homotopy method for solving general nonlinear optimal control problems via the indirect method, leveraging the Mainardi kernel as the smoothing kernel. The Mainardi kernel is firstly derived from the fundamental solution of the time-fractional diffusion-wave equation, representing a generalized form of the Gaussian kernel. By altering the fractional derivative order, the kernel can seamlessly switch between non-Gaussian and Gaussian forms. Then, parts of the two-point boundary value problems are convolved with the smoothing kernel, and the resulting surrogates are incorporated into the necessary conditions, replacing the terminal state and costate variables. The homotopy process is used for the smoothing parameter: increasing this parameter enhances the smoothing effect, simplifying the homotopy problems, while a parameter value of zero implies no smoothing, reverting to the original problems. Additionally, explicit expressions for the Mainardi kernel at specific derivative orders are derived, avoiding the inefficiencies associated with fractional derivatives. Simulation examples demonstrate that the proposed method offers significant advantages in flexibility and convergence compared to the traditional Gaussian smoothing homotopy method.

Sliding mode control for doubly fed induction generators system-based a wind turbine

This paper presents a contribution to the control of a Doubly-Fed Induction Generator (DFIG) integrated into a wind turbine using nonlinear control. The parameters involved in this study are the active and reactive powers exchanged between the DFIG stator and the grid. For this purpose, the modeling of the DFIG with the cascaded rectifier-inverter PWM structure was established. A numerical simulation of the DFIG, powered by the cascaded structure and controlled by the developed strategies, was performed. The simulation results show that the sliding mode control (SMC) provides a better transient response , with a shorter response time and reduced overshoot. Furthermore, it maintains good performance and stability in the presence of parameter variations such as resistance and inductance. The proposed control algorithm is also robust against parameter variations and the resulting dynamic response is fast. The simulation results confirm the validity of the mentioned advantages and the effectiveness of the proposed method. The effectiveness and robustness of the control technique were implemented and tested under MATLAB/Simulink environment.

Fuzzy Adaptive Approaches for Robust Containment Control in Nonlinear Multi-Agent Systems under False Data Injection Attacks

This study addresses the problem of fractional-order nonlinear containment control of heterogeneous multi-agent systems within a leader–follower framework, focusing on the impact of False Data Injection (FDI) attacks. By employing adaptive mechanisms and fuzzy logic, the suggested method enhances system resilience, ensuring reliable coordination and stability even in the presence of deceptive disturbances. To deal with these uncertainties, our controller makes use of interval type-II (IT2) fuzzy sets, and we create matrix equalities and inequalities to account for the asymmetry of Laplace matrices. Also, we use the Lyapunov functions for the stability analysis of our system. Lastly, we explain the numerical simulations for the effectiveness of our theoretical results, and these simulated examples are used to verify the effectiveness of our approach and designed model.

Nonlinear steering control law under input magnitude and rate constraints with exponential convergence

AbstractA ship steering control law is designed for a nonlinear maneuvering model whose rudder manipulation is constrained in both magnitude and rate. In our method, the tracking problem of the target heading angle with input constraints is converted into the tracking problem for a strict-feedback system without any input constraints. To derive this system, hyperbolic tangent ($$\tanh$$ tanh ) function and auxiliary variables are introduced to deal with the input constraints. Furthermore, using the feature of the derivative of $$\tanh$$ tanh function, auxiliary systems are successfully derived in the strict-feedback form. The backstepping method is utilized to construct the control input for the resulting cascade system. The proposed steering control law is verified in numerical experiments, and the result shows that the tracking of the target heading angle is successful using the proposed control law.