Adaptive Control Law Research Articles

Leader‐following consensus control of second‐order nonlinear multi‐agent systems with applications to slew rate control

AbstractThis paper addresses the distributed leader‐following consensus control of second‐order strict‐feedback nonlinear multi‐agent systems. By employing mean value theorem, variable separation technique, and backstepping methodology, a fully distributed adaptive control law is designed using only local relative state information. The proposed control law solves the leader‐following consensus problem for any directed communication graph that contains a spanning tree with the root node being the leader agent. The application to hovercraft slew rate control system is given to verify the effectiveness of the theoretical results.

Distributed Optimal Formation for Uncertain Euler-Lagrange Systems With Collision Avoidance

Based on the framework of distributed optimization algorithms, this brief studies distributed optimal formation behaviors of multi-agent systems modeled as a group of uncertain Euler-Lagrange systems with collision avoidance. Assume that each agent can only obtain measured position-based gradient value of a local objective function. By integrating a modified distributed optimization algorithm and an adaptive control law, the proposed distributed optimal formation controllers can lead the positions of agents asymptotically converging to the optimal solution to the total objective function with collision avoidance. The proposed design is verified by a numerical example of mobile relays for communication.

Adaptive Fuzzy Tracking Control of Uncertain Nonlinear Multi-Agent Systems with Unknown Control Directions and a Dead-Zone Fault

In this paper, a class of uncertain nonlinear multi-agent systems with unknown control directions and a dead-zone fault is addressed, where unknown control gains exist in each subsystem. In terms of the approximation characteristic of a fuzzy logic system, it is used to approximate uncertain nonlinear dynamics, and then the relevant adaptive control laws are designed. Considering the presence of unknown control directions and a dead-zone fault, the Nussbaum gain function technique is introduced to design the intermediate control law and the adaptive fuzzy control law. A theoretical analysis shows that the tracking control problem of the given multi-agent systems can be effectively solved through the application of the proposed adaptive fuzzy control law and the tracking errors can converge to a small neighborhood of zero through an adjustment of the relevant parameters. Finally, the effectiveness of the theoretical analysis results is verified by two simulation cases.

A universal error transformation strategy for distributed event-triggered formation tracking of pure-feedback nonlinear multiagent systems with communication and avoidance ranges

A universal error transformation method is proposed for designing a distributed event-triggered formation tracker with preserved network connectivity and collision avoidance for multiple pure-feedback nonlinear multiagent systems connected in a directed network. It is assumed that the communication and avoidance ranges of agents are heterogeneous and that all nonaffine nonlinear functions are unknown. The primary contribution of this study is to establish a universal nonlinear transformation of relative output errors among agents for dealing with the initial network interaction, collision prevention, and predefined-time tracking performance problems in a fully distributed manner. To this end, nonlinear relative output errors among agents are designed using performance functions dependent on communication and avoidance ranges. Local event-triggered adaptive control laws are recursively designed using nonlinear relative output errors and neural networks. It is proved that the boundedness of the presented nonlinear errors ensures the achievement of network interaction preservation, collision prevention, and formation tracking with predefined-time convergence. Furthermore, the existence of a minimum inter-event time is established for local event-triggered control laws. Finally, the effectiveness of the proposed theoretical strategy is validated by simulation examples.

RBF Neural Network Sliding Mode Control for Passification of Nonlinear Time-Varying Delay Systems with Application to Offshore Cranes.

This paper is devoted to studying the passivity-based sliding mode control for nonlinear systems and its application to dock cranes through an adaptive neural network approach, where the system suffers from time-varying delay, external disturbance and unknown nonlinearity. First, relying on the generalized Lagrange formula, the mathematical model for the crane system is established. Second, by virtue of an integral-type sliding surface function and the equivalent control theory, a sliding mode dynamic system can be obtained with a satisfactory dynamic property. Third, based on the RBF neural network approach, an adaptive control law is designed to ensure the finite-time existence of sliding motion in the face of unknown nonlinearity. Fourth, feasible easy-checking linear matrix inequality conditions are developed to analyze passification performance of the resulting sliding motion. Finally, a simulation study is provided to confirm the validity of the proposed method.

Adaptive Neural Tracking Control for Nonstrict-Feedback Nonlinear Systems with Unknown Control Gains via Dynamic Surface Control Method

This paper addresses the tracking control problem of nonstrict-feedback systems with unknown control gains. The dynamic surface control method, Nussbaum gain function control technique, and radial basis function neural network are applied for the design of virtual control laws, and adaptive control laws. Then, an adaptive neural tracking control law is proposed in the last step. By using the dynamic surface control method, the “explosion of complexity” problem of conventional backstepping is avoided. Based on the application of the Nussbaum gain function control technique, the unknown control gain problem is well solved. With the help of the radial basis function neural network, the unknown nonlinear dynamics are approximated. Furthermore, through Lyapunov stability analysis, it is proved that the proposed control law can guarantee that all signals in the closed-loop system are bounded and the tracking error can converge to an arbitrarily small domain of zero by adjusting the design parameters. Finally, two examples are provided to illustrate the effectiveness of the proposed control law.

Hybrid extended state observer-based integral sliding mode control of the propulsion for a hydraulic roofbolter

For a propulsion system with dead-zone, time-varying parameters and sudden disturbances, the existing hybrid control methods based on sliding-mode and extended state observer still face challenges such as chattering, high-frequency switching of controller, and low anti-disturbance ability. To solve the problems, this paper proposes an integral sliding-mode controller based on hybrid extended state observer (ISM-HESO), which includes a transition process, an Observer unit, a sliding-mode control (SMC) unit and a parameter adaptation law. Taking dead-zone, time-varying parameters and disturbances into consideration, the propulsion system of a hydraulic roofbolter is modeled after compensating for dead-zone. Based on this, a transition process is introduced to transform the reference propulsion of step input into a continuous one, with the purpose of improving the response speed and avoiding overshoot. Then, in Observer unit, a hybrid extended state observer is designed to effectively estimate the dynamic disturbances. SMC unit provides a continuous and effective sliding-mode control law for the propulsion system, with the purpose of speeding up the response and eliminating the chattering. In SMC unit: (1) A novel integral sliding-mode surface is presented to eliminate the negative effect of disturbance estimation error and avoid high-frequency switching of ISM-HESO; (2) A novel sliding-mode reaching law with a Saturation function is developed, with the purpose of enhancing robustness, improving reaching speed and eliminating chattering; (3) An adaptive sliding-mode control law is presented based the above two strategies, which aims to provide an effective and continuous control signal. Moreover, a parameter adaptation law is designed to tune the estimations of time-varying parameters and improve control performance. Finally, the effectiveness of ISM-HESO is verified by comparative experiments. The experimental results show that ISM-HESO has better dynamic and steady-state performance.

Simulated and Experimental Verification of Fuel-Efficient Truck Platooning With Model Predictive Control Under Grade and Traffic Disturbances

Abstract Truck platooning closely regulates gaps between heavy-duty freight trucks to exploit slipstream effects for reducing aerodynamic friction—and therefore reducing engine effort and fuel usage. Currently deployed applications of this have been classically actuated through error-correcting PID feedback loops with connectivity amongst trucks in a fleet to form a connected and adaptive cruise control law that attenuates disturbances between trucks to maintain tolerable gaps. Typically, performance of such systems is challenged by difficult, albeit not uncommon, transients when under traffic conditions and when under road grade variations. Because of this, such platooning control requires attentive and trained drivers to disengage the adaptive cruise control—which limits its potentials for reducing driver load. More advanced longitudinal motion planning under predictive optimal control can push for higher levels of autonomy under a larger range of scenarios, as well as improve fuel efficiency. Here, model predictive control for fuel-performant truck platooning is vetted in both simulation and experimentation for representative traffic and road grade routes. Several approaches are used exploiting physics-based models with and without the powertrain system, and neural network-encoded models. The fuel benefits of aerodynamic platooning are isolated from the more general eco-driving approach, which already provides fuel benefit to trucks by smartly selecting truck velocity. Results from simulation and validation in experimentation are presented—showing up to 6% benefit in fuel economy through eco-driving and an additional 3% achievable through platooning. Observed losses in fuel performance are explained by energy dissipation from braking.

Delay-Adaptive Predictor Feedback Control of Reaction–Advection–Diffusion PDEs With a Delayed Distributed Input

We consider a system of reaction–advection–diffusion partial differential equation (PDE) with a distributed input subject to an unknown and arbitrarily large time delay. Using Lyapunov technique, we derive a delay-adaptive predictor feedback controller to ensure the global stability of the closed-loop system in the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$L^2$</tex-math></inline-formula> sense. More precisely, we express the input delay as a 1-D transport PDE with a spatial argument leading to the transformation of the time delay into a spatially distributed shift. For the resulting mixed transport and reaction–advection–diffusion PDE system, we employ a PDE backstepping design and certainty equivalence principle to derive the suitable adaptive control law that compensates for the effect of the unknown time delay. Our controller ensures the global stabilization in the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$L^2$</tex-math></inline-formula> sense. Our result is the first delay-adaptive predictor feedback controller with a PDE plant subject to a delayed distributed input. The feasibility of the proposed approach is illustrated by considering a mobile robot that spread a neutralizer over a polluted surface to achieve efficient decontamination with an unknown actuator delay arising from the noncollocation of the contaminant diffusive process and the moving neutralizer source. Consistent simulation results are presented to prove the effectiveness of the proposed approach.

A Virtual Linkage-Based Dual Event-Triggered Formation Control Strategy for Multiple Amphibious Spherical Robots in Constrained Space With Limited Communication

Aiming to deal with the formation maintaining in constrained space for a group of robots, this paper proposed a virtual linkage-based dual event-triggered formation control strategy. Based on the idea of virtual linkage and event-trigger, a dual event trigger is proposed to guarantees robot formation keeping and collision avoidance. Unlike classical event-triggered control, the control strategy triggered by the detection of the state of virtual linkage determine the motion mode of the robot, which can reduce the control updating and eliminate continuous communication between robots. Moreover, an adaptive control law inspired by the motion of a simple pendulum was developed to adjust the given angle of the virtual linkage in the case that the multi-robot system pass the restricted region. Finally, to validate the performance of the formation control strategy, simulations and a series of experiments in an indoor swimming pool are presented. The results demonstrate the robustness and feasibility of the proposed formation control strategy.

Lag Synchronization of Noisy and Nonnoisy Multiple Neurobiological Coupled FitzHugh-Nagumo Networks with and without Delayed Coupling.

This paper presents a methodology for synchronizing noisy and nonnoisy multiple coupled neurobiological FitzHugh–Nagumo (FHN) drive and slave neural networks with and without delayed coupling, under external electrical stimulation (EES), external disturbance, and variable parameters for each state of both FHN networks. Each network of neurons was configured by considering all aspects of real neurons communications in the brain, i.e., synapse and gap junctions. Novel adaptive control laws were developed and proposed that guarantee the synchronization of FHN neural networks in different configurations. The Lyapunov stability theory was utilized to analytically derive the sufficient conditions that ensure the synchronization of the FHN networks. The effectiveness and robustness of the proposed control laws were shown through different numerical simulations.

Robust Adaptive Path-Tracking Control of Autonomous Ground Vehicles With Considerations of Steering System Backlash

Backlash phenomena have haunted control engineers for ages. Concerning the ground vehicle path-tracking control system design, the steering system's backlash attribute is often overlooked. If not properly compensated, the backlash nonlinearity tends to provoke unfavorable consequences including erroneous positioning of the road-wheel steering angle, response chattering, limit-cycle-like oscillations, and delays. This paper pioneers to employ an adaptive inverse controller to offset the dynamics of the steering system's backlash. Overall, the path-following objective is accomplished via a novel trio-loop control architecture, which decomposes the tracking objectives into kinematic, vehicular lateral dynamics, and steering backlash compensation sub-levels. All adaptive control laws are robustified by means of sigma modification. Hardware-in-the-loop experimental results are presented to demonstrate the superiorities of the proposed solution.

Attitude tracking control for fractionated spacecraft with actuator failures under adaptive event-triggered strategy

In this paper, two event-triggered algorithms are investigated to reduce the consumption and occupation of system resources for attitude tracking control of spacecraft system under external disturbances, model uncertainties, actuator failures, and limited communication. The first robust controller is designed with the triggering condition based on a time-based exponential function that has a dynamically decreasing trigger threshold. To improve the first controller, the second controller with the adaptive triggering condition based on a time-based exponential function is established to facilitate the realization of a comprehensive combination of feedback compensation mechanism and event-triggered control theory. It follows from the theoretical analysis that asymptotic convergence and Zeno-free are achieved under the proposed controller. Simulation results are provided to verify the effectiveness of the developed adaptive event-triggered fault-tolerant control laws.

Observer-based adaptive neural network control design for projective synchronization of uncertain chaotic systems

This paper addresses the design of an observer-based adaptive neural network chaos synchronization scheme for a general class of uncertain chaotic systems. The controller consists of an adaptive neural network control law and an extended state observer. The parameterization of the designed extended observer and the sufficient stability conditions are derived in the light of the singular perturbation theory. The extended observer is incorporated into the controller to reconstruct the synchronization error vector as well as to estimate the error between an ideal control law and the actual control. These estimated error signals are utilized in the adaptation mechanism of the neural network weight vector. In the presented chaos synchronization method, the knowledge of the models of the master–slave systems is not required and the controller only needs the projective synchronization error for its implementation. Numerical simulations are performed along with a comparative study to demonstrate the efficiency and effectiveness of the suggested chaos synchronization approach.

Fuzzy-Based Adaptive Dynamic Surface Control for a Type of Uncertain Nonlinear System with Unknown Actuator Faults

In this paper, the adaptive control problem of a type of uncertain nonlinear system is addressed. The system discussed includes unknown nonlinear functions, uncertain nonlinear dynamics, and unknown actuator faults. Based on the fuzzy logic systems and dynamic surface control technique, an adaptive fuzzy control law is designed to solve the tracking control problem. In control law design, fuzzy logic systems are utilized to approximate uncertain nonlinear functions, and with the help of the dynamic surface control technique, the problem of the “explosion of complexity” can be overcome. Through stability analysis, it is confirmed that all of the signals in the closed-loop system are semi-global bounded, and the convergence of the tracking error to the specified small neighborhood of the origin can be ensured by adjusting the control law parameters. Finally, the effectiveness of the proposed control law is verified by simulation examples.

Data driven adaptive robust attitude control for a small size unmanned helicopter

In this paper, the data driven based control design problem for a small size unmanned helicopter is investigated. The helicopter is subjected to the effects associated with modeling uncertainties and unknown external disturbances. A new model free robust adaptive attitude control law is proposed with the combination of the model-free-adaptive-control (MFAC) design, the immersion and invariance (I&I) approach, and the super-twisting technique. Different from the most existing linear or nonlinear model-dependent control designs for unmanned helicopters, the proposed control strategy requires very less model knowledge. The controller depends mainly on the input and output data of the helicopter, and no boundedness knowledge of the unknown disturbances is required. Stability of the closed-loop system has been proved. Real-time flight experiments have been performed on the self-developed helicopter testbed only with the available feedback data of the helicopter. The experimental results have validated the good robustness of the proposed control methodology.

Control Algorithm for Trajectory Tracking of an Underactuated USV under Multiple Constraints

A trajectory tracking control method based on the cascade of optimal guidance and adaptive control laws was proposed for trajectory tracking of an unmanned surface vehicle under multiple motion constraints including an ocean current disturbance environment. Considering the velocity and acceleration constraints, angular velocity, and angular acceleration constraints in guidance law design, motion planning was conducted with three degrees of freedom using a motion model and predictive control, while optimal guidance law was designed through a rolling optimization strategy to stabilize the position error under multiple constraints. Moreover, the stability of the guidance law was proven. In control law design, an adaptive observer was introduced to estimate and compensate for ocean current disturbance, which affected the precision of control. The course and velocity control laws were designed with the adaptive sliding mode control technology to stabilize the course angle and longitudinal velocity errors; the stability of these control laws was further proven. Based on the system design, the stability of the entire closed-loop control system was proven with the cascade system and Lyapunov theory. Theoretical analysis and simulation experiments demonstrated the effectiveness and advancement of the proposed algorithm.

Soft Sensor Modeling Method Based on Improved KH-RBF Neural Network Bacteria Concentration in Marine Alkaline Protease Fermentation Process.

Marine alkaline protease (MAP) fermentation is a complex multivariable, multi-coupled, and nonlinear process. Some unmeasured parameters will affect the quality of protease. Aiming at the problem that some parameters are difficult to be detected online, a soft sensing modeling method based on improved Krill Herd algorithm RBF neural network (LKH-RBFNN) is proposed in this paper. Based on the multi-parameter RBFNN model, the adaptive RBF neural network algorithm and control law are used to approximate the unknown parameters. The adaptive Levy flight strategy is used to improve the traditional Krill Herd algorithm, improve the global search ability of the algorithm, and avoid falling into local optimization. At the same time, the location update formula of Krill Herd algorithm is improved by using the calculation methods of similarity and agglomeration degree, and the parameters of adaptive RBFNN are optimized to improve its over correction and large amount of calculation. Finally, the soft sensing prediction model of bacterial concentration and relative active enzyme in map process based on LKH-RBFNN is established. The root mean square error and maximum absolute error of this model are 0.938 and 0.569, respectively, which are less than KH-RBFNN and PSO-RBFNN prediction models. It proves that the prediction error of LKH-RBFNN model is smaller and can meet the needs of online prediction of key parameters of map fermentation.

Concurrent Learning-Based Adaptive Control of an Uncertain Robot Manipulator With Guaranteed Safety and Performance

This article investigates the tracking problem of an uncertain <inline-formula> <tex-math notation="LaTeX">$n$ </tex-math></inline-formula>-link robot manipulator with guaranteed safety and performance. To tackle parametric uncertainties, the torque filtering-augmented concurrent learning (CL) method is introduced for online identification of the unknown system without requirements of joints acceleration. By using CL, the parameter convergence is guaranteed by exploiting the current and historical data simultaneously. This technique enjoys practicability compared with common methods that need to incorporate external noises to satisfy the persistence of excitation condition for the parameter convergence. Based on the estimated model, we design a barrier Lyapunov function (BLF)-based adaptive control law by the backstepping technique and Lyapunov analysis. By ensuring the boundness of the BLF, the system output and the tracking error are proved to lie in the safety set and performance set, respectively. Numerical simulation results and experiment tests validate the proposed strategy.

Study of adaptive control law of overhead crane using its model

Nowadays, cargo cranes are widely used in various areas of industries. Many of cranes use suspended load fastening, which is associated with load swinging during transportation. Load swinging is most often caused by acceleration or deceleration of the crane trolley, less often it occurs due to external disturbances, such as wind. One of the key directions of the development of this kind of cranes is the development of an automated control system that can dampen pendular oscillations of the load. At present, a considerable number of control systems have been developed, but most of them require preset adjustment of specific parameters of the transported load. The task of this study is to develop and debug a control algorithm using a model of an overhead crane of previously developed adaptive control law that can provide fine positioning and damping of load oscillations under the current parametric uncertainty. The study using the pilot plant will allow us to determine and analyze the features of the implementation of the control law before its application for industrial cranes. An adaptive control law is studied using the model of overhead crane under conditions of a current parametric uncertainty of the load and external disturbances. This control method is based on an adaptive control approach with an identifier and an implicit reference model using “simplified” adaptation conditions. A previously developed adaptive control law for an overhead crane is described. An experimental model of an overhead crane is described. An algorithm for adaptive control of an overhead crane model has been developed. The first experimental studies of the proposed control method have been carried out. They confirm its performance in real conditions. The results of experimental tests have shown the effectiveness of the adaptive control law. The system ensures fine motion of the load in a short period of time, dampens the pendular oscillations of the load during acceleration and deceleration of the trolley, as well as during external disturbances. The adaptive control law allows you to move the load to the designated position and dampen the pendular oscillations with minimal preset adjustment of the control system. Since the identification of parameters occurs at the current time, the changes of the parameters of the load and the length of suspension do not affect the quality of control.