Nonlinear Adaptive Control Law Research Articles

Nonlinear predictor‐feedback cooperative adaptive cruise control of vehicles with nonlinear dynamics and input delay

SummaryWe construct a nonlinear predictor‐feedback cooperative adaptive cruise control (CACC) design for homogeneous vehicular platoons subject to actuators delays, which achieves: (i) positivity of vehicles' speed and spacing states, (ii) string stability of the platoon, (iii) stability of each individual vehicular system, and (iv) regulation to the desired reference speed (dictated by the leading vehicle) and spacing. The design relies on a nominal, nonlinear adaptive cruise control (ACC) law that we construct, which guarantees (i)–(iv) in the absence of actuator delay, and nonlinear predictor feedback. We consider a classical (for ACC/CACC design) third‐order, nonlinear model subject to input delay, for the vehicles' dynamics. The proofs of the theoretical guarantees (i)–(iv) rely on derivation of explicit estimates on solutions (both during open‐loop and closed‐loop operation), capitalizing on the ability of predictor feedback to guarantee complete delay compensation after the dead‐time interval has elapsed, and derivation of explicit conditions on initial conditions and parameters of the nominal control law. We also present consistent simulation results, considering a platoon of ten vehicles, which validate the design developed.

Autonomous Trajectory Tracking and Collision Avoidance Design for Unmanned Surface Vessels: A Nonlinear Fuzzy Approach

An intelligent fuzzy-based control system that consists of several subsystems—a fuzzy collision evaluator, a fuzzy collision avoidance acting timing indicator, a collision-free trajectory generator, and a nonlinear adaptive fuzzy robust control law—is proposed for the collision-free condition and trajectory tracking of unmanned surface vessels (USVs). For the purpose of ensuring that controlled USVs are capable of executing tasks in an actual ocean environment that is full of randomly encountered ships under collision-free conditions, the real-time decision making and the desired trajectory arrangements of this proposed control system were developed by following the “Convention on the International Regulations for Preventing Collisions at Sea” (COLREGs). From the simulation results, several promising properties were demonstrated: (1) robustness with respect to modeling uncertainties and ocean environmental disturbances, (2) a precise trajectory tracking ability, and (3) sailing collision avoidance was shown by this proposed system for controlled USVs.

Design of an Adaptive Control to Feed Hydrogen-Enriched Ethanol-Gasoline Blend to an Internal Combustion Engine

In this work, an internal combustion (IC) engine air-fuel ratio (AFR) control system is presented and evaluated by simulation. The control scheme aims to regulate the overall air-fuel ratio (AFRoverall) in an IC engine fueled with a hydrogen-enriched ethanol-gasoline blend (E10) as fast as possible. The control scheme designed and developed in this work considers two control laws, a feedback control law to regulate the hydrogen and adaptive nonlinear control law for controlling the E10 mass flow injection. The main contribution of this work is the reduction of the number of controllers used for controlling the overall air-fuel ratio since other control strategies use two controllers for controlling the E10 mass flow injection. Simulation results have shown the effectiveness of the new control scheme.

MPPT for Photovoltaic System Using Adaptive Fuzzy Backstepping Sliding Mode Control

This paper presents an intelligent monitoring control strategy for a maximum power point tracking (MPPT) in photovoltaic (PV) system applications. The design of the proposed nonlinear adaptive control law (AFBSMC) is formulated based on adaptive fuzzy systems, backstepping approach and sliding mode technique to maximize the power output of a PV system under various sets of conditions and parameters variation. Unlike many conventional controllers, the main contribution of the present paper provides a soften control law which useful to handle parameters variations due to the different operating conditions occurring on the PV system and makes the controller easy to implement. This aim is achieved using fuzzy systems in an adaptive scheme to approximate the switching control function of the global control law while backstepping sliding mode control compensates uncertainties and external disturbances. The analytical stability proof of the closed-loop system is corroborated via Lyapunov synthesis while numerical simulations of different operating conditions of a PV system is conducted to validate the effectiveness of the proposed approach.

Hybrid adaptive negative imaginary- neural-fuzzy control with model identification for a quadrotor

Quadrotor system is subject to multiple disturbances, including both internal and external effects (e.g. wind gusts, coupling effects, and unmodeled dynamics). For example, severe wind disturbances may significantly degrade trajectory tracking during the flight of autonomous aerial vehicles, or even cause loss of control or failure of a tracking mission. This paper introduces a robust hybrid control system, including a linear Strictly Negative Imaginary (SNI) controller and an adaptive nonlinear Neural-Fuzzy control law, to enable high-precision trajectory tracking tasks for a quadcopter drone. Based on a parallel form, both proposed controllers are able to enhance the transient performance, the system response, and the robustness of the quadcopter controllers. Also, a linear time-invariant SNI UAV dynamic model, in combination with an online adaptive residual nonlinear model using the neural network identification, is proposed to model the natural behavior of a quadcopter system. Through a series of numerical simulations, this paper highlights the effectiveness of our hybrid controller in the face of some parameter variations, such as nonlinear aerodynamic models and exogenous disturbances (e.g., wind gusts). Moreover, it compares its tracking performance with that of a fixed-gain SNI controller and the adaptive Neural-Fuzzy controller separately. Finally, the stability of the closed-loop control system is also discussed using the SNI theorem.

Adaptive Fuzzy Asymptotic Tracking for Nonlinear Systems With Nonstrict-Feedback Structure.

In this article, the tracking control problems of the nonlinear nonstrict-feedback systems are considered. By combining the backstepping technique and bound estimation method, a novel nonlinear adaptive asymptotical control law is proposed, which offsets the effect of the unknown virtual control parameters and the uncertain nonlinearities. Correspondingly, an improved Lyapunov function by introducing the lower bounds of control parameters has been devised in this article. Compared with the existing adaptive tracking control schemes, the controller designed in this article can guarantee that the tracking control error converges to zero asymptotically and all the signals which contain the state variables and the adaptive laws are bounded. Moreover, the asymptotic stability of the system is realized for the first time. Finally, simulation examples are applied to test and prove the availability of the presented methods and the performance of the controlled system.

Energy-saving and accurate motion control of a hydraulic actuator with uncertain negative loads

Pump controlled hydraulic actuators are wildly used in the aerospace industry owing to the advantages of energy-saving and integrated configurations. Negative loads may occur to actuators due to external force loads or the inertial force when the actuator decelerates significantly. Uncertain negative load working conditions may cause cavitation, actuator vibration, and even instability to the motion control if the actuator is without sufficient meter-out damping. Various types of hydraulic configuration schemes have been proposed to deal with negative loads of hydraulic actuators. However, few of them can simultaneously achieve energy saving and high control accuracy. This study proposes an energy-saving and accurate motion tracking strategy for a hydraulic actuator with uncertain negative loads. The actuator’s motion is driven by a servomotor pump, which gives full play to the advantage of energy-saving. The meter-out pressure is controlled by proportional valves to provide the optimized meter-out damping. The nonlinear adaptive robust control law is designed, which guarantees the control stability and achieve high tracking accuracy. An integrated direct/indirect adaptation law obtains satisfactory parameter estimations and model compensation for asymptotic motion tracking. Comparative experiments under different working conditions were performed to validate the advantages of the proposed control strategy.

Nonlinear Adaptive Boundary Control of the Modified Generalized Korteweg–de Vries–Burgers Equation

In this paper, we study the nonlinear adaptive boundary control problem of the modified generalized Korteweg–de Vries–Burgers equation (MGKdVB) when the spatial domain is 0,1. Four different nonlinear adaptive control laws are designed for the MGKdVB equation without assuming the nullity of the physical parameters ν, μ, γ1, and γ2 and depending whether these parameters are known or unknown. Then, using Lyapunov theory, the L2-global exponential stability of the solution is proven in each case. Finally, numerical simulations are presented to illustrate the developed control schemes.

Observer-Based Adaptive Tracking Control of Wheeled Mobile Robots With Unknown Slipping Parameters

Based on wheeled mobile robots (WMRs) with unknown longitudinal slipping parameters, an adaptive control strategy for a tracked mobile robot is presented, in which the longitudinal slipping of the left and right wheels are described by two unknown parameters. The kinematic model of mobile robot with wheels’ slipping is derived from the motion model of mobile robot without wheels’ slipping. Employing the Lyapunov direct method, an adaptive nonlinear feedback control law that compensates for the longitudinal slipping is proposed to achieve an objective of tracking a given trajectory. The orientation angle observer is designed to estimate the immeasurable orientation angle of the robot by employing the coordinate information. Asymptotic stability of the closed-loop system is ensured by choosing an appropriate Lyapunov function. Numerical and experimental results show the effectiveness of the proposed control approach.

Dynamic modeling and adaptive vibration suppression of a high-speed macro-micro manipulator

This paper presents a dynamic modeling and microscopic vibration suppression for a flexible macro-micro manipulator dedicated to high-speed operation. The manipulator system mainly consists of a macro motion stage and a flexible micromanipulator bonded with one macro-fiber-composite actuator. Based on Hamilton's principle and the Bouc–Wen hysteresis equation, the nonlinear dynamic model is obtained. Then, a hybrid control scheme is proposed to simultaneously suppress the elastic vibration during and after the motor motion. In particular, the hybrid control strategy is composed of a trajectory planning approach and an adaptive variable structure control. Moreover, two optimization indices regarding the comprehensive torques and synthesized vibrations are designed, and the optimal trajectories are acquired using a genetic algorithm. Furthermore, a nonlinear fuzzy regulator is used to adjust the switching gain in the variable structure control. Thus, a fuzzy variable structure control with nonlinear adaptive control law is achieved. A series of experiments are performed to verify the effectiveness and feasibility of the established system model and hybrid control strategy. The excited vibration during the motor motion and the residual vibration after the motor motion are decreased. Meanwhile, the settling time is shortened. Both the manipulation stability and operation efficiency of the manipulator are improved by the proposed hybrid strategy.

Robust Adaptive Nonlinear Dynamic Inversion Control for an Air-breathing Hypersonic Vehicle

This paper presents a robust adaptive nonlinear dynamic inversion control approach for the longitudinal dynamics of an air-breathing hypersonic vehicle. The proposed approach adopts a fast adaptation law using high-gain learning rate, while a low-pass filter is synthesized with the modified adaptive scheme to filter out the high-frequency content of the estimates. This modified high-gain adaptive scheme achieves a good transient process and a nice robust property with respect to parameter uncertainties, without exciting high-frequency oscillations. Based on input-output linearization, the nonlinear hypersonic dynamics are transformed into equivalent linear systems. Therefore, the pole placement technique is applied to design the baseline nonlinear dynamic inversion controller. Finally, the simulation results of the modified adaptive nonlinear dynamic inversion control law demonstrate the proposed control approach provides robust tracking of reference trajectories.

Aerodynamic Three-Axis Attitude Stabilization of a Spacecraft by Center-of-Mass Shifting

This paper proposes a spacecraft attitude control technique based on the use of center-of-mass shifting. In particular, the position vector of the spacecraft’s center of pressure with respect to the center of mass is modified by shifting masses, which results in a change of the aerodynamic torque vector within the plane perpendicular to the aerodynamic drag. This results in an underactuated control system. To achieve full three-axis stabilization, additional actuators (either a reaction wheel or a set of magnetic torquers) are considered. An adaptive nonlinear attitude regulation control law was designed in order to obtain an ideal control torque based on the Lyapunov method and its stability was proven by LaSalle’s invariance principle. The control torque was then allocated to steer three shifting masses and either a reaction wheel or three magnetic torquers. Numerical simulations are reported, confirming the analytic results. The proposed method decreases the residual oscillation error typically associated with magnetic controlled attitude in the presence of residual aerodynamic torque. Therefore, it might contribute to achieve higher pointing accuracy of small spacecraft in low Earth orbit.

Fault-tolerant control with mixed aerodynamic surfaces and RCS jets for hypersonic reentry vehicles

This paper proposes a fault-tolerant strategy for hypersonic reentry vehicles with mixed aerodynamic surfaces and reaction control systems (RCS) under external disturbances and subject to actuator faults. Aerodynamic surfaces are treated as the primary actuator in normal situations, and they are driven by a continuous quadratic programming (QP) allocator to generate torque commanded by a nonlinear adaptive feedback control law. When aerodynamic surfaces encounter faults, they may not be able to provide sufficient torque as commanded, and RCS jets are activated to augment the aerodynamic surfaces to compensate for insufficient torque. Partial loss of effectiveness and stuck faults are considered in this paper, and observers are designed to detect and identify the faults. Based on the fault identification results, an RCS control allocator using integer linear programming (ILP) techniques is designed to determine the optimal combination of activated RCS jets. By treating the RCS control allocator as a quantization element, closed-loop stability with both continuous and quantized inputs is analyzed. Simulation results verify the effectiveness of the proposed method.

Adaptive idling control scheme and its experimental validation for gasoline engines

In this paper, the idle speed control problem is investigated for spark-ignition (SI) engines. To scope with physical model parameter-free control scheme, a nonlinear adaptive control law is proposed for the speed regulation loop. The stability analysis result shows that the idle speed converges to the set value and the estimated parameter converges to an equivalent static value of the intake manifold. Furthermore, the proposed fuel injection control law consists of a feedforward and a simple feedback loop. Finally, the proposed control scheme is validated based on a full-scaled six-cylinder gasoline engine test bench.

Leader-following consensus for a class of second-order nonlinear multi-agent systems

This paper deals with the leader-following consensus problem for a class of multi-agent systems with nonlinear dynamics and directed communication topology. The control input of the leader agent is assumed to be unknown to all follower agents. A distributed adaptive nonlinear control law is constructed using the relative state information between neighboring agents, which achieves leader-following consensus for any directed communication graph that contains a spanning tree with the root node being the leader agent. Compared with previous results, the nonlinear functions are not required to satisfy the globally Lipschitz or Lipschitz-like condition and the adaptive consensus protocol is in a distributed fashion. A numerical example is given to verify our proposed protocol.

Dual-quaternion based fault-tolerant control for spacecraft formation flying with finite-time convergence

Study results of developing control system for spacecraft formation proximity operations between a target and a chaser are presented. In particular, a coupled model using dual quaternion is employed to describe the proximity problem of spacecraft formation, and a nonlinear adaptive fault-tolerant feedback control law is developed to enable the chaser spacecraft to track the position and attitude of the target even though its actuator occurs fault. Multiple-task capability of the proposed control system is further demonstrated in the presence of disturbances and parametric uncertainties as well. In addition, the practical finite-time stability feature of the closed-loop system is guaranteed theoretically under the designed control law. Numerical simulation of the proposed method is presented to demonstrate the advantages with respect to interference suppression, fast tracking, fault tolerant and practical finite-time stability.

Adaptive control for two-spacecraft electromagnetic formation keeping

Electromagnetic spacecraft formation flying is a new type of spacecraft formation using electromagnetic forces between spacecraft to control relative motion. Primary principles of the relative motion of a two-craft electromagnetic formation were discussed. Analytical solutions of control magnetic moments according to commanded control forces for the case of two-spacecraft electromagnetic formation were developed considering the energy consumption equilibrium. Nonlinear relative motion dynamic models for a two-spacecraft electromagnetic formation were derived based on polar coordinates. Parameter uncertainties of the equations because of the approximation of the electromagnetic model and unknown disturbed forces were analyzed. Nonlinear adaptive feedback control laws for formation keeping were then designed,and the closed-loop dynamic procedure of a two-spacecraft electromagnetic formation in a low earth circular orbit was simulated. Results indicate that the relative motion equations and the adaptive control laws are valid. The formation can effectively converge to desired states and the unknown parameters are estimated accurately. The simulations demonstrate that electromagnetic forces between spacecraft can be used to realize spacecraft formation keeping and the electromagnetic formation flying is feasible.

Nonlinear Adaptive Bottom-Following Control of an AUV in the Presence of Ocean Currents

This paper addresses the bottom-following control problem of an underactuated autonomous underwater vehicle (AUV) in the presence of ocean currents and model parameters uncertainties. The Serret-Frenet frame is used to describe the bottom following of the AUV. An extra degree of freedom for controller design is introduced. The extra degree of freedom makes the virtual AUV can regulate its velocity along with the real AUV. Based on Lyapunov theory and backstepping techniques, a nonlinear adaptive control law is derived. The control law yields convergence of the AUV to the desired path asymptotically. Simulations results show the effectiveness and robustness of the derived controllers.

Asymptotic pseudo-state stabilization of commensurate fractional-order nonlinear systems with additive disturbance

The pseudo-state stabilization problem of commensurate fractional-order nonlinear systems is investigated. The concerned fractional-order nonlinear system is of parametric strict-feedback form with both unknown parameters and the additive disturbance. To solve this problem, a new nonlinear adaptive control law is constructed via fractional-order backstepping scheme. The developed fractional-order controller does not require the knowledge about both the interval of uncertain parameters and the upper bound of the additive disturbance. The asymptotic pseudo-state stability of the closed-loop system is proved in terms of fractional Lyapunov stability. Several examples are performed finally, and the efficiency is verified.

Adaptive antiswing control for cranes in the presence of rail length constraints and uncertainties

In practical applications, crane systems usually suffer from unfavorable factors, such as parametric uncertainties consisting of unknown friction forces, trolley mass, payload mass, and wire length. Moreover, existing crane control methods cannot guarantee the motion scope of the trolley, since merely asymptotic results, at best, can be obtained because of the nonlinear underactuated nature. Due to unexpected overshoots, existing methods, unless well tuned, may drive the trolley to go beyond the scope of the rail. In this paper, we consider the control problem for underactuated crane systems by considering the aforementioned two points and present an adaptive nonlinear control law. The control framework is established by total energy shaping, and a novel additional term is introduced into the controller to prevent the trolley from running out of the permitted range. We employ Lyapunov-based analysis to prove that the equilibria of the closed-loop system is asymptotically stable. Hardware experimental results are included to suggest that the proposed method achieves increased control performance vis-a-vis existing methods and admits strong robustness with regard to uncertainties and external disturbances, while ensuring the trolley motion range limitation.