Adaptive Control Law Research Articles

A Double-Layer Adaptive Scheme for Fully Distributed Nash Equilibrium Seeking

We present a fully distributed Nash equilibrium seeking strategy by designing a double-layer adaptive control law in this paper, by which players can update their actions without knowing any global information. In comparison with existing fully distributed approaches, the proposed algorithm employs a damping term in the adaptive parameter design, which is more preferable for practical implementations as it avoids continuously increasing adaptive gains. Analytical analysis on the convergence of the designed strategy is carried out by Lyapunov stability analysis, and it is verified that the Nash equilibrium is globally asymptotically stable by using the proposed algorithm. The effectiveness of the proposed method is illustrated by a numerical example finally.

Data-Driven Model-Free Adaptive Positioning and Anti-Swing Control for Bridge Cranes

In the positioning and anti-swing control of bridge crane, a model-free adaptive control (MFAC) based on data-driven is proposed in order to eliminate the dependence of controller design on the model and the influence of unmodeled dynamics and uncertain disturbances on the controller performance. Only using the input and output data of the bridge crane system, the virtual full format dynamic linearized data model of the bridge crane nonlinear system is obtained through the data-driven modeling method. On the basis of this virtual data model, a model-free adaptive control law and a pseudo-Jacobian matrix estimation algorithm are designed according to the optimization theory under the constraint conditions. The stability of the closed loop system and the convergence of the system error are analyzed and proved by Lipschitz condition and inequality theory. The effectiveness of the control strategy for positioning and anti-swing control of bridge cranes is verified on simulated simulation and experimental platform of bridge crane. The results show that the proposed method is feasible and has good anti-disturbance performance and robustness.

Direct Adaptive Control for Stochastic Systems with Risk-Sensitive Indices

We propose a direct adaptive control law based on the adaptive dynamic programming (ADP) algorithm for continuous-time stochastic linear systems with partially unknown system dynamics and infinite horizon quadratic risk-sensitive indices. A control design methodology is employed to iteratively solve the generalized algebraic Riccati equation by using the online information of the state and input, and to directly learn the optimal control law. We prove the convergence of the online ADP algorithm and show that the direct adaptive control law approximates the optimal control law as time goes on. Finally, a numerical simulation example is presented to demonstrate the effectiveness of our algorithm.

Adaptive Compensation of Unmatched Disturbances in Unstable MIMO LTI Plants with Distinct Input Delays

The paper concerns the problem of adaptive compensation of unmatched disturbances in linear time-invariant (LTI) multi-input multi-output (MIMO) unstable plants with multiple distinct input delays. The external disturbances affect both the input and the output of the plant and are represented by multi-harmonic signals with unknown parameters (frequencies, phases, and amplitudes). The paper extends results of the paper Nikiforov et al. (2021) on adaptive compensation of unmatched disturbances to the case of distinct input delays. To overcome the problem of multiple distinct input delays, a special scheme of the disturbance prediction is proposed and used for design of the adaptive control law.

Adaptive boundary control of an axially moving system with large acceleration/deceleration under the input saturation.

We present the dynamical equation model of the axially moving system, which is expressed through one partial differential equation (PDE) and two ordinary differential equations (ODEs) obtained using the extended Hamilton's principle. In the case of large acceleration/deceleration axially moving system with system parameters uncertainty and input saturation limitation, the combination of Lyapunov theory, S-curve acceleration and deceleration (Sc A/D) and adaptive control techniques adopts auxiliary systems to overcome the saturation limitations of the actuator, thus achieving the purpose of vibration suppression and improving the quality of vibration control. Sc A/D has better flexibility than that of constant speed to ensure the operator performance and diminish the force of impact by tempering the initial acceleration. The designed adaptive control law can avoid the control spillover effect and compensate the system parameters uncertainty. In practice, time-varying boundary interference and distributed disturbance exist in the system. The interference observer is used to track and eliminate the unknown disturbance of the system. The control strategy guarantees the stability of the closed-loop system and the uniform boundedness of all closed-loop states. The numerical simulation results test the effectiveness of the proposed control strategy.

Finite-Time Rapid Global Sliding-Mode Control for Quadrotor Trajectory Tracking

To enhance the position and attitude-control of quadrotor for trajectory tracking, we propose a fast decay function utilizing exponential property to improve the performance of global sliding-mode control, allowing the initial value to quickly reach equilibrium. The main research is focused on deriving the finite settling time using the proposed decay function and presenting a detailed calculation process, instead of making a simple modification to a monotonic exponential-decay function. Moreover, we adopt an adaptive control law to ensure the robustness of the quadrotor, even without knowing the upper bound for disturbances. In addition, we perform time-varying mass simulations because the quadrotor’s load mass may change during maneuvering. Furthermore, using the Lyapunov function, the stability of the entire closed-loop system is ensured by the step-by-step stabilization of each subsystem. The simulation results show that the rapid global sliding-mode control (RGSMC) we designed is more effective than the conventional global sliding-mode control and adaptive sliding mode control with respect to stabilization and tracking against external disturbances. Hence, the fast decay property of the proposed global function is verified.

Modeling and adaptive control of air vehicles with partial nonlinear parametrization

This paper studies the control of a generic longitudinal air vehicle dynamic model during the cruise phase with nonlinearly parametrized uncertain aerodynamic functions. Verified by the improved coefficient precision of the aerodynamic forces and moments, using a curve fitting technique on available flight data, it is demonstrated that a nonlinearly parametrized model can more accurately capture the vehicle dynamics than a linearly parametrized model. For control design, the air vehicle model is decomposed into a flight-path angle subsystem with rotational dynamics and a speed subsystem with engine actuation dynamics. An adaptive control scheme is developed using the combination of a function bounding technique and a modified backstepping control method for two interconnected subsystems. The designed adaptive control laws ensure both global stabilization and adaptive non-zero equilibrium point regulation of the closed-loop control system. A thorough simulation study is presented to show the effectiveness of the developed adaptive control scheme for a nonlinearly parametrized air vehicle system model.

Optimal control for anti-lock braking system: Output feedback adaptive controller design and processor in the loop validation test

In this paper, the problem of controlling anti-lock braking system (ABS) was considered. Based on LuGre friction model, an output-feedback adaptive controller that enjoys good braking performances whatever the road conditions, was developed. Specifically, the controller tracks the optimal slip coefficient and, unlike previous work, the reference slip ratio is online estimated according to road conditions as well as longitudinal vehicle speed. The adaptive feature of the controller proves to be crucial for compensating the uncertainty on the changing road characteristics. The controller consists of: (i) a generator of the reference signal for the slip coefficient designed in the form of a neural network; (ii) a nonlinear observer for estimating the internal friction state; (iii) a backstepping adaptive control law, designed on the basis of a quarter-car model, that ensures tracking of the optimal slip value and providing estimates of the model unknown parameters. The controller stability properties are analyzed using Lyapunov stability tools. The theoretical stability results are confirmed by processor-in-the-loop (PIL) experiments in different road conditions. A comparative study, a robustness test, and a co-simulation involving CarSim and MATLAB/Simulink were made to highlight the much better performances, in terms of stability, tracking, robustness, and practicability of the new controller.

Speed-Gradient Adaptive Control for Parametrically Uncertain UAVs in Formation

The paper is devoted to the problem of the decentralized control of unmanned aerial vehicle (UAV) formation in the case of parametric uncertainty. A new version of the feedback linearization approach is proposed and used for a point mass UAV model transformation. As result, a linear model is obtained containing an unknown value of the UAV mass. Employing the speed-gradient design method and the implicit reference model concept, a combined adaptive control law is proposed for a single UAV, including the UAV’s mass estimation and adaptive tuning of the controller parameters. The obtained new algorithms are then used to address the problem of consensus-based decentralized control of the UAV formation. Rigorous stability conditions for control and identification are derived, and simulation results are presented to demonstrate the quality of the closed-loop control system for various conditions.

Adaptive lead-through teaching control for spray-painting robot with closed control system

AbstractIndustrial robots are widely used in the painting industry, such as automobile manufacturing and solid wood furniture industry. An important problem is how to improve the efficiency of robot programming, especially in the current furniture industry with multiple products, small batches and increasingly high demand for customization. In this work, we propose an outer loop adaptive control scheme, which allow users to realize the practical application of the zero-moment lead-through teaching method based on dynamic model without opening the inner torque control interface of robots. In order to accurately estimate the influence of joint friction, a friction model is established based on static, Coulomb and viscous friction characteristics, and the Sigmoid function is used to represent the transition between motion states. An identification method is used to quickly identify the dynamic parameters of the robot. The joint position/speed command of the robot’s inner joint servo loop is dynamically generated based on the user-designed adaptive control law. In addition, the zero-moment lead-through teaching scheme based on the dynamic model is applied to a spray-painting robot with closed control system. In order to verify our method, CMA GR630ST is used to conduct experiments. We identified the parameters of the dynamic model and carried out the zero-moment lead-through teaching experiment to track the target trajectory. The results show that the proposed method can realize the application of modern control methods in industrial robot with closed control systems, and achieve a preliminary exploration to improve the application scenarios of spray-painting robots.

Adaptive integral‐type terminal sliding mode control: Application to trajectory tracking for mobile robot

SummaryThis paper presents an Adaptive Terminal Integral Sliding Mode Control (ATISMC) scheme for trajectory tracking problems applied to a differential Wheeled Mobile Robot (WMR). First, a terminal integral sliding variable is designed. Based on the finite‐time concept, an adaptive control law has been developed in which a switching gain is adjusted adaptively by using a novel strategy. This control method aims to deal with unknown bounded disturbances and uncertainties. Moreover, it allows fast convergence of the system states to an equilibrium point. The main features of the proposed ATISMC are its robustness, fast convergence rate, and chattering avoidance. To realize trajectory tracking for WMR, the ATISMC is incorporated into a double closed loop scheme. Stability analysis is performed using the Lyapunov stability theory. Numerical simulations and real‐time experiments demonstrate the feasibility of the proposed controller scheme. A comparison study with the classical ISMC was performed to show the superiority of the developed method.

Adaptive Fuzzy Command Filtered Finite-Time Tracking Control for Uncertain Nonlinear Multi-Agent Systems with Unknown Input Saturation and Unknown Control Directions

This paper investigates the finite-time consensus tracking control problem of uncertain nonlinear multi-agent systems with unknown input saturation and unknown control directions. An adaptive fuzzy finite-time consensus control law is proposed by combining the fuzzy logic system, command filter, and finite-time control theory. Using the fuzzy logic systems, the uncertain nonlinear dynamics are approximated. Considering the command filter and backstepping control technique, the problem of the so-called “explosion of complexity” in the design of virtual control laws and adaptive updating laws is avoided. Meanwhile, the Nussbaum gain function method is applied to handle the unknown control directions and unknown input saturation problems. Based on the finite-time control theory and Lyapunov stability theory, it was found that all signals in the closed-loop system remained semi-global practical finite-time stable, and the tracking error could converge to a sufficiently small neighborhood of the origin in the finite time. In the end, simulation results were provided to verify the validity of the designed control law.

Fully distributed event‐driven cooperation with unknown parameters under directed graphs

AbstractIn this article, a novel fully distributed dynamic event‐driven strategy is designed for linear multi‐agent systems (MASs) containing unknown parameters under general directed graphs. Each agent can achieve consensus asymptotically by communicating with its neighbors and does not need to use global information, so the proposed dynamic event‐driven algorithm can work in a fully distributed manner. Existing fully distributed event‐based consensus works rely on two or more event monitoring conditions. Too much event monitoring logic will put an extra computational burden on the MASs; instead, for the first time, this article proposes a fully distributed event‐driven strategy with a single event monitoring condition under directed graphs. In addition, the proposed strategy (adaptive control law and event monitoring condition) does not involve the dynamics parameters of MASs and provides better applicability. Finally, we rule out Zeno behavior by showing that any adjacent event interval for each agent is greater than zero. The simulations verify our results.

Data-Driven Adaptive Control: An Incremental Triangular Dynamic Linearization Approach

This brief investigates the data-driven control problem for a class of nonlinear systems. An incremental triangular dynamic linearization (ITDL) model is presented to equivalently describe these systems, and it contains three parameters including a single time-varying parameter, all of which have clear physical meanings. The ITDL model has obvious advantages compared with the existing partial form dynamic linearization (PFDL) model, although it is a special case of the PFDL model in form. An online estimation algorithm is designed for the single time-varying parameter, and then an adaptive control law is designed. The convergence and stability of the closed-loop system are analyzed, and the corresponding explicit conditions are derived. Finally, a comparative simulation study is conducted to illustrate the effectiveness of the proposed method.

Neural Network-Based Adaptive Boundary Control of a Flexible Riser With Input Deadzone and Output Constraint.

In this article, vibration abatement problems of a riser system with system uncertainty, input deadzone, and output constraint are considered. For obtaining better control precision, a boundary control law is constructed by employing the backstepping method and Lyapunov's theory. The output constraint is guaranteed by utilizing a barrier Lyapunov function. Adaptive neural networks are designed to cope with the uncertainty of the riser and compensate for the effect caused by the asymmetric deadzone nonlinearity. With the designed controller, the output constraint is satisfied, and the system stability is guaranteed through Lyapunov synthesis. In the end, numerical simulation results are provided to display the performance of the developed adaptive neural network boundary control law.

Adaptive Deformation Control of a Flexible Variable-Length Rotary Crane Arm With Asymmetric Input-Output Constraints.

This article constructs two adaptive control laws to achieve deformation reduction and attitude tracking for a rotary variable-length crane arm with system parameter uncertainties and asymmetric input-output constraints. Two auxiliary systems are given to deal with the input constraints, an asymmetric-logarithm-barrier Lyapunov function is established for achieving the asymmetric output constrains, and five adaptive laws are constructed to handle system parameter uncertainties. Besides, the control design is based on a partial differential equation model, and the S-curve acceleration and deceleration method is used for regulating the arm extension speed. Both the system stability and uniform ultimate boundedness of the controlled crane arm are analyzed. Simulation results validate the effectiveness of our established control laws.

Precision Force Tracking Control of a Surgical Device Interacting With a Deformable Membrane

Well-designed robotic-assisted surgical systems have been widely applied in medical treatments to make surgical operations precise and efficient. For these, precise tracking of the interaction force between the surgical device and affected human tissues is an important aspect to improve the safety and surgery success rate. In this development, an adaptive integral terminal sliding mode force control scheme for a piezoelectric actuator-based ear surgical device is presented to achieve precision force tracking during the interaction with the tympanic membrane that is soft and deformable, an important aspect in the course of such a surgery. Particularly, a force error-based integral terminal sliding manifold is employed to guarantee the finite-time convergence performance. A related adaptive control law is developed and deployed to estimate the controller’s parameters and update the switching gain to accommodate system uncertainties, disturbances, and the complex contact environment. Then, the stability of the proposed control method is analyzed and discussed rigorously based upon the Lyapunov theory and method. Furthermore and rather importantly, comparative experiments with three other force controllers are conducted for both S-curve and sine waves with different frequencies. The force tracking results interacting with the deformable membrane demonstrate that the best performance is achieved by the proposed method with all the statistical errors within a suitably effective range of 2.5% and 9.0% of the maximum amplitude.

Adaptive Dynamic Surface Control of Strict-Feedback Fractional-Order Nonlinear Systems with Input Quantization and External Disturbances

In this work, an adaptive dynamic surface control law for a type of strict-feedback fractional-order nonlinear system is proposed. The considered system contained input quantization and unknown external disturbances. The virtual control law is presented by utilizing a dynamic surface control approach at each step, where the nonlinear compensating term with the estimation of unknown bounded parameters is introduced to overcome the influence of unknown external disturbances and surface errors. Meanwhile, the adaptive laws of relevant parameters are also designed. In addition, an improved fractional-order nonlinear filter is developed to deal with the explosion of complexity raised by the recursive process. In the last step, an adaptive dynamic surface control law is proposed to ensure the convergence of tracking error, in which the Nussbaum gain function is applied to solve the problem of the unknown control gain generated by input quantization. Then, the fractional Lyapunov stability theory is applied to verify the stability of the proposed control law. Finally, simulation examples are given to illustrate the effectiveness of the proposed control law.

Adaptive Least Mean Square Controller for Power Quality Enhancement in Solar Photovoltaic System

The objective of the proposed work is to develop a Maximum Power Point Tracking (MPPT) controller and inverter controller by applying the adaptive least mean square (LMS) algorithm to control the total harmonics distortion of a solar photovoltaic system. The advantage of the adaptive LMS algorithm is given by its simplicity and reduced required computational time. The adaptive LMS algorithm is applied to modify the Perturb and Observe (P&O), MPPT controller. In this controller, the adaptive LMS algorithm is used to predict solar photovoltaic power. The adaptive LMS maximum power point tracking controller gives better optimal solutions with less steady error 0.7% (6 watts) and 0% peak overshot in power with the tradeoff being more settling time at 0.33 s. The development of the inverter control law is performed using the d-q frame theory. This helps to reduce the number of equations to build a control law. The load current, grid current and grid voltage are sensed and transformed into d and q components. This adaptive LMS control law is used to extract the reference grid currents and, later, to compare them with the actual grid currents. The result of this comparison is used to generate the switching gate pulses for the inverter switches. The proposed controllers are developed and implemented with a solar PV system in MATLAB Simulink. The total harmonics distortion in grid and load current (3.25% and 7%) and voltage (0%) is investigated under linear and non-linear load conditions with changes in solar irradiations. The analysis is performed by selecting step incremental values and sampling time.

Adaptive fuzzy resilient control for switched systems with state constraints under deception attacks

This paper studies an adaptive fuzzy resilient control strategy for switched systems with deception attacks and state constraints. With the deception attacks on both the sensors and actuators, the feedback data is unreliable and the direction of control is unknown, which make it difficult to design the adaptive resilient control for switched systems. By combining Nussbaum-based adaptive control, fuzzy control and a two-step backstepping approach, a novel adaptive resilient controller and mode-dependent switching law are designed to against deception attacks. Considering the buffeting problem triggered by the Nussbaum function, the states are constrained in this paper and the barrier Lyapunov function is utilized. Based on the designed adaptive fuzzy resilient control method, both the asymptotic stability and the state constraints of the switched systems under deception attacks can be guaranteed. The feasibility of the proposed resilient control strategy is demonstrated through an application of the strategy to an attacked single-link robot arm (SLRA) model.