Adaptive Law Research Articles

Accelerated Gradient Approach For Deep Neural Network-Based Adaptive Control of Unknown Nonlinear Systems.

Recent connections in the adaptive control literature to continuous-time analogs of Nesterov's accelerated gradient method have led to the development of new real-time adaptation laws based on accelerated gradient methods. However, previous results assume that the system's uncertainties are linear-in-the-parameters (LIP). To compensate for non-LIP uncertainties, our preliminary results developed a neural network (NN)-based accelerated gradient adaptive controller to achieve trajectory tracking for nonlinear systems; however, the development and analysis only considered single-hidden-layer NNs. In this article, a generalized deep NN (DNN) architecture with an arbitrary number of hidden layers is considered, and a new DNN-based accelerated gradient adaptation scheme is developed to generate estimates of all the DNN weights in real-time. A nonsmooth Lyapunov-based analysis is used to guarantee the developed accelerated gradient-based DNN adaptation design achieves global asymptotic tracking error convergence for general nonlinear control affine systems subject to unknown (non-LIP) drift dynamics and exogenous disturbances. A comprehensive set of simulation studies are conducted on a two-state nonlinear system, a robotic manipulator, and a complex 20-D nonlinear system to demonstrate the improved performance of the developed method. Our simulation studies demonstrate enhanced tracking and function approximation performance from both DNN architectures and accelerated gradient adaptation.

Rotor Flux and EEMF Observer for Interior Permanent Magnet Synchronous Machine

In recent years, the use of the Interior Permanent Magnet Synchronous Machine (IPMSM) in various applications has grown significantly due to numerous benefits. Sensors are used to achieve high efficiency and good dynamic response in IPMSM drives but due to their high cost and reduce overall size of system,sensorless control techniques are preferred. Non-sinusoidal distribution of rotor flux and slot harmonics are present in the considered IPMSM. In this article, these problems are considered as control system disturbances. With the above-mentioned problems, the classical observer structure based on (d-q) fails to estimate at low-speed ranges. This article proposes an observer structure based on a rotor flux vector in (α-β) stationary reference frame, which works using the adaptive control law to estimate speed and position, and a non-adaptive EEMF-based observer to estimate speed and position. Moreover, a comparative analysis between both observer structures at the different speed ranges is also considered in this article. The effectiveness of the observer structure is validated by simulation tests and experimental tests using the sensorless control system with a field-oriented control scheme for 3.5 kW IPMSM drive system.

RBS and ABS Coordinated Control Strategy Based on Explicit Model Predictive Control

During the braking process of electric vehicles, both the regenerative braking system (RBS) and anti-lock braking system (ABS) modulate the hydraulic braking force, leading to control conflict that impacts the effectiveness and real-time capability of coordinated control. Aiming to enhance the coordinated control effectiveness of RBS and ABS within the electro-hydraulic composite braking system, this paper proposes a coordinated control strategy based on explicit model predictive control (eMPC-CCS). Initially, a comprehensive braking control framework is established, combining offline adaptive control law generation, online optimized control law application, and state compensation to effectively coordinate braking force through the electro-hydraulic system. During offline processing, eMPC generates a real-time-oriented state feedback control law based on real-world micro trip segments, improving the adaptiveness of the braking strategy across different driving conditions. In the online implementation, the developed three-dimensional eMPC control laws, corresponding to current driving conditions, are invoked, thereby enhancing the potential for real-time braking strategy implementation. Moreover, the state error compensator is integrated into eMPC-CCS, yielding a state gain matrix that optimizes the vehicle braking status and ensures robustness across diverse braking conditions. Lastly, simulation evaluation and hardware-in-the-loop (HIL) testing manifest that the proposed eMPC-CCS effectively coordinates the regenerative and hydraulic braking systems, outperforming other CCSs in terms of braking energy recovery and real-time capability.

Vision-based adaptive LT sliding mode admittance control for collaborative robots with actuator saturation

Abstract In this paper, we propose a novel vision-based adaptive leakage-type (LT) sliding mode admittance control for actuator-constrained collaborative robots to realize the synchronous control of the precise path following and compliant interaction force. Firstly, we develop a vision-admittance-based model to couple the visual feedback and force sensing in the image feature space so that a reference image feature trajectory can be obtained concerning the contact force command and predefined trajectory. Secondly, considering the system uncertainty, external disturbance, and torque constraints of collaborative robots in reality, we propose an adaptive sliding mode controller in the image feature space to perform precise trajectory tracking. This controller employs a leakage-type (LT) adaptive control law to reduce the side effects of system uncertainties without knowing the upper bound of system uncertainties. Moreover, an auxiliary dynamic is considered in this controller to overcome the joint torque constraints. Finally, we prove the convergence of the tracking error with the Lyapunov stability analysis and operate various semi-physical simulations compared to the conventional adaptive sliding mode and parallel vision/force controller to demonstrate the efficacy of the proposed controller. The simulation results show that compared with the controller mentioned above, the path following accuracy and interaction force control precision of the proposed controller increased by 50% and achieved faster convergence.

Prescribed-time fault-tolerant tracking control for Markov jump nonlinear systems based on saturation dynamics filters

This paper investigates the problem of prescribed-time fault-tolerant tracking control for a class of Markov jump nonlinear systems affected by actuator faults and input saturation. First, a new time-varying constraint function and an error transformation are invoked to transform the original prescribed-time tracking control problem into a tracking control problem with deferred constraint for tracking error. Furthermore, the parameter correction terms are designed, on which a novel Markov jump saturation dynamic filter is constructed to handle the unfavorable effect of input saturation. Meanwhile, the projection operator technique and the norm estimation methodology are integrated to devise adaptive laws to estimate the unknown actuator faults evolving in accordance with the Markov chain. A new prescribed-time fault-tolerant tracking control scheme is put forward that realizes the deferred constraint on the tracking error, which in turn ensures that the tracking error of the system converges to a prescribed accuracy within a prescribed-time. Finally, two simulation examples, one of which implements a prescribed-time fault-tolerant tracking control for rotary steerable drilling tool system, are presented to illustrate the effectiveness and practicality of the developed scheme.

Discrete-Time Adaptive Control for Three-Phase PWM Rectifier

This paper proposes a dual-loop discrete-time adaptive control (DDAC) method for three-phase PWM rectifiers, which considers inductance-parameter-mismatched and DC load disturbances. A discrete-time model of the three-phase PWM rectifier is established using the forward Euler discretization method, and a dual-loop discrete-time feedback linearization control (DDFLC) is given. Based on the DDFLC, the DDAC is designed. Firstly, an adaptive inductance disturbance observer (AIDO) based on the gradient descent method is proposed in the current control loop. The AIDO is used to estimate lump disturbances caused by mismatched inductance parameters and then compensate for these disturbances in the current controller, ensuring its strong robustness to inductance parameters. Secondly, a load parameter adaptive law (LPAL) based on the discrete-time Lyapunov theory is proposed for the voltage control loop. The LPAL estimates the DC load parameter in real time and subsequently adjusts it in the voltage controller, achieving DC load adaptability. Finally, simulation and experimental results show that the DDAC exhibits better steady and dynamic performances, less current harmonic content than the DDFLC and the dual-loop discrete-time PI control (DDPIC), and a stronger robustness to inductance parameters and DC load disturbances.

Adaptive Critic Learning-Based Optimal Bipartite Consensus for Multiagent Systems With Prescribed Performance.

Developing a distributed bipartite optimal consensus scheme while ensuring user-predefined performance is essential in practical applications. Existing approaches to this problem typically require a complex controller structure due to adopting an identifier-actor-critic framework and prescribed performance cannot be guaranteed. In this work, an adaptive critic learning (ACL)-based optimal bipartite consensus scheme is developed to bridge the gap. A newly designed error scaling function, which defines the user-predefined settling time and steady accuracy without relying on the initial conditions, is then integrated into a cost function. The backstepping framework combines the ACL and integral reinforcement learning (IRL) algorithm to develop the adaptive optimal bipartite consensus scheme, which contributes a critic-only controller structure by removing the identifier and actor networks in the existing methods. The adaptive law of the critic network is derived by the gradient descent algorithm and experience replay to minimize the IRL-based residual error. It is shown that a compute-saving learning mechanism can achieve the optimal consensus, and the error variables of the closed-loop system are uniformly ultimately bounded (UUB). Besides, in any bounded initial condition, the evolution of bipartite consensus is limited to a user-prescribed boundary under bounded initial conditions. The illustrative simulation results validate the efficacy of the approach.

Adaptive backstepping sliding mode compensation control for electro‐hydraulic load simulator with backlash links

AbstractWhen a mechanical backlash between the loading piston rod and the steering gear piston rod connection of the electro‐hydraulic load simulator (EHLS), it will lead to poor loading accuracy. To solve this problem, an adaptive backstepping sliding mode controller based on the backlash feedforward compensation and state observer is proposed. First, the mechanism of surplus force generation in the EHLS is analyzed, and a mathematical model containing position disturbance and backlash nonlinearity is established based on the analysis results. Second, a state observer is designed to estimate the system state and the parameter adaptive law is designed to estimate the system parameters. Third, the adaptive backstepping method is combined with the non‐singular terminal sliding mode control (NTSMC) strategy to deal with the position disturbance and parameter uncertainty and to enhance the system's dynamic performance. Finally, a backlash feed‐forward compensator is engineered to restrain the detrimental effects caused by the backlash nonlinearity, and the simulation experimental results show that the designed new method can realize the precise loading of the EHLS under different working conditions, and the surplus force is suppressed better at the same time.

Dynamic event-triggered fixed-time consensus control for coupled multi-permanent magnet synchronous motors stochastic system with prescribed performance

With the ubiquity of permanent magnet synchronous motors (PMSM), multi-PMSMs are increasingly being elastically coupled to achieve greater output power. The authors establish a general mathematical model of coupled multi-PMSMs system. The dynamic analysis of the coupled multi-PMSMs system is analyzed using coupled three-PMSMs system as an example, and a dynamic event-triggered fixed-time consensus controller with prescribed performance is constructed for coupled PMSMs stochastic system. In addition, Interval Type-3 Fuzzy System (IT3FS) is employed to estimate unknown functions, the computing cost is reduced by updating the weights based on only one adaptive law per PMSM. To enhance the efficiency of communication resource utilization, a dynamic event-triggered mechanism is introduced, where the triggering condition depends on a dynamic auxiliary variable. Moreover, fixed-time control technical is applied to guarantee the setting time and a novel fixed-time prescribed performance function (PPF) is constructed to constrain consensus errors. To cope with the “complexity explosion”, a fixed-time tracking differentiator (TD) is introduced and the corresponding filtered error compensation signals is designed. Finally, the authors demonstrate the system is fixed-time stabilized in probability by applying fixed-time stabilization Lyapunov stability criterion, and the simulation results of a coupled three-PMSMs stochastic system show that the presented algorithm is feasible.

A new control method for leader–follower consensus problem of uncertain constrained nonlinear multi-agent systems

The design of Adaptive Fuzzy Sliding-Mode Control (AFSMC) is discussed in this study for the distributed leader–follower consensus problem of nonlinear uncertain multi-agent systems with input and state constraints. Avoiding the critical circumstances related to the violation of input and state constraints is an important issue in the design of consensus control systems. The limitations of existing adaptive consensus controllers developed for full-state constrained systems motivated the present novel method without restrictive structural assumptions. To convert the original problem to an unconstrained consensus control problem, the proposed control system uses a barrier function-based state transformation method and the input-state linearization methodology. As a result, each agent’s adaptive fuzzy sliding-mode control input, which consists of a fuzzy system and a robust term, is constructed based on the derived representation of the system dynamics. The fuzzy system is used to approximate the dynamic equations of the agent, its neighbors, and maybe the leader in each local feedback control law structure, and the robust term is designed to compensate for the fuzzy approximation error. The magnitudes of the robust terms and the output vectors of the fuzzy systems are also determined using the proposed adaptation laws. The second Lyapunov theorem and Barbalat’s lemma are used to verify the closed-loop system’s asymptotic stability. The effectuality of the proposed methodology is confirmed by numerical simulations for several Autonomous Underwater Vehicles (AUVs). Simulation results show that by means of the proposed AFSMC, the leader–follower consensus is achieved without state constraint violation and performance degradation.

Climate adaptation law: a European perspective

AbstractIn contrast to climate protection law, which regulates the mitigation of climate change, climate adaptation law deals with the management of the unavoidable consequences of climate change. This article provides an overview of its legal basis from a European perspective. In addition to international law, especially the Paris Agreement, EU law is of central importance in this respect. It is primarily shaped by the EU Climate Law enacted in 2021. However, this Law only sets a general framework and is further defined by legal acts of various sectoral policies, especially in the field of environment. Climate adaptation regulations at the level of European member states are presented using the example of Germany, where a Federal Climate Adaptation Act is currently being drafted. Due to Germany's federal state structure, state legislation is also analysed. Most of the German states (“Länder”) have their own climate laws, although their content varies. The municipal level is only addressed with restraint in these laws. The reasons for this are of a fiscal constitutional nature and will be explained in more detail.

Design and Implementation of an L1 Adaptive Proportional Output Feedback Controller

A new approach for output feedback L1 adaptive control based on a proportional adaptation law is presented. The effectiveness of this design is assessed in simulation and validated through real-time testing on an airfoil pitch control wind tunnel experimental rig. Experimental evaluation of the robustness of the controllers, assessed by introducing various disturbances into the control signals, shows that the adaptive control has a better performance compared to PID control, particularly in scenarios with reduced control effectiveness and time-varying disturbances. The experimental results demonstrate the efficacy of the proposed method in practical applications.

Self-error learning framework-based algorithm for parameter recovery of extended Wiener–Hammerstein systems subject to quantised measurements

In this study, a novel estimation scheme is proposed for identifying extended Wiener–Hammerstein systems with hysteresis nonlinearity subject to quantised measurements. The proposed scheme is established in a self-error learning framework to achieve high-performance parameter estimation compared with classic error feedback learning estimation algorithms. Initially, the useful identification data can be extracted from contaminated system data by introducing an adaptive filter. Then, with the help of the filtered data, the identification error expression used to establish the estimator is derived. Subsequently, an online compensation estimation error variable is proposed to eliminate the effect of the regression vector on the convergence performance. A new adaptive law is designed with adaptive recursive gain, considering the compensation estimation error data and parameter initial error data. Under general persistent excitation (PE) condition, the PE condition of the regressor information is verified online, and the estimator convergence is strictly proven. Finally, the statistical results of two illustrated examples and a real-word example are provided to validate the positive features and effectiveness of the proposed estimation scheme.

Event-Triggered Output-Feedback Adaptive Control of Interconnected Nonlinear Systems: A Cyclic-Small-Gain Approach.

This article proposes a novel output-feedback event-triggered control protocol for a class of interconnected parametric nonlinear systems. Different from most existing works where event-triggering mechanisms are considered for only the controller-to-actuator channel or the sensor-to-controller channel, this work adopts event-triggering mechanisms for both channels as well as adaptive laws. An adaptive states observer is designed to estimate the unavailable system state and then a novel adaptive event-triggered controller is proposed based on the celebrated backstepping technique. By utilizing the cyclic small-gain theorem and Lyapunov theory, it is shown that the proposed control scheme ensures that all the closed-loop signals are semi-globally uniformly ultimately bounded (SGUUB), and the Zeno behavior is successfully excluded. Finally, a practical example is provided to illustrate the effectiveness and advantages of the proposed approach.

Disturbance Observer-Based Adaptive Intelligent Control of Marine Vessel With Position and Heading Constraint Condition Related to Desired Output.

This article studies the adaptive control about the geodetic fixed positions and heading of three-degree-of-freedom dual-propeller vessel. During the navigation of a vessel at sea, due to the unpredictable sea, on the one hand, it is important to ensure that the vessel can smoothly follow the desired geodesic fixed position and heading; on the other hand, when the sailing environment is harsh, it is even more important that the vessel can adapt to the desired geodesic fixed position and heading that change at any time for safe driving. Therefore, this article selects the time-varying function related to the desired geodesic fixed position and heading as the constraint condition, and the constraint condition will change in real time as the expected position and heading change. The design of the control strategy is difficult, and the designed control strategy will be more suitable for complex maritime navigation conditions. First, the article constructs a log-type barrier Lyapunov function. Second, by introducing an unknown external disturbance observer, the external disturbances caused by the environment that may be encountered during the vessel's voyage can be observed. Then, combined with the backstepping algorithm, a neural network (NN) control strategy and adaptive law are designed. Among them, for the uncertain function in the process of designing the control strategy, the NN is used to approximate it. Furthermore, through the Lyapunov stability analysis, it is shown that applying the designed control strategy to the vessel system in this article can ensure that the system is closed-loop stable. The final simulation experiment shows the effectiveness of the designed control strategy.

Neural Network Boundary Approximation for Uncertain Nonlinear Spatiotemporal Systems and Its Application of Tracking Control.

This brief addresses the neural network (NN) approximation problem for uncertain nonlinear systems with time-varying parameters (that is, unknown nonlinear spatiotemporal systems). Due to the fact that the unknown spatiotemporal functions cannot be directly approximated by NNs, a so-called time-varying parameter extraction is given to separate time-varying parameters from uncertain nonlinear spatiotemporal functions. By using the supremum of Euler norm of the extracted time-varying parameters, the nonlinear spatiotemporal function is mapped to an unknown state-based boundary function, which can be approximated by NNs. Based on the time-varying parameter extraction, an adaptive neural tracking control law is designed for uncertain strict-feedback nonlinear spatiotemporal systems, which guarantees the convergence of the tracking error with a trajectory performance. The effectiveness of the designed method is verified by simulations.

RBF neural network disturbance observer-based backstepping boundary vibration control for Euler–Bernoulli beam model with input saturation

The main objective of this paper is to address the issue of vibration control for a class of Euler–Bernoulli beam systems that are subject to external disturbances and input saturation. The proposed controller differs from other backstepping methods in that it employs a radial basis function (RBF) neural network to accurately estimate boundary disturbances and incorporates the hyperbolic tangent function to ensure input constraints. The nonlinear partial differential equation (PDE) model is initially derived based on Hamilton’s principle to capture the dominant dynamic characteristics of the flexible beam. In the framework of the Lyapunov direct approach, an adaptive RBF neural network-based law is subsequently designed to estimate the state-related boundary disturbances. The backstepping approach is then developed to propose sufficient conditions for ensuring the stability and convergence of closed-loop systems subject to input saturation. Finally, the effectiveness and superiority of the proposed methodology are further demonstrated by comparing the simulation results of constrained backstepping controllers.

Model-Free RBF Neural Network Intelligent-PID Control Applying Adaptive Robust Term for Quadrotor System

This paper proposes a quadrotor system control scheme using an intelligent–proportional–integral–differential control (I-PID)-based controller augmented with a radial basis neural network (RBF neural network) and the proposed adaptive robust term. The I-PID controller, similar to the widely utilized PID controller in quadrotor systems, demonstrates notable robustness. To enhance this robustness further, the time-delay estimation error was compensated with an RBF neural network. Additionally, an adaptive robust term was proposed to address the shortcomings of the neural network system, thereby constructing a more robust controller. This supplementary control input integrated an adaptation term to address significant signal changes and was amalgamated with a reverse saturation filter to remove unnecessary control input during a steady state. The adaptive law of the proposed controller was designed based on Lyapunov stability to satisfy control system stability. To verify the control system, simulations were conducted on a quadrotor system maneuvering along a spiral path in a disturbed environment. The simulation results demonstrate that the proposed controller achieves high tracking performance across all six axes. Therefore, the controller proposed in this paper can be configured similarly to the previous PID controller and shows satisfactory performance.

Adaptive fractional-order nonsingular terminal sliding mode control and sequential quadratic programming torque distribution for lateral stability of FWID-EVs with actuator constraints

This paper proposes a novel sliding mode control (SMC) algorithm for direct yaw moment control of four-wheel independent drive electric vehicles (FWID-EVs). The algorithm integrates adaptive law theory, fractional-order theory, and nonsingular terminal sliding mode reaching law theory to reduce chattering, handle uncertainty, and avoid singularities in the SMC system. A sequential quadratic programming (SQP) method is also proposed to optimize the yaw moment distribution under actuator constraints. The performance of the proposed algorithm is evaluated by a hardware-in-the-loop test with two driving maneuvers and compared with two existing SMC-based schemes together with the cases with the change of vehicle parameters and disturbances. The results demonstrate that the proposed algorithm can eliminate chattering and achieve the best lateral stability as compared with the existing schemes.

Practical Finite-Time Command-Filtered Adaptive Backstepping With Its Applications to Quadrotor Hovers.

In this article, a practical finite-time command-filtered adaptive backstepping (PFTCFAB) control method is presented for a class of uncertain nonlinear systems with nonparametric unknown nonlinearities and external disturbances. Unlike PFTCFAB control techniques that use neural networks (NNs) or fuzzy-logic systems (FLSs) to deal with system uncertainties, the proposed method is capable of handling such uncertainties without the need for NNs or FLSs, thus reducing complexity and increasing reliability. In the proposed approach, novel function adaptive laws are designed to directly estimate unknown nonparametric nonlinearities and external disturbances by means of command filter techniques, and a type of practical finite-time command filters is proposed to obtain such laws. Moreover, the PFTCFAB controllers and finite-time command filters are designed with practical finite-time Lyapunov stability, which ensures finite-time stability of system tracking and filter estimation errors. Experimental results with a quadrotor hover system are presented and discussed to demonstrate the advantages and effectiveness of the proposed control strategy.