Control Gain Functions Research Articles

Distributed Adaptive Secure Consensus Tracking Control for Asynchronous Switching Nonlinear MASs Under Sensor Attacks and Actuator Faults

A distributed adaptive secure control algorithm is proposed for asynchronous switching nonlinear multi-agent systems (MASs) in pure-feedback form while considering the sensor attacks and actuator faults, which eliminates the effect of attack signals, actuator faults and uncertainties without knowing the sign of the control gain functions. Since the system states measured by the sensors are corrupted by the malicious attacker, only the post-attack system states can be obtained. Thus, an improved coordinate transformation is constructed by using the post-attack system states and a backstepping method based on the improved coordinate transformation is developed to solve the consensus tracking control problem of the researched systems under sensor attacks. The common Lyapunov function is designed to ensure the stability of all asynchronous switching subsystems of each agent. In the end, a simulation example is presented to illustrate the theoretical results’ validity. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —This paper deal with the distributed adaptive secure consensus tracking control problem for asynchronous switching nonlinear MASs, whose models can describe many phenomena in nature such as biological processes, robot team formation and sensor networks. It is extremely challenging to achieve the tracking control problem of the researched asynchronous switching nonlinear system in an unsafe network environment, where the unknown sensor attacks signals, actuator faults coefficients, and randomly switched non-affine nonlinearities exist together for the followers. Furthermore, the control design and stability analysis of the researched system is based on the common Lyapunov approach, which makes the developed approach more engineering oriented.

A finite-time path-tracking control algorithm for nonholonomic mobile robots with unknown dynamics and subject to wheel slippage/skid disturbances

Path planning and tracking control are two performance-critical tasks for wheeled mobile robots, particularly when nonholonomic constraints are imposed on robots in dynamically uncertain conditions. Accomplishing certain performance and safety considerations related to path-tracking, such as global stability, transient performance, and smooth finite-time convergence, becomes more difficult for nonholonomic robots. This paper is concerned with proposing a new adaptive robust finite-time tracking control approach for a large class of differential drive autonomous nonholonomic wheeled mobile robots (NWMRs) that are subject to structured uncertainties and extraneous disturbances with fully unknown dynamics. For this purpose, nonlinear kinodynamics of a type of rear-wheel drive NWMRs are developed by incorporating the skid/slippage constituents of the wheel motion. Then, a path-tracking controller is proposed using a continuous finite-time adaptive integral sliding mode control coupled with an integral backstepping approach (FTAISM-IBC). For the adaptive controller design, the entire nonlinear dynamics of the robot, including nonlinear vector functions and control gain functions, together with extraneous disturbances, are estimated by leveraging the universal approximation capabilities of radial basis neural networks (RBFNNs). The finite-time stability proof is presented by utilizing the Lyapunov stability theorem. Furthermore, the adaptive gains are derived to ensure the finite-time stability of the system subject to unknown functions, parametric variations, and unknown but bounded disturbances. Finally, the effectiveness of the proposed controller is evaluated through simulations in terms of several key performance indicators against several reported studies.

Decentralized model reference adaptive control for interconnected systems with time‐varying delays and unknown dead‐zone inputs

AbstractIn this study, the decentralized model reference adaptive control (DMRAC) problem is tackled for a class of time‐varying delay interconnect systems that comprise unknown system matrices and unknown dead‐zone inputs. Two robust adaptive control methods are proposed for state tracking based on the moderate matching time‐varying delay nonlinear assumptions and the matching between the controlled system and reference model matrices, respectively. The control gain function is explicitly expressed, and it is applied to the adaptive law gains simultaneously. Moreover, a Lyapunov–Krasovskii functional with two integral functions is developed. Besides the properties of the type‐B Nussbaum function, the circumstance where the system parameters are fully unknown is considered. As indicated by the results, all signals in the closed‐loop system are bounded while fulfilling asymptotically tracked control objectives. The simulation example of this study verifies the effectiveness and feasibility of the proposed design method.

Prescribed-time adaptive stabilization of high-order stochastic nonlinear systems with unmodeled dynamics and time-varying powers

&lt;p&gt;In this paper, the control problem of prescribed-time adaptive neural stabilization for a class of non-strict feedback stochastic high-order nonlinear systems with dynamic uncertainty and unknown time-varying powers is discussed. The parameter separation technique, dynamic surface control technique, and dynamic signals were used to eradicate the influences of unknown time-varying powers together with state and input unmodeled dynamics, and to mitigate the computational intricacy of the backstepping. In a non-strict feedback framework, the radial basis function neural networks (RBFNNs) and Young's inequality were deployed to reconstruct the continuous unknown nonlinear functions. Finally, by establishing a new criterion of stochastic prescribed-time stability and introducing a proper bounded control gain function, an adaptive neural prescribed-time state-feedback controller was designed, ensuring that all signals of the closed-loop system were semi-global practical prescribed-time stable in probability. A numerical example and a practical example successfully validated the productivity and superiority of the control scheme.&lt;/p&gt;

Active disturbance rejection control: an application to continuous microalgae photobioreactors

AbstractBACKGROUNDMathematical modelling is a widely employed approach for investigating the growth behaviour of microalgae. As a result, the development of model‐based controllers to regulate process variables has garnered increasing attention. However, despite the significant efforts invested in this area, control performance can be adversely affected by unmodelled dynamics and disturbances.RESULTSTwo active disturbance rejection controllers (ADRC) were designed to enable robust tracking of biomass concentration in continuous microalgae photobioreactors, with reduced reliance on the mathematical model of the system. The controllers were tuned to achieve a nonovershoot response and minimize settling time based on the culture's characteristics. Simulations were performed using optimal setpoints specific to each model. The results showcased a maximum output signal deviation of ±2.2%, ±7.8% and ± 7.62% for the Dunaliella tertiolecta, Isochrysis affinis galbana and Chlorella vulgaris models, respectively, regardless of the presence of simulated disturbances.CONCLUSIONSThe findings of this study significantly contribute to the advancement of the field of sustainable microalgae production. By introducing less dependent model‐based controllers, this research enhances the feasibility of implementing robust control strategies. These controllers require only knowledge of the equation system's order and the control gain function, simplifying the design process. This approach effectively addresses control performance degradation arising from unmodelled dynamics and disturbances. The ability to maintain desired process variables through ADRC controllers not only ensures improved control performance, but also supports the cultivation of specific microalgal species, when an accurate model is not available, thus promoting the overall progress and viability of microalgae biomass production. © 2023 Society of Chemical Industry.

Adaptive Containment Control for a Class of Uncertain Multi-agent Systems With Unknown Virtual Control Gain Functions

Adaptive Containment Control for a Class of Uncertain Multi-agent Systems With Unknown Virtual Control Gain Functions

Composite learning control of strict‐feedback nonlinear system with unknown control gain function

AbstractThe composite learning control with the heterogeneous estimator is proposed to deal with the multiple uncertainties of strict‐feedback nonlinear systems. The article applies the recorded data‐based neural learning and the disturbance observer (DOB) to learn the multiple uncertainties, including the nonlinear dynamics, the unknown control gain function (CGF), and the time‐varying disturbance. The lumped prediction error is constructed and included into the update law by neural approximation and disturbance observation. Furthermore, the asymmetric saturation nonlinearity (ASN) of the control input is represented by the smooth form model to ensure the input limitation, and a projection algorithm is adopted to avoid the singularity problem. The closed‐loop system stability is rigorously analyzed and the boundedness of the system tracking error is guaranteed. Through the tests of the third‐order nonlinear system and the autonomous underwater vehicle (AUV), it is observed that the proposed approach can improve the system tracking accuracy with the expected learning performance.

Decentralized Adaptive Control of Large-Scale Nonlinear Systems With Time-Delay Interconnections and Asymmetric Dead-Zone Input

In this article, a decentralized adaptive control strategy is proposed for a class of large-scale nonlinear systems with interconnections. Each subsystem contains multiple state delays, asymmetric dead-zone inputs, and bounded time-varying disturbances. Every error subsystem is first decomposed according to input matrix assumption. Then, the decentralized adaptive controller is developed to handle uncertain functions in the subsystem. The nonlinear control gain function is constructed and used in adaptive control design. Two robust adaptive control schemes are, respectively, addressed for the cases of matched and mismatched time-delay nonlinearities. It is proved that all closed-loop signals are bounded, and the tracking error converges to an adjustable region. A simulation example is presented to show the effectiveness of the proposed method.

Event-triggered adaptive neural control for state-constrained switched nonlinear systems based on nonlinear shifting function technique

This paper addresses the event-triggered tracking control design for state-constrained switched nonstrict feedback nonlinear systems. With the help of a time-varying nonlinear shifting function (TVNSF) introduced into the switched nonlinear system, the proposed solution is seen as a unified tool regardless of whether the constraint conditions are state constraints, output constraint, or even no constraint. Also, by allowing the triggering error to vary with the switching signal in time, the negative effects of the mismatch between the individual controller and the subsystem on system performance are trumped. Moreover, by using constructed individual Lyapunov function that depends on the lower bound of the control gain function of individual subsystem, a novel switching signal satisfying the average dwell time (ADT) is provided to ensure the boundedness of all variables in the closed-loop system. Finally, the proposed theory is carried over into a mass-spring-damper system to verify its effectiveness.

An Observer-Based Fuzzy Adaptive Consensus Control Method for Nonlinear Multiagent Systems

This article investigates the problem of fuzzy adaptive consensus tracking control for nonlinear multiagent systems with unknown nonlinear control gain functions. In the control design, fuzzy logic systems (FLSs) are adopted to approximate the unknown nonlinear dynamics, and a distributed state observer is constructed to estimate the unmeasured states. Under the case of directed graph, by constructing the logarithm Lyapunov functions, an adaptive fuzzy distributed control method is presented, which removes the restrictive assumptions about the unknown control gain functions must be constants in traditional adaptive intelligent output feedback control methods. The developed control scheme cannot only ensure that all signals of the controlled system are semiglobal uniformly ultimately bounded, but also make the outputs of all the followers keep consensus with the output trajectory of the leader. Finally, simulation results are given to illustrate the effectiveness of the developed consensus control scheme and theorem.

Fuzzy Control of Switched Systems With Unknown Backlash and Nonconstant Control Gain: A Parameterized Smooth Inverse

This article addresses fuzzy tracking control question when switched systems are subjected to unknown input backlash, nonconstant control gain, and asymmetric full-state constraints. A new mode-dependent integral barrier Lyapunov function (MIBLF) can handle conservative feasibility conditions that only assure asymmetric full-state constraints and all subsystems share a common controller. To handle unknown input backlash nonlinearities in the presence of unknown nonconstant control gain function, fuzzy logic systems are utilized and a new parameterized smooth backlash inverse (PSBI) is presented. It is hard to construct the barrier Lyapunov function-based controller in the presence of unknown backlash, switching framework, and full-state constraints. By employing the fuzzy logic systems and the PSBI, a novel MIBLF-based adaptive fuzzy controller is presented to overcome this challenge. Furthermore, the presented controller not only prevents violation of all constrained states, but also ensures the boundedness of the closed-loop system. Eventually, feasibility of achieved theoretical results can be proven by two examples.

Adaptive learning control for triggered switched systems based on unknown direction control gain function

This paper investigates event-triggered switched heuristic dynamic programming (HDP) control for switched systems based on an unknown direction control gain function (UDCGF). First, the Nussbaum gain function is introduced to describe the unknown control direction, which makes the control behaviour of switched systems more flexible. The proposed variable threshold event-triggering (VTET) condition can significantly reduce computation while maintaining a certain system performance. Then, a detailed Lyapunov stability analysis based on the new tight bound is given, which reflects the asymptotic stability of the switched systems under the proposed switched HDP control method. The system mode-matched action-critic neural networks are employed to approximate the optimal triggered control law and the optimal switching value function, respectively. Subsequently, the boundedness analysis of neural network (NN) weights and the convergence analysis of HDP algorithm are given. At last, a numerical example is provided to verify the effectiveness of the proposed method.

Event-Based Adaptive Neural Asymptotic Tracking Control for Networked Nonlinear Stochastic Systems

This paper investigates the adaptive asymptotic tracking control for networked nonlinear stochastic systems. Different from having the necessity of prior knowledge of the unknown control coefficients in the conventional adaptive control of nonlinear stochastic systems, in this study, the limitation of control coefficients in the stability analysis is relaxed by constructing a new Lyapunov function that contains the lower bounds of the control gain function. By constructing a smooth function with a positive time-varying integral function and utilizing the boundary estimation method, asymptotic tracking control can be guaranteed. At the same time, for nonlinear stochastic systems with unknown control coefficients, a neural adaptive event-triggered strategy that greatly saves communication resources while ensuring system performance is proposed. Finally, simulation results show that the proposed control scheme can guarantee the realization of the control objectives.

Optimized tracking control using reinforcement learning strategy for a class of nonlinear systems

AbstractThis paper is to develop a simplified optimized tracking control using reinforcement learning (RL) strategy for a class of nonlinear systems. Since the nonlinear control gain function is considered in the system modeling, it is challenging to extend the existing RL‐based optimal methods to the tracking control. The main reasons are that these methods' algorithm are very complex; meanwhile, they also require to meet some strict conditions. Different with these exiting RL‐based optimal methods that derive the actor and critic training laws from the square of Bellman residual error, which is a complex function consisting of multiple nonlinear terms, the proposed optimized scheme derives the two RL training laws from negative gradient of a simple positive function, so that the algorithm can be significantly simplified. Moreover, the actor and critic in RL are constructed by employing neural network (NN) to approximate the solution of Hamilton–Jacobi–Bellman (HJB) equation. Finally, the feasibility of the proposed method is demonstrated in accordance with both Lyapunov stability theory and simulation example.

Reinforcement learning‐based optimized backstepping control of nonlinear strict feedback system with unknown control gain function

AbstractThe article develops an optimized control via learning from the design idea of optimized backstepping (OB) technique for the nonlinear strict feedback systems containing the unknown dynamic and control gain functions. OB technique requires to deal with the actual and virtual controls of backstepping as the optimized solutions of corresponding subsystems so that the entire backstepping control is optimized. In the work, for achieving the optimization control, reinforcement learning (RL) of critic‐actor structure is constructed in every backstepping step on the basis of the neural network approximation of the Hamilton–Jacobi–Bellman equation's solution. Since the unknown nonlinear control gain function is considered, the complexity of control algorithm is greatly increased. However, the proposed RL is with the simple training laws, it can greatly alleviate the algorithm complexity for the optimized control. Finally, the feasibility of the method is demonstrated by both theory and simulation.

Predefined Time Synchronization Control for Uncertain Chaotic Systems.

In this study, the predefined time synchronization problem of a class of uncertain chaotic systems with unknown control gain function is considered. Based on the fuzzy logic system and varying-time terminal sliding mode control technology, the predefined time synchronization between the master system and the slave system can be realized by the proposed control method in this study. The simulation results confirm the theoretical analysis.

Decentralized Model Reference Adaptive Control for Systems With Time Delays and Dead Zones

The decentralized robust model reference adaptive control (MRAC) problem is studied for a class of large-scale systems with unknown plant parameters, unknown time-varying delayed interconnections, and unknown dead-zone inputs. Two robust adaptive control schemes are proposed for the cases of symmetric dead-zone input and asymmetric dead-zone input under the assumption of moderate time-delay nonlinearity and the matching conditions of the plant model and the reference model matrix, respectively. The control gain function is explicitly expressed, and its useful properties are established. The Lyapunov-Krasovskii functional with two integral functions is constructed. It is shown that all signals in the closed-loop system are bounded and the state tracking error converges exponentially to a tunable region. The effectiveness and feasibility of the proposed design approach is illustrated by a simulation example.

Quantized-State-Feedback-Based Neural Control for a Class of Switched Nonlinear Systems With Unknown Control Directions

This paper investigates the problem of unknown virtual control directions in a state-quantized adaptive recursive control design for a class of arbitrarily switched uncertain pure-feedback nonlinear systems in a band-limited network. State quantization is considered for state feedback control in a band-limited network. The primary contribution of this study is to provide a quantized state feedback adaptive control strategy to address the unknown control direction and arbitrarily switched nonaffine nonlinearities. Herein, a coupling problem between Nussbaum functions and quantization errors caused by quantized state feedback control laws is considered in the Lyapunov-based design and stability analysis. A state-quantized adaptive recursive control scheme using the function approximation is constructed without a priori knowledge of the signs of the control gain functions, where the estimated parameters and Nussbaum-type functions are adaptively updated via quantized states. Theoretical lemmas are derived to show that the adaptive parameters and quantization errors of the closed-loop signals are bounded using the proposed control scheme. The boundedness of the closed-loop signals and the convergence of tracking error to a neighborhood of the origin are proved using the common Lyapunov function approach. Two simulation examples are shown to illustrate the effectiveness of the proposed theoretical result.

Robust adaptive stabilization of nonlinear systems with mismatched time delays

For a class of nonlinear systems with mismatched time delays and disturbances, robust adaptive stabilization control is studied. The control law is split into two terms. One is used to cope with the delayed states, and the other is to handle the disturbance. The improved robust adaptive laws with control gain function and time-varying σ-modification are constructed to estimate the unknown integrated parameters. It is proved that the designed adaptive controller can ensure the asymptotic convergence of the closed-loop system states. Another adaptive algorithm is also proposed to ensure the asymptotic stability of the closed delayed nonlinear system without external disturbance.

Mean‐square output consensus of heterogeneous multi‐agent systems with communication noises

This paper focuses on the mean-square output consensus of heterogeneous multi-agent systems, in which the communication noises are taken into consideration. Through internal model principle and control gain function, the novel state feedback and output feedback control strategies are designed for leaderless and a leader situation respectively to attenuate disturbances caused by communication noises. In addition, based on matrix theory and stochastic analysis, the sufficient condition for output consensus in the corresponding case is obtained. In the end, the simulations are used to confirm the correctness of the conclusion.