Control Of Nonlinear Systems Research Articles

Predefined time fuzzy adaptive control for stochastic nonlinear systems with limited time interval output constraints

This article investigates the problem of fuzzy adaptive predefined time tracking control for stochastic nonlinear systems with limited time interval output constraints. Firstly, the considered output constraints occur within a finite time interval after the system starts running. By constructing shift functions and barrier Lyapunov functions (BLFs), the constrained system is converted into an unconstrained system, which solves the problem of function discontinuity resulting from output constraints within limited time intervals. Then, with the help of adaptive backstepping technique and predefined time control method, which reduces the parameters to be designed and removes the limitation of relatively large initial control input in existing approaches. The designed control technique ensures the boundedness of all variables of the stochastic system, the tracking error converges within a predetermined time, and the outputs do not exceed their constraint boundaries in a finite time interval. And this algorithm is applicable to both infinite time constraints and unconstrained outputs cases. Finally, the validity of this approach is demonstrated through simulation examples.

Optimized Inverse Dead‐Zone Control Using Reinforcement Learning for a Class of Nonlinear Systems

ABSTRACTIn this article, an optimized inverse dead‐zone control using reinforcement learning (RL) is developed for a class of nonlinear dynamic systems. The dead‐zone is frequently occurred in the nonlinear control system, and it can affect the control performance and even cause the system instable. Hence, it is very requisite to consider the effect of dead‐zone in the design of control strategy. In this proposed optimized inverse dead‐zone control, the basic idea is to find the optimized control as input and the adaptive algorithm to estimate the unknown parameters for the inverse dead‐zone function, so that the available dead‐zone input for system control can be derived. Comparing with traditional methods, on the one hand, the proposed dead zone inverse method is with fewer adaptive parameters, on the other hand, the RL under identifier‐critic‐actor architecture is with the simplified algorithm. Finally, theoretical and simulation results manifest the feasibility of the proposed method.

Containment control for non-linear fractional-order multi-agent systems via refined sample data controller

Abstract This manuscript concentrates on the problem of designing a sampled data controller (SDC) for the consensus of a fractional-order multi-agent system (FOMAS) with Lipschitz non-linearity via an algebraic approach. The solution of the FOMAS is represented by using the Laplace transform approach. An upper bound of the sampling period is determined through various integral inequality techniques. Distinguished from the existing works, the estimate for an upper bound is more accurate which involves the Lipschitz constant of the non-linear function. Finally, numerical examples are given to validate the correctness of results. Furthermore, the comparison results are presented to show the proposed method determines a better upper bound of the sampling period.

Dynamic event‐triggered model‐free adaptive control for networked control systems with random packet loss

AbstractA novel dual‐channel dynamic event‐triggered model‐free adaptive control method with compensation is proposed for nonlinear networked control systems (NCSs) subjected to random packet loss. In order to tackle the issue of redundant data transmission, a dual‐channel triggering control framework is designed, where data transmission only occurs upon meeting the triggering conditions. Compared with the traditional static event‐triggered schemes with fixed triggering thresholds, the proposed method allows for dynamically adjustable triggering thresholds. This means that the number of data transmissions in the forward and feedback channels can be further reduced. In addition, considering the detrimental impact of random packet loss and output event‐triggered on the system, compensation is applied to the system's output data using the linear data model of the nonlinear system, which is directly derived from I/O data without incorporating any other mechanistic model information, thereby ensuring optimal control performance. In contrast to existing results, the proposed control strategy can enhance system performance while conserving network communication resources. The effectiveness and superiority of the proposed scheme have been validated through two simulations.

Adaptive switching control of full state constrained nonlinear systems with unknown control directions

AbstractIn this article, an adaptive switching controller is designed for the stabilization control and the tracking control of nonlinear systems suffering from full state constraints, unknown control directions, and system uncertainties. Featured with changing signs and unbounded increasing magnitudes, a switching control structure is proposed to deal with the unknown control direction problem. In order to explore and finally fix the correct control direction, an adaptive switching rule, a switching function, and a reference function are constructed. An integral Lyapunov function is adopted for the design of the control law, which ensures that full state constraints will not be violated. Using this method, the nonlinear system can be properly controlled without extra estimations or approximations. The boundedness of all the states and the stability of the system are analyzed and guaranteed. Finally, simulations are conducted to validate the proposed method, and the results illustrate its effectiveness.

Self-evolving fuzzy system based inverse dynamics learning control for nonlinear systems with uncertainties

Self-evolving fuzzy system based inverse dynamics learning control for nonlinear systems with uncertainties

Research on random dynamic cylinder deactivation control strategy of engine based on nonlinear model prediction

In the process of cycle cylinder deactivation, the different proportion of cylinder deactivation between adjacent working cycles will cause the problem of uneven operation of each cylinder. In this paper, a random dynamic cylinder deactivation (RD-CDA) control method based on nonlinear model prediction is proposed. The RBF neural network model of the RD-CDA system is built. The K-means algorithm is applied to the offline training of the center position c of the hidden layer node. The P-nearest algorithm is used to train the hidden layer node width σ offline. The recursive least squares (RLS) algorithm is applied to train the output layer weight vector w online. The online adaptive change of the model is realized, and the model verification is carried out. Then, the nonlinear model predictive control system structures with the minimum torque fluctuation and brake specific fuel consumption rate (BSFC) are built respectively. Under different working conditions, the average torque fluctuation per cycle is improved by about 9% to 18.75%, and the average BSFC is improved by about 2 % -3.9 %, which verifies the effectiveness of this strategy in reducing the dynamic fluctuation of random dynamic cylinder deactivation torque and improving fuel economy.

Disturbance Observer-Based-Model-Free Adaptive Fuzzy Fractional-Order Prescribed Performance Control for Nonlinear PEMFC System with Uncertainties and Performance Constraints

Disturbance Observer-Based-Model-Free Adaptive Fuzzy Fractional-Order Prescribed Performance Control for Nonlinear PEMFC System with Uncertainties and Performance Constraints

A novel intelligent control of discrete-time nonlinear systems in the presence of output saturation

In this paper, a model free control method for a class of discrete time nonlinear systems is introduced. A type-3 fuzzy system estimates the unknown parameters required by the control system. The control system only uses the input and output data of the plant and therefore does not need to know its mathematical equations. On the other hand, the phenomenon of output saturation is a challenging problem for all control systems, addressed in detail in the proposed method. The convergence of the proposed method is guaranteed, and the control system is very robust in the face of changes in the dynamics of the plant. The simulation results on discrete-time nonlinear systems show that the proposed method is very accurate despite the high speed of convergence. In addition, the proposed method is robust for modeling uncertainties and has a better root mean square error and step response time compared to the other methods. Also, a comparison has been made between type-1 to type-3 fuzzy systems and control system based on trial and error, which shows firstly the importance of the presence of fuzzy system and secondly the superiority of type-3 fuzzy system compared to the other two types.

Robust position regulation of a 2-DOF experimental helicopter using higher order super twisting sliding mode control

This study presents a third-order super twisting sliding mode control algorithm for robust position regulation of a two-degree-of-freedom (2-DOF) experimental helicopter. The proposed approach explores high-order sliding mode control, offering advantages such as finite-time convergence and continuous control signals. The controller is implemented and validated on the Quanser Aero 2 platform, an inherently unstable and nonlinear system that presents significant challenges for control design including cross-coupling effects, model uncertainties, and external disturbances. Extensive simulations and experimental results are presented to validate the efficacy and robustness of the proposed control strategy. They highlight the controller's ability to achieve precise position control while significantly mitigating the chattering phenomenon, a common drawback associated with traditional sliding mode control. This study contributes to the field of nonlinear control systems by demonstrating the potential of high-order sliding mode control in managing nonlinear, coupled dynamic systems. The successful implementation on a real-world platform underscores the practical applicability of the proposed method in aerospace and robotics applications.

Disturbance observer-based nonsingular fixed-time fuzzy adaptive event-triggered output feedback control of uncertain nonlinear systems

This article examines the fuzzy adaptive event-triggered output feedback control issue of eliminating fixed-time singularity for a type of uncertain nonlinear systems with disturbance observer structures. By introducing novel bounded time-varying functions (TVFs), a set of more general intermediate-variable-based disturbance observers (IVBDOs) is constructed. Combining the corresponding auxiliary reduced-power function and the quartic Lyapunov method, a co-design scheme for a fuzzy approximation high-order controller and an improved event-triggered mechanism with a judgment indicator threshold is proposed. Especially, the developed framework not only removes the singularity during the fixed-time design process but also further reduces the communication resources. By means of theoretical analysis, the devised solution achieves fixed-time stable control (FTSC) of the system and the tracking error converges to the desired neighborhood around the origin. After verifying the absence of Zeno behavior, the efficacy of the presented methodology is supported by two simulation examples.

Deep neural networks-prescribed performance optimal control for stochastic nonlinear strict-feedback systems

This article explores the application of deep neural networks (DNNs) for optimized backstepping control design in a category of stochastic nonlinear strict-feedback systems with unknown dynamics, focusing on prescribed performance. DNNs, distinguished by their ability to handle high-complexity functions and enhance function approximation, are employed to estimate unknown nonlinear functions. The weight updating strategy for each layer of DNNs is determined through a Lyapunov function analysis. Tomitigate potential issues such as the tracking error exploding at uncertain moments, prescribed performance control (PPC) is introduced to constrain the tracking error within a predetermined range. Subsequently, a novel optimal tracking control scheme, integrating the backstepping method and Hamilton–Jacobi–Bellman (HJB) equation, is presented. The results indicate that all signals in the closed-loop system are bounded in probability, and the tracking error is maintained within a set of predefined arbitrarily small residuals. Simulation outcomes affirm the efficacy of the proposed control scheme.

Global output feedback control for uncertain nonlinear systems with input quantisation and sensor gain perturbation

A new quantised control method via output feedback is proposed by establishing two pairs of time-varying coupled matrix inequalities. Compared to relevant quantised control results, our control method has the novelty: (i) the sensor gain perturbation is allowed to be large and nondifferentiable; (ii) the growth constraint of system nonlinearities is relaxed to depend on unmeasured states and x 1 -polynomial function; (iii) a dynamic scaling technique, instead of backstepping design, is introduced to reduce the computational complexity of controller design. In particular, by using a symbolic function (or hyperbolic tangent function), global asymptotic stability is achieved under any hysteresis quantiser.

Practical fixed-time non-singular sliding mode control of second order nonlinear dynamic systems with chattering and overshooting avoidance

This paper introduces a Practical Fixed-Time Stabilization technique (PFxT) designed for a specific class of nonlinear second-order systems. The closed-loop systems, when appropriately parameterized, exhibit convergence within a predetermined time frame to a confined region near the origin. This outcome is achieved by amalgamating a nonlinear sliding mode approach with a practical fixed-time tracking virtual trajectory. The control algorithmś design incorporates considerations for overshoot reduction and chattering cancellation. Furthermore, the Lyapunov method is employed to establish the practical fixed-time stability of the proposed solution, providing insights into the limits within which the algorithm can be effectively deployed. To complete the algorithm specification, a parameter selection approach is introduced, enabling customization of the desired settling time. Comprehensive simulations are conducted to validate the effectiveness and viability of the proposed PFxT technique.

Neural network optimal control for tripartite UAV confrontation systems based on fuzzy differential game

The neural network optimal control strategy based on a fuzzy differential game is proposed for the tripartite UAV confrontation systems consisting of the attackers, defenders, and targets. Firstly, the tripartite UAV mutual confrontation model is constructed and a nonlinear differential control system is established. Secondly, combining the fuzzy evaluation method and differential game theory, the tripartite UAV are divided into two parts of the confrontation game: attackers-defenders and attackers-targets. The optimal control strategies for the attackers, defenders and targets parties are derived separately. Then, the tripartite UAV game model is considered to be difficult to solve directly. The evaluation neural network is introduced to approximate the optimal value function using an adaptive dynamic programming method. The convergence of the evaluation neural network weights and the stability of the nonlinear differential control system are proved by using Lyapunov stability theory. Finally, the effectiveness of the tripartite UAV confrontation game control strategy designed in this paper is verified by simulation.

Stabilization of fractional nonlinear systems with disturbances via sliding mode control

AbstractIn this article, the sliding mode control (SMC) of fractional nonlinear systems (FNSs) with disturbances is studied. First, a useful fractional power‐rate inequality for is extended to a more general form . Based on the generalized inequality, the method of a modified fractional integral SMC is completed, in which the parameter of the symbolic function is extended to and . This increases the degree of freedom of the sliding mode surface (SMS). Then, the SMC of FNSs is studied for the cases of known and unknown disturbances. In the case of known disturbance, it is proved by the generalized inequality and quadratic Lyapunov function method that the state of the FNSs can converge asymptotically to zero on the SMS. For the case of unknown disturbance, a fractional disturbance observer is used to estimate the disturbance by introducing auxiliary variables . The disturbance estimation error of the proposed FNSs is proved to be bounded. An equivalent global control law is obtained and asymptotic convergence of the FNSs under the action of the controller is proved. Finally, two numerical simulation examples are given to verify the feasibility of the method proposed in this article.

Consensus tracking control for nonlinear second-order multi-agent systems with input magnitude and rate constraints

Consensus tracking control for nonlinear second-order multi-agent systems with input magnitude and rate constraints

A new adaptive fuzzy logic control for nonlinear car active suspension systems based on the time-delay

A new adaptive fuzzy logic control for nonlinear car active suspension systems based on the time-delay

Resilient adaptive quantized control for nonlinear cyber-physical systems under deception attacks

Resilient adaptive quantized control for nonlinear cyber-physical systems under deception attacks

Estimation-based event-triggered fixed-time fuzzy tracking control for high-order nonlinear systems

This paper investigates adaptive-estimation-based dynamic event-triggered fuzzy tracking control scheme for high-order nonlinear systems in fixed-time interval. The growing assumptions of coexistence unknown nonlinear uncertainties are removed with the aid of fuzzy logic systems. Contrary to the existing results, an adaptive estimation tactic is formulated to estimate the severe coexistence uncertainties online such that no boundaries are needed for the adaptive parameters, despite approximation errors, unknown virtual control gains and time-varying disturbances. On this estimation mechanism, the virtual control gains have been relaxed to unknown, which is more applicable. In view of controller and actuator, the communication burden is reduced with the aid of dynamic event-triggered rule, and Zeno behavior can be prevented successfully during dynamic sampling and updating of the control signal. Moreover, the singularity problem has been conquered by using the inequality transformation technique and all signals are bounded in fixed-time interval. Finally, two examples are used to verify the feasibility and rationality.