Control Of Nonlinear Systems Research Articles

Low-Complexity Prescribed Performance Control of Nonlinear Systems With Full-State Constraints

Low-Complexity Prescribed Performance Control of Nonlinear Systems With Full-State Constraints

Resilient event-triggered observer-based control of non-linear systems under denial-of-service attacks with actuator saturation

This paper studies the control problem for a continuous-time networked system with non-linearity in the state equation as well as in the input, as saturation. The system is considered under denial-of-service (DoS), attacks which cause the blockage of input and/or output components in the overall closed-loop model. An event-triggering scheme that is resilient in nature, along with an observer-based control, has been considered under DoS attacks. The resultant scheme ensures efficient network resources and excludes Zeno behavior naturally due to the presence of a minimum positive interevent delay. Then, an event-based switched non-linear model is presented to address both the event-triggering scheme and the presence of DoS blocking attacks. A piece-wise Lyapunov–Krasovskii functional method on the described non-linear model, resulting in the switched system, is considered for achieving an exponentially stable response by driving the required feasibility conditions. In the presence of a non-linear system with saturation in the actuator, the presented design establishes quantitative relationships among the exponential decay rate, active/sleeping intervals of attacks, parameters of the event-triggering condition, and sampling period of the system. After that, linear matrix inequalities are presented for designing an event-triggered controller with an observer, while the design also includes the region of convergence for dealing with the input non-linearity. Finally, comparative results for an offshore structure model with non-linearity in states as well as in actuator, are demonstrated to verify the results of the control scheme that is developed. It has been verified that our design is less conservative than the previous designs, and can handle the non-linearities in the dynamics of plant and actuator saturation more efficiently, while DoS attacks are also present. By applying our proposed method, the overshoot and undershoot are less than ±2.5 percent, while system states converge to the origin within 55 s.

Predefined‐time adaptive fuzzy control for a class of stochastic nonlinear uncertain systems

SummaryThis article is mainly concentrated on the predefined‐time adaptive fuzzy control of stochastic nonlinear systems. To handle nonlinear functions that are uncertain, fuzzy logic systems (FLSs) are used to approximate them. Compared with the existing studies, a Lyapunov‐type criterion for practically predefined‐time stochastic stabilization (PPSS) is put forward to guarantee the stabilization of the system. The stabilization time is merely dependent on one design parameter, which means the parameter can be adjusted to set the stability time.

Adaptive asymptotic tracking control of uncertain fractional-order nonlinear systems with unknown control coefficients and actuator faults

For uncertain fractional-order nonlinear systems (UFONS) with unknown control coefficients and intermittent actuator faults, the asymptotic tracking control problem is investigated in this paper. Firstly, to weaken the influence of virtual control coefficients and intermittent actuator faults, a smooth fractional-order projection operator-based adaptive compensation mechanism is presented. Additionally, a fractional-order nonlinear filter is constructed to replace the fractional-order derivative of virtual control functions approximately, which not only avoids the issue of complexity explosion existed in backstepping control frame, but fully compensates the effects of boundary errors caused by the employed filter in spite of the unknown virtual control coefficient. By constructing a fractional Lyapunov function from the property of projection operator, it is proved that all signals in the closed-loop system are bounded, and the asymptotic tracking control object is achieved. Definitively, a simulation study is presented to verify the availability of the presented method.

Command filter-based adaptive neural two-bit-triggered containment control for saturated nonlinear multi-agent systems

Abstract This paper considers the adaptive two-bit-triggered containment control problem for nonlinear multi-agent systems in the presence of input saturation. Since input saturation occurs frequently in practical systems, which can affect the stability of the multi-agent systems under consideration, an auxiliary design system is introduced to address this issue. Meanwhile, considering limited transmission resources in practical systems, this paper mainly focuses on the triggering condition and the control signal transmission bits, presenting a two-bit-triggered control approach to optimize the utilization of transmission resources. Furthermore, a command filter is introduced into the design process to solve the problem of complexity explosion. The proposed method ensures that all signals of the closed-loop system are bounded and the output signals of all followers converge to a convex hull spanned by the outputs of the leaders. Finally, two simulation examples are provided to verify the validity of the presented control scheme.

An adaptive predefined time sliding mode control for uncertain nonlinear cyber-physical servo system under cyber attacks

Malicious attacks are often inevitable in cyber-physical systems (CPS). Accuracy in Cyber physical system for position tracking of servos is the major concern now a days. In high precision industrial automation, it is very hard to achieve accuracy in tracking especially under malicious cyber-attacks, control saturations, parametric perturbations and external disturbances. In this paper, we have designed a novel predefined time (PDT) convergence sliding mode adaptive controller (PTCSMAC) for such kind of cyber physical control system. Main key feature of our control is to cope these challenges that are posed by CPS systems such as parameter perturbation, control saturation, and cyber-attacks and the whole system then upgrade to a third-order system to facilitate adaptive control law. Then, we present an adaptive controller based on the novel PDT convergent sliding mode surface (SMS) combined with a modified weight updated Extreme Learning Machine (ELM) which is used to approximate the uncertain part of the system. Another significant advantage of our proposed control approach is that it does not require detailed model information, guaranteeing robust performance even when the system model is uncertain. Additionally, our proposed PTCSMAC controller is nonsingular regardless of initial conditions, and is capable of eradicating the possibility of singularity problems, which are frequently a concern in numerous CPS control systems. Finally, we have verified our designed PTCSMAC control law through rigorous simulations on CPS seeker servo positioning system and compared the robustness and performance of different existing techniques.

Optimized leader–follower consensus control for high-order nonlinear multi-agent system modeled in canonical dynamic form

This paper addresses the optimized leader–follower consensus control problem of nonlinear canonical dynamic multi-agent system (MAS). Since every agent is modeled in high-order dynamic, they contain the various state variables having derivative relations. Consequently, to attain the optimized consensus control, backstepping technique and reinforcement learning (RL) are combined together. In the first backstepping step, the virtual control is formulated to have the consensus error term consisting of neighbor agents’ output states. In the last backstepping step, since the nonlinearity dynamic is arisen, the optimized actual control is derived by performing the critic-actor RL. It is worth mentioning that, in the traditional RL optimal control, the critic and actor updating laws are obtained by performing the gradient descent algorithm to square of the approximated Hamilton–Jacobi-Bellman (HJB) equation, which includes multiple nonlinearity items, as a result, the algorithm is very intricate. However, in this optimized consensus control, since the RL training laws are yielded in the light of negative gradient of a simple positive function that is relevant to the HJB equation, its algorithm is very simple. At the same time, it can also avoid the persistence excitation conditions. Finally, theory and simulation confirm the validity of this optimized consensus method.

Controllability of the time-varying fractional dynamical systems with a single delay in control

In this article, we explored the controllability of fractional dynamical systems with a single delay in the control function with the Caputo fractional derivative. It is the first work in which the author studies the controllability of a time-varying fractional dynamical system with a delay in the control function. We develop the necessary and sufficient criteria for the solution representation of controllability of time-varying fractional linear dynamical systems by utilizing the Grammian matrix. We use Schauder’s fixed point theorem to establish sufficient conditions for the controllability of time-varying nonlinear fractional dynamical systems. With the help of successive approximation techniques, numerical examples validate the theoretical results.

Fast finite-time control for a class of stochastic low-order nonlinear system with uncertainties

This work explores the challenge of adaptive fast finite-time control for stochastic low-order nonlinear systems with uncertainties. It introduces an improved practical finite-time criterion that aims to achieve accelerated convergence. The criterion aims to extend to a larger range of stochastic nonlinear systems, accommodating state uncertainties and integrating Lyapunov functions with varying powers to ensure rapid convergence in the presence of uncertainties. The entire control design approach is based on the backstepping method. Specifically, fuzzy logic systems are employed in the recursive design of controllers and adaptive laws to address complex uncertain terms. Additionally, the desired magnitude target powers of the Lyapunov function in the criterion are effectively obtained by a clever overlapping selection of parameters. Finally, this study demonstrates the practical finite-time stability of stochastic low-order uncertain nonlinear systems and validates the effectiveness of the proposed approach through simulation example, highlighting its ability to achieve fast convergence.

К выбору периода дискретизации нелинейных гибридных систем управления

Hybrid systems are often used in various technical applications, such as robotics, aviation, space, energy, etc. The emergence of hybrid control systems is due to the use of computers to implement control laws, including nonlinear ones. Digital means cannot implement continuous control laws. However, the known methods of design, especially of nonlinear systems, lead precisely to continuous controls, which caused the need to discretize the continuous control with the largest possible period. Solving the problem of determining the maximum permissible sampling period of a nonlinear control system is a rather complex stage of its creation. In this article the problem of definition of the maximum allowed sample period of the nonlinear hybrid system control and its dependence on the module of the maximum eigenvalue of the functional matrix of quasilinear model of the continuous system is also considered. The nonlinear hybrid system is created by discretizing the control of the nonlinear continuous system. This continuous system is synthesized using the algebraic polynomial and matrix method of the nonlinear control systems design in which quasilinear models are used. It has been is established that the value of the maximum permissible sample period depends not only on the module of the maximum eigenvalue, but also on initial conditions and external influences. These dependences are complex and it is difficult to find them theoretically. Experimentally, based on the example of the specific nonlinear hybrid control system it is shown that eigenvalues smaller on the module lead to larger values of the maximum of the permissible sample period. The problem of choosing the sample period of control laws of the real hybrid control systems can be solved in the similar way based on a compromise between the system high-speed performance and the sample period.

A novel investigation on the effects of state and reward structure in designing deep reinforcement learning-based controller for nonlinear dynamical systems

A novel investigation on the effects of state and reward structure in designing deep reinforcement learning-based controller for nonlinear dynamical systems

Command filtering event-triggered secure control for nonlinear cyber-physical systems under denial-of-service attacks and input saturation

For nonlinear cyber-physical systems (CPSs) with input saturation and denial-of-service (DoS) attacks, an adaptive secure control strategy is investigated in this paper. To estimate the unmeasurable states, a novel switched neural network (NN) observer is designed, where two sub-observers can be freely switched from each other. Considering unnecessary packet transmissions, an improved event-triggered mechanism (ETM) is introduced to reduce the communication burden in the controller-to-actuator channel. In addition, in order to simultaneously solve the input saturation and unknown control direction problems, a Nussbaum-type function is introduced to the control design process. Finally, it is proven that all closed-loop signals are the semiglobal uniformly ultimately bounded, and simulation results demonstrate the effectiveness of the proposed secure control scheme.

Surge and stall instabilities finite-time control of nonlinear uncertain-disturbed compression system by using a novel robust approach

This paper describes a new approach to control stall and surge instabilities in the compressor system by using of finite time backstepping-based adaptive sliding mode method. The most important innovation of this study is to provide a finite time adaptive control method to simultaneously prevent the stall and surge instabilities in a compressor system in the presence of disturbance and uncertainty in the compressor characteristic curve as well as the throttle valve. The disturbance and uncertainty issues are covered by a robust sliding mode control and the gain coefficients of this controller as well as the estimation of uncertain terms are obtained by using the adaptive method. The Lyapunov stability criterion is used to evaluate the finite-time stability of the closed-loop system. The performance of the proposed method is compared with other literature methods through simulation in Matlab. The simulation results show that the proposed controller is better than the existing methods in terms of surge preventing and robustness against uncertainty and disturbance.

Adaptive Output Feedback Tracking Control for Nonlinear Systems with Unknown Growth Rate

Article Adaptive Output Feedback Tracking Control for Nonlinear Systems with Unknown Growth Rate Manman Yuan 1,2,*, and Wei Qian 1,2,* 1 School of Electrical Engineering and Automation, Henan Polytechnic University, Jiaozuo 454003, China 2 Henan Key Laboratory of Intelligent Detection and Control of Coal Mine Equipment, Jiaozuo 454003, China * Correspondence: ymmamhappy@163.com; qwei@hpu.edu.cn Received: 4 September 2023 Accepted: 7 November 2023 Published: 26 March 2024 Abstract: In this paper, the problem of adaptive output feedback tracking is considered for a class of nonlinear systems with lower-triangular structures. A novel dynamic gain is introduced to deal with the unknown growth rate. By coupling the dynamic gain with the observer and the controller, an adaptive output tracking controller is developed, which can guarantee that all signals of the closed-loop system are globally bounded. Finally, the effectiveness of the presented control scheme is illustrated by a numerical example.

Predefined-time distributed optimization and anti-disturbance control for nonlinear multi-agent system with neural network estimator: A hierarchical framework

This paper addresses the predefined-time distributed optimization of nonlinear multi-agent system using a hierarchical control approach. Considering unknown nonlinear functions and external disturbances, we propose a two-layer hierarchical control framework. At the first layer, a predefined-time distributed estimator is employed to produce optimal consensus trajectories. At the second layer, a neural-network-based predefined-time disturbance observer is introduced to estimate the disturbance, with neural networks used to approximate the unknown nonlinear functions. A neural-network-based anti-disturbance sliding mode control mechanism is presented to ensure that the system trajectories can track the optimal trajectories within a predefined time. The feasibility of this hierarchical control framework is verified by utilizing the Lyapunov method. Numerical simulations are conducted separately using models of robotic arms and mobile robots to validate the effectiveness of the proposed method.

Practical fixed-time event-triggered output feedback containment control for second-order nonlinear multi-agent systems with switching topologies

This paper studies the fixed-time containment of the second-order nonlinear multi-agent system (MAS) accompanied by switching topologies and event-triggered communication. The agent is subjected to unknown nonlinear dynamics. A fixed-time RBF observer was constructed based on information obtained from neural networks and event-triggered communication. By combining the controller with the identification information from the observer, it is demonstrated that the system can achieve practical fixed-time output feedback containment and exclude Zeno behavior during the control process. The effectiveness of the proposed event-triggered control method for fixed-time output feedback containment control of the second-order nonlinear MAS is verified by simulation examples.

Event-based adaptive active disturbance rejection control for nonlinear large-scale systems with input delay

This paper explores the active disturbance rejection control (ADRC) issue for interconnected large-scale systems with unmeasured states, input delay and a total disturbance composed of unknown constrained external disturbances. An enhanced extended state observer is built via fuzzy logic systems to identify system uncertainties and states and keep restraining the total disturbance of uncertain systems. When the triggering condition is met, the tracking differentiator component of the ADRC is able to reduce the communication overhead by successfully applying the backstepping control approach and the dynamic event-triggered mechanism. Meanwhile, the integral compensation method eliminates the negative effect cased by the input delay. Furthermore, the developed decentralised fuzzy control scheme can ensure that all signals in the closed-loop systems are semiglobally uniformly ultimately bounded and Zeno behaviour does not occurs. Finally, an example is used to depict the validity of the control approach.

Funnel-Based Adaptive Neural Fault-Tolerant Control for Nonlinear Systems with Dead-Zone and Actuator Faults: Application to Rigid Robot Manipulator and Inverted Pendulum Systems

This study addresses an adaptive neural funnel fault-tolerant control problem for a class of strict-feedback nonlinear systems with actuator faults and input dead zone. To guarantee the boundedness of the tracking error, a modified transformation for funnel error is devised and incorporated into the control design process. To manage unknown nonlinear functions, radial basis function neural networks (RBFNN) are employed in designing an adaptive neural funnel fault-tolerant controller through the backstepping technique. The proposed controller guarantees the output tracking error stays within a predefined funnel, and all signals in the closed-loop system are semiglobally uniformly ultimately bounded (SGUUB). Finally, simulations of a rigid robot manipulator system and an inverted pendulum system are conducted to validate the practicality and effectiveness of the proposed control method.

Detection‐based compound event‐triggered secure control for nonlinear multiagent systems

SummaryThis paper designs a distributed dynamic‐detection‐based event‐triggered control method to address the secure tracking control problem. A distributed online iterative dynamic detection mechanism is designed to detect denial‐of‐service (DoS) attacks. The detection results are transmitted into a proposed ET method to adjust the triggering threshold, which can mitigate the impact of DoS attacks. Moreover, the signals of state, observations of disturbance observers and adaptive laws are calculated to generate the trigger signals in the control signal simultaneously, which can help conserve communication resources and reduce the occurrence of pulse phenomenon. Meanwhile, since the predictor exists certain prediction errors that will reduce the tracking performance, a speed function is introduced to ensure the achievement of the control objective. The designed solution guarantees semiglobally uniformly ultimately bounded for all signals within the closed‐loop system. Finally, the effectiveness of control scheme is demonstrated through several simulation results.

Practical Tracking Control for High-order Nonlinear Systems With Dynamic Uncertainties and Unknown Powers via Event-triggered Mechanism

Practical Tracking Control for High-order Nonlinear Systems With Dynamic Uncertainties and Unknown Powers via Event-triggered Mechanism