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15 pages, 467 KiB

Open AccessArticle

Practical Fixed-Time Tracking Control for Strict-Feedback Nonlinear Systems with Flexible Prescribed Performance

by Xing Wang, Yongzhi Wang, Yulong Ji, Ben Niu and Jianing Hu

Mathematics 2025, 13(13), 2213; https://doi.org/10.3390/math13132213 - 7 Jul 2025

Viewed by 207

This paper addresses the issue of practical fixed-time tracking control for a class of strict-feedback nonlinear systems subject to external disturbances, while ensuring flexible prescribed performance. First, a fixed-time disturbance observer is designed to estimate the unknown external disturbances. The primary advantage of [...] Read more.

This paper addresses the issue of practical fixed-time tracking control for a class of strict-feedback nonlinear systems subject to external disturbances, while ensuring flexible prescribed performance. First, a fixed-time disturbance observer is designed to estimate the unknown external disturbances. The primary advantage of the proposed fixed-time disturbance observer lies in its capability to estimate both the disturbance itself and its higher-order derivatives in fixed time. In addition, various prescribed performance behaviors can be realized via a set of function transformations, merely by modifying certain critical parameters, without the need to redesign the controller. It is shown that, under the proposed control strategy, the system output can track the reference signal in fixed time, and the tracking error always remains within the prescribed performance boundaries. Finally, the simulation results are provided to demonstrate the feasibility and effectiveness of the proposed control scheme. Full article

(This article belongs to the Special Issue Advances in Switched Systems and Control Theory: Theory and Application)

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13 pages, 2098 KiB

Open AccessArticle

A Prescribed-Time Consensus Algorithm for Distributed Time-Varying Optimization Based on Multiagent Systems

by Yanling Zheng, Siyu Liu and Jie Zhong

Mathematics 2025, 13(13), 2190; https://doi.org/10.3390/math13132190 - 4 Jul 2025

Viewed by 275

Abstract

This paper presents a distributed optimization algorithm for time-varying objective functions utilizing a prescribed-time convergent multi-agent system within undirected communication networks. Departing from conventional time-invariant optimization paradigms with static optimal solutions, our approach specifically addresses the challenge of tracking dynamic optimal trajectories in [...] Read more.

This paper presents a distributed optimization algorithm for time-varying objective functions utilizing a prescribed-time convergent multi-agent system within undirected communication networks. Departing from conventional time-invariant optimization paradigms with static optimal solutions, our approach specifically addresses the challenge of tracking dynamic optimal trajectories in evolving environments. A novel continuous-time distributed optimization algorithm is developed based on prescribed-time consensus, guaranteeing the consensus attainment among agents within a user-defined timeframe while asymptotically converging to the time-dependent optimal solution. The proposed methodology enables explicit predetermination of convergence duration, representing a significant advancement over existing asymptotic convergence methods. Moreover, two simulation examples on the rendezvous problem and multi-robots control are presented to validate the theoretical results, exhibiting precise time-controlled convergence characteristics and effective tracking performance for time-varying optimization targets. Full article

(This article belongs to the Special Issue Advances in Switched Systems and Control Theory: Theory and Application)

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19 pages, 4711 KiB

Open AccessFeature PaperArticle

Dynamical Analysis and Optimization of Combined Vibration Isolator with Time Delay

by Yaowei Wang and Xiangyu Li

Mathematics 2025, 13(13), 2188; https://doi.org/10.3390/math13132188 - 4 Jul 2025

Viewed by 214

Abstract

Vibration control has long been a key concern in engineering, with low-frequency vibration isolation remaining particularly challenging. Traditional linear isolators are limited in their ability to provide high load-bearing capacity and effective low-frequency isolation simultaneously. In contrast, quasi-zero stiffness (QZS) isolators offer low [...] Read more.

Vibration control has long been a key concern in engineering, with low-frequency vibration isolation remaining particularly challenging. Traditional linear isolators are limited in their ability to provide high load-bearing capacity and effective low-frequency isolation simultaneously. In contrast, quasi-zero stiffness (QZS) isolators offer low dynamic stiffness near equilibrium while maintaining high static stiffness, thereby enabling superior isolation performance in the low and ultra-low frequency range. This paper proposes a novel vibration isolation system that combines a grounded dynamic absorber with a QZS isolator, incorporating time-delay feedback control to enhance performance. The dynamic equations of the system are derived using Newton’s second law. The harmonic balance method combined with the arc-length continuation technique is employed to obtain steady-state responses under harmonic force excitation. The influence of feedback gain and time delay on vibration isolation effectiveness and dynamic behavior is analyzed, demonstrating the ability of time-delay feedback to modulate system responses and suppress primary resonance peaks. To further enhance performance, a genetic algorithm is used to optimize the control parameters under harmonic force excitation. The force transmissibility is defined as fitness functions, and the effects of control parameters on these metrics are examined. The results show that the optimized time-delay feedback parameters significantly reduce the transmitted force, improving the overall isolation efficiency. The proposed system provides a promising approach for achieving high-performance vibration isolation in low-frequency environments. Full article

(This article belongs to the Special Issue Advances in Switched Systems and Control Theory: Theory and Application)

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22 pages, 4907 KiB

Open AccessArticle

Predefined Time Control of State-Constrained Multi-Agent Systems Based on Command Filtering

by Jianhua Zhang, Xuan Yu, Quanmin Zhu and Zhanyang Yu

Mathematics 2025, 13(13), 2151; https://doi.org/10.3390/math13132151 - 30 Jun 2025

Viewed by 256

Abstract

This paper resolves the predefined-time control problem for multi-agent systems under predefined performance metrics and state constraints, addressing critical limitations of traditional methods—notably their inability to enforce strict user-specified deadlines for mission-critical operations, coupled with difficulties in simultaneously guaranteeing transient performance bounds and [...] Read more.

This paper resolves the predefined-time control problem for multi-agent systems under predefined performance metrics and state constraints, addressing critical limitations of traditional methods—notably their inability to enforce strict user-specified deadlines for mission-critical operations, coupled with difficulties in simultaneously guaranteeing transient performance bounds and state constraints while suffering prohibitive stability proof complexity. To overcome these challenges, we propose a predefined performance control methodology that integrates Barrier Lyapunov Functions command-filtered backstepping. The framework rigorously ensures exact convergence within user-defined time independent of initial conditions while enforcing strict state constraints through time-varying BLF boundaries and further delivers quantifiable performance such as overshoot below 5% and convergence within 10 s. By eliminating high-order derivative continuity proofs via command-filter design, stability analysis complexity is reduced by 40% versus conventional backstepping. Stability proofs and dual-case simulations (UAV formation/smart grid) demonstrate over 95% tracking accuracy under disturbances and constraints, validating broad applicability in safety-critical multi-agent systems. Full article

(This article belongs to the Special Issue Advances in Switched Systems and Control Theory: Theory and Application)

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20 pages, 788 KiB

Open AccessArticle

Fuzzy Resilient Control of DC Microgrids with Constant Power Loads Based on Markov Jump Models

by Wei Hu, Yu Shen, Fan Yang, Zhen Chang and Shanglin Zhao

Mathematics 2024, 12(17), 2656; https://doi.org/10.3390/math12172656 - 27 Aug 2024

Cited by 2 | Viewed by 826

Abstract

This paper addresses the fuzzy resilient control of DC microgrids with constant power loads. The DC microgrid is subject to abrupt parameter changes which are described by the Markov jump model. Due to the constant power loads, the DC microgrid exhibits nonlinear dynamics [...] Read more.

This paper addresses the fuzzy resilient control of DC microgrids with constant power loads. The DC microgrid is subject to abrupt parameter changes which are described by the Markov jump model. Due to the constant power loads, the DC microgrid exhibits nonlinear dynamics which are characterized by a T-S fuzzy model. According to the parallel distributed compensation principle, mode-dependent fuzzy resilient controllers are designed to stabilize the resultant T-S fuzzy Markov jump DC microgrid. The “resilient” means the controller could cope with the uncertainty caused by the inaccurate execution of the control laws. This uncertainty is governed by a Bernoulli distributed random variable and thus may not occur. Then, the mean square exponential stability is analyzed for the closed-loop system by using the mode-dependent Lyapunov function. Since the stability conditions are not convex, a design algorithm is further derived to calculate the fuzzy resilient controller gains. Finally, simulations are provided to test the effectiveness of the proposed results. Full article

(This article belongs to the Special Issue Advances in Switched Systems and Control Theory: Theory and Application)

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15 pages, 409 KiB

Open AccessArticle

Double-Observer-Based Bumpless Transfer Control of Switched Positive Systems

by Yahao Yang, Zhong Huang and Pei Zhang

Mathematics 2024, 12(11), 1724; https://doi.org/10.3390/math12111724 - 1 Jun 2024

Cited by 1 | Viewed by 957

Abstract

This paper investigates the bumpless transfer control of linear switched positive systems based on state and disturbance observers. First, state and disturbance observers are designed for linear switched positive systems to estimate the state and the disturbance. By combining the designed state observer, [...] Read more.

This paper investigates the bumpless transfer control of linear switched positive systems based on state and disturbance observers. First, state and disturbance observers are designed for linear switched positive systems to estimate the state and the disturbance. By combining the designed state observer, the disturbance observer, and the output, a new controller is constructed for the systems. All gain matrices are described in the form of linear programming. By using co-positive Lyapunov functions, the positivity and stability of the closed-loop system can be ensured. In order to achieve the bumpless transfer property, some additional sufficient conditions are imposed on the control conditions. The novelties of this paper lie in that (i) a novel framework is presented for positive disturbance observer, (ii) double observers are constructed for linear switched positive systems, and (iii) a bumpless transfer controller is proposed in terms of linear programming. Finally, two examples are given to illustrate the effectiveness of the proposed results. Full article

(This article belongs to the Special Issue Advances in Switched Systems and Control Theory: Theory and Application)

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14 pages, 450 KiB

Open AccessArticle

Cooperative Adaptive Fuzzy Control for the Synchronization of Nonlinear Multi-Agent Systems under Input Saturation

by Jinxia Wu and Pengfei Cui

Mathematics 2024, 12(10), 1426; https://doi.org/10.3390/math12101426 - 7 May 2024

Cited by 2 | Viewed by 1019

Abstract

This research explores the synchronization issue of leader–follower systems with multiple nonlinear agents, which operate under input saturation constraints. Each follower operates under a spectrum of unknown dynamic nonlinear systems with non-strict feedback. Additionally, due to the fact that the agents may be [...] Read more.

This research explores the synchronization issue of leader–follower systems with multiple nonlinear agents, which operate under input saturation constraints. Each follower operates under a spectrum of unknown dynamic nonlinear systems with non-strict feedback. Additionally, due to the fact that the agents may be geographically dispersed or have different communication capabilities, only a subset of followers has direct communication with the leader. Compared to linear systems, nonlinear systems can provide a more detailed description of real-world physical models. However, input saturation is present in most real systems, due to various factors such as limited system energy and the physical constraints of the actuators. An auxiliary system of Nth order is introduced to counteract the impact of input saturation, which is then employed to create a collaborative controller. Due to the powerful capability of fuzzy logic systems in simulating complex nonlinear relationships, they are deployed to approximate the enigmatic nonlinear functions intrinsic to the systems. A distributed adaptive fuzzy state feedback controller is designed by approximating the derivative of the virtual controller by filters. The proposed controller ensures the synchronization of all follower outputs with the leader output in the communication graph. It is shown that all signals in the closed-loop system are semi-globally uniformly ultimately bounded, and the tracking errors converge to a small neighborhood around the origin. Finally, a numerical example is given to demonstrate the effectiveness of the proposed approach. Full article

(This article belongs to the Special Issue Advances in Switched Systems and Control Theory: Theory and Application)

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14 pages, 343 KiB

Open AccessArticle

The Strictly Dissipative Condition of Continuous-Time Markovian Jump Systems with Uncertain Transition Rates

by WonIl Lee, JaeWook Shin and BumYong Park

Mathematics 2024, 12(5), 639; https://doi.org/10.3390/math12050639 - 21 Feb 2024

Viewed by 1265

Abstract

This study addresses the problem of strictly dissipative stabilization for continuous-time Markovian jump systems (MJSs) with external disturbances and generally uncertain transition rates that contain completely unknown transition rates and their bound values. A stabilization condition is obtained to guarantee strict dissipativity for [...] Read more.

This study addresses the problem of strictly dissipative stabilization for continuous-time Markovian jump systems (MJSs) with external disturbances and generally uncertain transition rates that contain completely unknown transition rates and their bound values. A stabilization condition is obtained to guarantee strict dissipativity for the MJSs with partial knowledge in terms of the transition rates. To reduce the conservativity of the proposed condition, we used a boundary condition related to the bounds of the transition rate with slack variables. Finally, two simulation results are presented to describe the feasibility of the proposed controller. Full article

(This article belongs to the Special Issue Advances in Switched Systems and Control Theory: Theory and Application)

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15 pages, 3931 KiB

Open AccessArticle

Normalized Error-Based PI Controller and Its Application to the DC–DC Buck Converter

by Satyajit Chincholkar, Mohd Tariq, Majid Poshtan and Mohamed Sharaf

Mathematics 2024, 12(2), 240; https://doi.org/10.3390/math12020240 - 11 Jan 2024

Cited by 7 | Viewed by 2095

Abstract

In this article, the structure of the normalized error-based proportional-integral (PI) controller is presented and its application to the DC–DC buck converter is discussed. The main motivation is to overcome the drawbacks of saturation and the limited range of controller gains offered by [...] Read more.

In this article, the structure of the normalized error-based proportional-integral (PI) controller is presented and its application to the DC–DC buck converter is discussed. The main motivation is to overcome the drawbacks of saturation and the limited range of controller gains offered by the traditional PI controller. Initially, the theoretical structure and advantages of an improved PI controller are shown. Next, the problem of regulation of the step-down DC–DC converter is addressed using the proposed controller. The objective is to keep the load voltage constant even when the converter parameters vary. The averaged state-space model of the converter is presented and a detailed stability analysis based on the Lypunov indirect method is carried out. The results show an improved range of controller parameters when the proposed controller is employed. Finally, some simulation results are shown to illustrate the effect of controller parameter variations on the output response. These results also verify the ability of the proposed controller to handle the changes in the load, input voltage, and reference voltage of the converter. Moreover, a comparative simulation study validates the superior transient response of the proposed normalized error-based PI controller over the traditional PI controller. Full article

(This article belongs to the Special Issue Advances in Switched Systems and Control Theory: Theory and Application)

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