Nonlinear Control Research Articles

Novel flexible fixed-time stability theorem and its application to sliding mode control nonlinear systems.

For the fixed-time nonlinear system control problem, a new fixed-time stability (FxTS) theorem and an integral sliding mode surface are proposed to balance the control speed and energy consumption. We discuss the existing fixed time inequalities and set up less conservative inequalities to study the FxTS theorem. The new inequality differs from other existing inequalities in that the parameter settings are more flexible. Under different parameter settings, the exact upper bound on settling time in four cases is discussed. Based on the stability theorem, a new integral sliding mode surface and sliding mode controller are proposed. The new control algorithm is successfully applied to the fixed-time control of chaotic four-dimensional Lorenz systems and permanent magnet synchronous motor systems. By comparing the numerical simulation results of this paper's method and traditional fixed-time sliding mode control (SMC), the flexibility and superiority of the theory proposed in this paper are demonstrated. Under the same parameter settings, compared to the traditional FxTS SMC, it reduces the convergence time by 18%, and the estimated upper bound of the fixed time reduction in waiting time is 41%. In addition, changing the variable parameters can improve the convergence velocity.

Nonlinear Optimal Control of No-Insulation and Controlled-Insulation HTS Coils and Magnets

Nonlinear Optimal Control of No-Insulation and Controlled-Insulation HTS Coils and Magnets

Efficient implementation of the functional links artificial neural networks with cross-terms for nonlinear active noise control

This paper proposes an efficient extension of functional links artificial neural networks (EE-FLANN) for the active noise control (ANC) application. The developed EE-FLANN controller can upgrade the model accuracy with the actual system thanks to adding the cross-terms to the trigonometric function. Unlike the method in the generalized FLANN (GFLANN) controller, the EE-FLANN exploits include cross-term symmetry. However, this causes the computational burden to increase remarkably. To reduce this disadvantage, we truncate the cross-terms appropriately based on the simplified strategy. Furthermore, the adaptive algorithm is designed to partially update the filter coefficients appropriately. Specifically, the cross-terms that do not satisfy certain magnitude conditions will be omitted during the update process to reduce costs. Experiments have shown that the proposed EE-FLANN controller can achieve comparable performance to the GFLANN controller but the complexity is reduced by up to 20%.

Amplitude Saturated Nonlinear Output Feedback Controller Design for Underactuated 5-DOF Tower Cranes Without Velocity Measurement

Amplitude Saturated Nonlinear Output Feedback Controller Design for Underactuated 5-DOF Tower Cranes Without Velocity Measurement

An optimal midcourse guidance method for dual pulse air-to-air missiles using linear Gauss pseudospectral model predictive control method

This paper proposes an optimal midcourse guidance method for dual pulse air-to-air missiles, which is based on the framework of the linear Gauss pseudospectral model predictive control method. Firstly, a multistage optimal control problem with unspecified terminal time is formulated. Secondly, the control and terminal time update formulas are derived analytically. In contrast to previous work, the derivation process fully considers the Hamiltonian function corresponding to the unspecified terminal time, which is coupled with control, state, and costate. On the assumption of small perturbation, a special algebraic equation is provided to represent the equivalent optimal condition for the terminal time. Also, using Gauss pseudospectral collocation, error propagation dynamical equations involving the first-order correction term of the terminal time are transformed into a set of algebraic equations. Furthermore, analytical modification formulas can be derived by associating those equations and optimal conditions to eliminate terminal error and approach nonlinear optimal control. Even with their mathematical complexity, these formulas produce more accurate control and terminal time corrections and remove reliance on task-related parameters. Finally, several numerical simulations, comparisons with typical methods, and Monte Carlo simulations have been done to verify its optimality, high convergence rate, great stability and robustness.

An asymmetrically variable wingtip anhedral angles morphing aircraft based on incremental sliding mode control: Improving lateral maneuver capability

This paper presents the design of an asymmetrically variable wingtip anhedral angles morphing aircraft, inspired by biomimetic mechanisms, to enhance lateral maneuver capability. Firstly, we establish a lateral dynamic model considering additional forces and moments resulting during the morphing process, and convert it into a Multiple Input Multiple Output (MIMO) virtual control system by importing virtual inputs. Secondly, a classical dynamics inversion controller is designed for the outer-loop system. A new Global Fast Terminal Incremental Sliding Mode Controller (NDO-GFTISMC) is proposed for the inner-loop system, in which an adaptive law is implemented to weaken control surface chattering, and a Nonlinear Disturbance Observer (NDO) is integrated to compensate for unknown disturbances. The whole control system is proven semi-globally uniformly ultimately bounded based on the multi-Lyapunov function method. Furthermore, we consider tracking errors and self-characteristics of actuators, a quadratic programming-based dynamic control allocation law is designed, which allocates virtual control inputs to the asymmetrically deformed wingtip and rudder. Actuator dynamic models are incorporated to ensure physical realizability of designed allocation law. Finally, comparative experimental results validate the effectiveness of the designed control system and control allocation law. The NDO-GFTISMC features faster convergence, stronger robustness, and 81.25% and 75.0% reduction in maximum state tracking error under uncertainty compared to the Incremental Nonlinear Dynamic Inversion Controller based on NDO (NDO-INDI) and Incremental Sliding Mode Controller based on NDO (NDO-ISMC), respectively. The design of the morphing aircraft significantly enhances lateral maneuver capability, maintaining a substantial control margin during lateral maneuvering, reducing the burden of the rudder surface, and effectively solving the actuator saturation problem of traditional aircraft during lateral maneuvering.

Nonlinear model predictive control of vehicle trajectory tracking using tilting technology

Nonlinear model predictive control of vehicle trajectory tracking using tilting technology

Output feedback active disturbance rejection control of an electro-hydraulic servo system based on command filter

The output feedback active disturbance rejection control of a valve-controlled cylinder electro-hydraulic servo system is investigated in this paper. First, a comprehensive nonlinear mathematical model that encompasses both matched and mismatched disturbances is formulated. Due to the fact that only position information can be measured, a linear Extended State Observer (ESO) is introduced to estimate unknown states and matched disturbances, while a dedicated disturbance observer is constructed to estimate mismatched disturbances. Different from the traditional observer results, the design of the disturbance observer used in this study is carried out under the constraint of output feedback. Furthermore, an output feedback nonlinear controller is proposed leveraging the aforementioned observers to achieve accurate trajectory tracking. To mitigate the inherent differential explosion problem of the traditional backstepping framework, a finite-time stable command filter is incorporated. Simultaneously, considering transient filtering errors, a set of error compensation signals are designed to counter their negative impact effectively. Theoretical analysis affirms that the proposed control strategy ensures the boundedness of all signals within the closed-loop system. Additionally, under the specific condition of only time-invariant disturbances in the system, the conclusion of asymptotic stability is established. Finally, the algorithm’s efficacy is validated through comparative experiments.

Robotic technologies for in-orbit assembly of a large aperture space telescope: A review

Space telescopes have been instrumental in enlightening our understanding of the universe, from the iconic Hubble Space Telescope to specialized instruments like Chandra and Kepler. Pushing the frontiers of cosmic exploration, the future of space exploration hinges on modular Large Aperture Space Telescopes (LAST), much larger than the recently launched 6.5 m James Webb Space Telescope, necessitating robotic assembly in orbit. This paper introduces a paradigm shift in astronomical observation by featuring robotic in-orbit assembly of a large aperture space telescope. This review paper starts by tracing the evolution of telescopes and presents a comprehensive overview of the state-of-the-art space telescopes. This paper then reinforces the need for LAST to address the constant clamour for higher-resolution astronomy. While current semi-autonomous robotic manipulators operate from the International Space Station, their limited walking capabilities constrain their workspace, making them unsuitable for the LAST mission. This paper presents a detailed trade-off analysis of the challenges associated with the in-orbit assembly of LAST using candidate robots to understand the technological gaps. Further, the evolution of space robotic manipulators is presented, highlighting design features, advantages, and drawbacks for in-orbit spacecraft servicing and assembly missions. To tackle design and modelling challenges for robotic systems in space, amidst the various perturbations in the extreme space environment, linear and non-linear control systems necessary for achieving ultra-high precision performance are also discussed. This paper advances the walking space manipulator technology by introducing the next generation of walking space manipulators – the End-Over-End Walking Robot (E-Walker). The dexterous and modular design of the E-Walker makes it an ideal candidate for missions involving assembly, manufacturing, servicing, and maintenance.

A time-efficient nonlinear control method for the hyperchaotic finance system synchronization

Irregular and complex behavior in the financial system can disrupt stability and smooth economic growth. It causes randomness within the system, generating chaos; hindering synchronization behaviour. Achieving smooth and rapid synchronization between two coupled hyperchaotic finance (HF) systems with lessened fluctuation of input and output signals is vital for continuing financial stability and fostering economic growth, a challenge addressed in this article. The paper proposes a novel time-efficient nonlinear control (TENLC) technique and investigates HF systems synchronization using the drive-response system (DRS) arrangement. The proposed TENLC strategy realizes fast and smooth synchronization behaviour between two coupled HF systems, reducing closed-loop state-variable trajectory oscillations. The controller is designed to retain the nonlinear components within the closed-loop system and does not depend on the system's parameters, simplifying the design and analysis process. The Lyapunov stability technique confirms the closed-loop's global stability at the origin. Proofs of mathematical analysis and computer-based simulation results validate the theoretical findings, showing that the presented TENLC strategy converges the state error trajectories to zero in a short transient time with lessened fluctuations for all signals. The comparative computer-based simulation analysis confirms that the presented TENLC approach outperforms other synchronization control techniques.

Advanced control of double stage grid-tied three phase photovoltaic systems with shunt active power filter

This paper explores the challenges associated with the control of a two-stage three-phase electrical grid connected to a photovoltaic (PV) system. The objectives encompass: i) maximizing the available PV power, ii) controlling the DC-link voltage to a predetermined setpoint, and iii) considering that power quality has become an important measure in a distribution electrical network where different loads are connected, the third objective will mainly focus on ensuring power factor correction (PFC). To achieve these objectives, two loops of nonlinear controller are developed. In the outer loop, the duty cycle of a boost converter is controlled using a hybrid technique of backstepping technique and the perturb & observe (P&O) algorithm. In addition, the inner loop employs a hybrid automaton approach to tackle the challenges of a three-phase shunt active power filter (SAPF). The results have been verified through numerical simulation using MATLAB/Simulink power systems environment.

Modeling and Control of Multi‐Stack Fuel Cell Air System based on Nonlinear Model Predictive Control Method

Hydrogen is crucial for achieving SDGs by driving energy transition and combating climate change. Proton exchange membrane fuel cell technology, leveraging hydrogen, faces challenges in meeting high‐power demands. The multistack fuel cell system (MFCS) tackles this by integrating multiple substacks, yet its air supply needs meticulous control. Proportional integral derivative (PID) decoupling from single‐stack falls short of MFCS. This article proposes nonlinear model predictive control (NMPC) for optimized air flow and pressure decoupling. Modeling MFCS's air system and designing a predictive model, it is aimed to ensuring precise control of air flow and pressure in each substack. The decoupling experiments show that NMPC outperforms PID, accurately managing air flow and pressure and reducing load fluctuations. For air mass flow, NMPC cuts mean‐absolute error (MAE) by 64.56% and root‐mean‐square error (RMSE) by 81.36%. For pressure, MAE drops 81.23% and RMSE 83.59%. Comprehensive step load tests confirm NMPC's precise, dynamic regulation too, compared to PID, NMPC lowers average MAE for air mass by 20.67%, pressure by 32.22%. RMSE improvements of 31.08% and 33.23% highlight NMPC's strength. NMPC's quick response mitigates coupling issues, enhancing vehicle load adaptability.

Experimental backward integration for state-dependent differential Riccati equation (SDDRE): A case study on flapping-wing flying robot

Backward integration (BI) is a classical approach for solving optimal control arising from linear quadratic regulator (LQR) design in differential form. It proposes a two-round solution, the first one starting from a final boundary condition to the initial one to generate the optimal gain, and the next one, solving the control system in a forward loop. Implementation of the BI on the nonlinear optimal control, the state-dependent differential Riccati equation (SDDRE), is a challenge since in the backward loop, the state information is missing and is not straightforward like the LQR. Hence, a control for backward motion is required to regulate the system from the terminal to the initial desired states. While there have been some valuable works on the theoretical implementation of the BI in simulations for the SDDRE, this approach has not been reported in experiments for the best knowledge of the authors. Here in this work, the SDDRE is solved using the BI and two backward and forward solution steps, and it is experimentally applied for a flapping-wing flying robot (FWFR). The execution of the control system is done onboard using Raspberry Pi 4B as the processor which has limited computational capacity. The trajectory tracking of a line in a closed limited space is proposed for the FWFR flight. The objective is to position the robot bird at the corner of the rectangular limited space with minimum error in translation. The results have been presented for 21 flights to show the repeatability and presented the best-case minimum error of 10 (cm) at the end of the trajectory, in the YZ-plane. Considering approximately 12 (m) flight path, the error is found less than 1 percent of the travel distance. The results were compared with forward integration to confirm the correctness of the computation. The experimental flight dataset, MATLAB simulation codes, and experimental Python codes are available as supplementary material for this work in the online version of the paper.

Novel terminal region computation method for quasi-infinite horizon NMPC

An algorithm for invariant region characterization for a nonlinear system controlled by an LQR is proposed. The quasi-infinite horizon nonlinear model predictive controller formulation is extended for zone control with optimizing targets. The novel invariant region characterization proposed promotes hypervolume gains of up to two orders of magnitude for an unstable CSTR. Extension of the NMPC formulation to the case of zone control with optimizing targets improves the formulation’s practical deployment capability. A comparison between QIH-NMPC and NMPC with a terminal equality constraint is drawn, showing considerable closed-loop performance loss when employing a terminal equality constraint. The proposed invariant region shows feasibility set gains from the proposed invariant region characterization, when compared to a recent approach. Closed-loop simulations of both controllers from the enlarged feasibility set show how sensible the closed-loop performance is to one infeasible controller iteration.

A gradient-based optimization algorithm to solve optimal control problems with conformable fractional-order derivatives

In this paper, we solve numerically a class of fractional optimal control problems in the conformable sense. We first propose a nonlinear fractional optimal control problem subject to general equality and inequality constraints. Then, based on a novel numerical integration scheme, we present a discretization method for the governed fractional-order system as well as the cost and constraint functionals, which yields a discretized approximate problem. We further derive the gradients of the cost and constraint functionals in regard to the discretized controls. On the basis of this result, a numerical optimization approach to solve the approximate problem is developed. Finally, three non-trivial example problems are solved to illustrate the applicability and effectiveness of the developed approach.

MPC-based motion control of AGV with improved A* and artificial potential field

Nowadays, automatic guided vehicles (AGV) are extensively utilized for transportation and inspection tasks in workshops. The A* and artificial potential field (APF) are classic algorithms employed for path planning of AGVs. However, these algorithms still fail to meet the actual production needs and cannot avoid stuttering while encountering obstacles, leading to excessive energy consumption and unnecessary pause. In the paper, an improved A* algorithm is proposed to reduce route length and improving efficiency. On this basis, an integrated fusion strategy consisting of improved APF and nonlinear model predictive control (NMPC) is designed for collision avoidance and path tracking control. The proposed algorithm is tested both on simulation and a laser-guided real automatic guided vehicle experimental platform. Experimental results prove that the proposed algorithm has a great tracking performance under complex workplace.

Active nonlinear vibration control of a buckled beam based on deep reinforcement learning

Active nonlinear vibration control of a buckled beam based on deep reinforcement learning

Mittag-Leffler asymptotic stabilization of random initial-time nonlinear real-order control systems

Mittag-Leffler asymptotic stabilization of random initial-time nonlinear real-order control systems

Destroying Phantom Jams with Connectivity and Automation: Nonlinear Dynamics and Control of Mixed Traffic

Connected automated vehicles (CAVs) have the potential to improve the efficiency of vehicular traffic. In this paper, we discuss how CAVs can positively impact the dynamic behavior of mixed traffic systems on highways through the lens of nonlinear dynamics theory. First, we show that human-driven traffic exhibits a bistability phenomenon, in which the same drivers can both drive smoothly or cause congestion, depending on perturbations like a braking of an individual driver. As such, bistability can lead to unexpected phantom traffic jams, which are undesired. By analyzing the corresponding nonlinear dynamical model, we explain the mechanism of bistability and identify which human driver parameters may cause it. Second, we study mixed traffic that includes both human drivers and CAVs, and we analyze how CAVs affect the nonlinear dynamic behavior. We show that a large-enough penetration of CAVs in the traffic flow can eliminate bistability, and we identify the controller parameters of CAVs that are able to do so. Ultimately, this helps to achieve stable and smooth mobility on highways. History: This paper has been accepted for the Transportation Science Special Issue on ISTTT25 Conference. Funding: This work was supported by the University of Michigan’s Center for Connected and Automated Transportation [U.S. DOT Grant 69A3551747105]. Supplemental Material: The online appendix is available at https://doi.org/10.1287/trsc.2023.0498 .

MPC-Based Dynamic Velocity Adaptation in Nonlinear Vehicle Systems: A Real-World Case Study

Technological advancements have positively impacted the automotive industry, leading to the development of autonomous cars, which aim to minimize human intervention during driving, and thus reduce the likelihood of human error and accidents. These cars are distinguished by their advanced driving systems and environmental benefits due to their integration of cutting-edge autonomous technology and electric powertrains. This combination of safety, efficiency, and sustainability positions autonomous vehicles as a transformational solution for modern transportation challenges. Optimizing vehicle speed is essential in the development of these vehicles, particularly in minimizing energy consumption. Thus, in this paper, a method to generate the maximum velocity profile of a vehicle on a real road, extracted using online mapping platforms while ensuring compliance with maximum legal speed limits, is proposed. A nonlinear model, closely aligned with real-world conditions, captures and describes vehicle dynamics. Further, a nonlinear model predictive control strategy is proposed for optimizing the vehicle’s performance and safety in dynamic driving conditions, yielding satisfactory results that demonstrate the effectiveness of the method.