Nonlinear Control Research Articles

A Design of Model Predictive Control and Nonlinear Disturbance Observer-based Backstepping Sliding Mode Control for Terrain Following

In this study, we propose the terrain following algorithm using model predictive control and nonlinear disturbance observer-based backstepping sliding mode controller for an aircraft system. Terrain following is important for military missions because it helps the aircraft avoid detection by the enemy radar. The model predictive control is used to replace the generating trajectory and guidance with the flight path angle constraint. In addition, the aircraft is affected to the parameter uncertainty and unknown disturbance such as wind near the mountainous terrain. Therefore, we suggest the nonlinear disturbance-based backstepping sliding mode control method for the aircraft that has highly nonlinearity to enhance flight path angle tracking performance. Through the numerical simulation, the proposed method showed the better tracking performance than the traditional backstepping method. Furthermore, the proposed method presented the terrain following maneuver maintaining the desired altitude.

Second Harmonic Generation from exciton-polaritons: Strong coupling between monolayer WS[formula omitted] and multilayer WSe[formula omitted] metasurfaces Quasibound states in the continuum

The second harmonic generation (SHG) from exciton-polaritons, produced by the strong coupling between quantum emitters and cavity photons, can provide a unique insight for controlling nonlinear responses on the nanoscale. Achieving SHG generally depends on phase matching, limited by nonlinear materials and nanostructure fabrication. Here, we demonstrate a novel way to obtain tunable SHG from van der Waals metasurfaces composed of nanostructured multilayer WSe2 strong coupling with monolayer WS2. By breaking symmetry via varying the metasurface unit tilted angle and period, quasibound state in the continuum (q-BIC) mode resonances energy is tuned across the monolayer WS2 exciton resonance energy, enabling anticrossing behavior of strong coupling in both reflection spectrum and SHG spectrum, which means that SHG was successfully observed by strong coupling. Furthermore, the SHG spectrum can be tuned by changing the armchair direction of the monolayer WS2 and pump polarization direction. Moreover, the mechanism of exciton-polaritonic SHG is investigated by a coupled nonlinear oscillator model, which reveals the SHG origin from exciton-polaritons, providing a new rule for fine-tuning the SHG. Our work provides a new strategy and additional freedom in the nonlinear light-matter interaction and coherent control of the SHG in integrated photonic devices.

Observer based nonlinear robust control for a flexible wing with unknown time-varying output constraints

Observer based nonlinear robust control for a flexible wing with unknown time-varying output constraints

Experimental realization of active nonlinear feedback control from hot rubidium vapor

Feedback control plays a crucial role in preparation and manipulation of quantum states, to evolve the quantum system towards a desired result. Here we report a novel feedback control system utilizing two four-wave mixing (FWM) processes, in which the first FWM process functions as an amplifier while the second FWM process serves as an active nonlinear controller. We experimentally investigate the classical properties of the output states, and demonstrate the manipulation of quantum states through the active nonlinear controller. Remarkably, we observe that the quantum correlation of the quantum states can be efficiently controlled and enhanced, even when the amplifier operates at a significantly low level of pump power. Furthermore, we identify an optimal intensity gain for the active nonlinear controller, which maximizes the quantum correlation of the system. These findings present a new strategy employing an active controller to enhance quantum correlation, which holds the potential to improve the communication fidelity of quantum information processing and enhance the measurement precision of quantum metrology in future applications.

Fast computation of function composition derivatives for flatness-based control of diffusion problems

The chain rule is a standard tool in differential calculus to find derivatives of composite functions. Faà di Bruno’s formula is a generalization of the chain rule and states a method to find high-order derivatives. In this contribution, we propose an algorithm based on Faà di Bruno’s formula and Bell polynomials (Bell in Ann Math 29:38–46, 1927; Parks and Krantz in A primer of real analytic functions, 2012) to compute the structure of derivatives of function compositions. The application of our method is showcased using trajectory planning for the heat equation (Laroche et al. in Int J Robust Nonlinear Control 10(8):629–643, 2000).

End-to-end reinforcement learning of koopman models for economic nonlinear model predictive control

(Economic) nonlinear model predictive control ((e)NMPC) requires dynamic models that are sufficiently accurate and computationally tractable. Data-driven surrogate models for mechanistic models can reduce the computational burden of (e)NMPC; however, such models are typically trained by system identification for maximum prediction accuracy on simulation samples and perform suboptimally in (e)NMPC. We present a method for end-to-end reinforcement learning of Koopman surrogate models for optimal performance as part of (e)NMPC. We apply our method to two applications derived from an established nonlinear continuous stirred-tank reactor model. The controller performance is compared to that of (e)NMPCs utilizing models trained using system identification, and model-free neural network controllers trained using reinforcement learning. We show that the end-to-end trained models outperform those trained using system identification in (e)NMPC, and that, in contrast to the neural network controllers, the (e)NMPC controllers can react to changes in the control setting without retraining.

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%.

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.

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.

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.