Closed-loop Stability Research Articles

Adaptive Multi-Model Predictive Control with Optimal Model Bank Formation: Consideration of Local Models Uncertainty and Stability

The Multiple Model Control (MMC) structure comprises three main components: the model bank, controller bank, and supervisor algorithm. Precise design of these components is crucial for achieving high control performance within the MMC framework, albeit this effort is not without its challenges. These challenges involve optimizing the model and controller banks ensuring system stability when dealing with uncertainties in the local models and enabling smooth switching between model-controller pairs. This paper addresses these challenges by presenting a comprehensive approach. Firstly, the optimal model bank is designed using an automatic clustering approach. Then, the design of the adaptive multi-model predictive controller bank and a supervisor algorithm capable of performing soft switching are discussed. The proposed control system exhibits the capability to ensure closed-loop system stability within each individual subspace, as well as during the transitioning between distinct subspaces. This stability is preserved even in the face of inherent uncertainties associated with the local models comprising the model bank. To evaluate and validate the performance of the proposed control system, it is applied to a satellite attitude control system. The results confirm the effectiveness and performance of the control system. The proposed control system holds promise for controlling highly nonlinear, complex, or switched systems, ensuring closed-loop system stability, and achieving high control performance.

Dynamic inversion and optimal tracking control on the ball-plate system based on a linearized nonholonomic multibody model

This paper addresses the optimal control of the ball-plate system, a well-known nonholonomic system in the context of nonprehensile manipulation, using a multibody dynamics approach. The trajectory tracking control of a steady-state circular motion of the ball on the plate, for any radius and potentially off-centric with respect to the plate’s pivoting point, is achieved by designing a Linear-Quadratic Regulator. A spatial multibody model of the ball-plate system is considered. A key contribution is the analytical computation of the circular steady motion of the ball by dynamic inversion, including the control actions to achieve this reference solution. This enables the analytical computation of the linearized equations along this reference motion, resulting in a periodic linear time-varying (LTV) system, and the application of linear controllability criteria for LTV systems. A controllable linear system, involving the Cartesian coordinates of the contact point and the yaw angle of the sphere, is obtained using a convenient coordinate partition in the linearization. Compared to existing results on the same problem, closed-loop stability about the desired trajectory is achieved for any radius of the circular trajectory.

Adaptive control of magnetic levitation system based on fuzzy inversion

A novel adaptive tracking controller for magnetic levitation systems (MLS) is developed. The controller is based on a special adaptive control scheme incorporating fuzzy model of electromagnetic acceleration enabling fast and accurate fuzzy inversion. The controller ensures accurate tracking of any smooth desired position signal, despite unknown MLS parameters. The closed-loop system stability, in the sense of uniform ultimate boundedness (UUB) of error trajectories, is proved using Lyapunov approach. The closed-loop system performance is investigated during numerical experiments. Finally the proposed controller is verified by successful implementation on a DSP board controlling a typical magnetic levitation ball system. Performed tests and experiments demonstrate that the proposed control technique is robust against discretization and unknown MLS model parameters, provides high tracking accuracy, is easily implementable, and simple to tune.

On-line and real-time controller tuning architecture based on Youla–Kucera controller parameterization

This paper presents an on-line and real-time controller tuning architecture based on Youla–Kucera controller parameterization. First, a coarse controller is designed to satisfy nominal performance of closed-loop system. Second, Youla parameter is used to construct an on-line and real-time fine tuning mechanism including a group of controller candidates under arbitrary switching strategy. The mechanism can adjust the control performance on-line to achieve the balance between dynamic and steady-state performance without resulting in any closed-loop stability problems.

Optimized Trajectory Tracking for ROVs Using DNN + ENMPC Strategy

This study introduces an innovative double closed-loop 3D trajectory tracking approach, integrating deep neural networks (DNN) with event-triggered nonlinear model predictive control (ENMPC), specifically designed for remotely operated vehicles (ROVs) under external disturbance conditions. In contrast to single-loop model predictive control, the proposed double closed-loop control system operates in two distinct phases: (1) The outer loop controller uses a DNN controller to replace the LMPC controller, overcoming the uncertainties in the kinematic model while reducing the computational burden. (2) The inner loop velocity controller is designed using a nonlinear model predictive control (NMPC) algorithm with its closed-loop stability proven. A DNN + ENMPC 3D trajectory tracking method is proposed, integrating a velocity threshold-triggered mechanism into the inner-loop NMPC controller to reduce computational iterations while sacrificing only a small amount of tracking control performance. Finally, simulation results indicate that compared with the ENMPC algorithm, NMPC + ENMPC can better track the desired trajectory, reduce thruster oscillations, and further minimize the computational load.

Multi-bandwidth observer-based adaptive robust pressure control for electro-hydraulic brake system with uncertainties and measurement noise

Accurate pressure regulation of electro-hydraulic brake system (EHB) is essential for enhancing braking performance in automobiles. However, component wear and pressure measurement noise can cause model parameters and controlled states to drift, resulting in system chattering. This nonlinear and uncertain state can significantly degrade pressure control performance. Motivated by this, the article presents a controlled state reconstruction-based adaptive robust pressure control technique with noise suppression. Firstly, a reduced dynamics model is established for controller design, which effectively captures the fundamental characteristic of the EHB. Secondly, a multi-bandwidth extended state observer (MBESO) capable of noise suppression is designed to reconstruct controlled states, including unknown disturbances and unmeasured pressure change rates of the EHB. Thirdly, an MBESO-based adaptive robust pressure control technique is introduced, where the control gain and robust factor are updated based on control and observation errors. In addition, the overall performance of the proposed control strategy is analyzed in the frequency domain, and close-loop stability is demonstrated via the Lyapunov method. Finally, the pressure control precision and robustness of the proposed algorithm are validated in both dynamic and static scenarios through sinusoidal and step-response experiments on a hardware-in-loop test bench. The results indicate that the proposed algorithm reduces dynamic pressure-tracking error by up to 62% compared to traditional method under sinusoidal conditions, with steady-state error remaining within 1 bar under step-response conditions.

Memoryless Dual-Observer-Based Output Feedback Stabilization of Linear Systems With Input and Output Delays.

This article focuses on the dual-observer-based stabilization of linear systems with delays in both the inputs and outputs. By a model reduction approach the system can be converted to an equivalent linear system without delays, for which a dual-observer-based stabilizing controller can be designed. However, such a controller is infinite dimensional or memory-based. To solve such a problem, a modified memoryless dual-observer-based stabilizing controller is designed, and the closed-loop stability is proven under some additional conditions. Compared with the reduced-order observer-based controller, the dimension of the dual-observer-based controller is smaller if the system has more inputs than outputs. At the same time, the design approach is more challenging in proving closed-loop stability, as for example a more intricate Lyapunov-Krasovskii functional has to be constructed associated with the proposed approach. The proposed approach is applicable to both continuous-time and discrete-time systems. Numerical simulations validate the effectiveness of the proposed method.

Dynamic Event-Triggered Control for Sensor–Controller–Actuator Networked Control Systems

We consider the problem of output feedback stabilization of LTI systems under event-triggering implementation. In particular, we assume that both the plant output and the control input are both transmitted over the network in an asynchronous manner. To that end, two independent event-triggering rules are constructed to generate the transmission instants of the submitted signals. The proposed approach is dynamic in the sense that the triggering rules involve internal dynamical variables to allow for further reduction in the communication load. Moreover, the inter-transmission times for both sides of the channel are lower bound by enforced dwell times to prevent the occurrence of Zeno phenomena. The problem is challenging due to mutual interactions between the sampling errors of the plant output and the control input, which requires careful handling to ensure closed-loop stability. The triggering mechanisms are designed by emulation as we first ignore the effect of the network and stabilize the plant in continuous-time. Then, the communication constraints are taken into account to derive the triggering conditions such that the stability of the networked control system is preserved. The required conditions are formulated in terms of a linear matrix inequality. The effectiveness of the technique is demonstrated by numerical simulations.

Two Adaptive Sliding Mode Control Algorithms for Vehicle Stability Enhancement

This paper discusses two adaptive sliding mode control (ASMC) algorithms for enhancing vehicle stability through direct yaw moment control (DYC). DYC is based on a logic process derived from the understeering and oversteering behavior of a cornering vehicle. Furthermore, to achieve DYC in a four-wheeled passenger vehicle, the reference yaw moment computed by the proposed algorihms is converted into a braking pressure that is to be applied to the four wheels. The objective is to minimize the yaw rate error and constrain the sideslip angle to an acceptable range. According to Lyapunov theory, complete stability analysis guarantees the closed-loop stability and robustness of a control system. Simulation results were used to compare the two ASMC algorithms, and both algorithms showed high performance even under critical operating conditions.

Inversion-based fuzzy adaptive control with prespecifiable tracking accuracy for uncertain hysteretic systems

Inversion-based control strategies have the outstanding effectiveness in the compensation for hysteresis nonlinearities. However, when the plant is driven by smart material-based actuator with the information absence of hysteresis output, there still exist technical gaps in the construction of hysteresis inverse controller. Therefore, this study aims to address this gap by proposing a novel control scheme. Technically, a novel hysteresis inverse algorithm, significantly reducing computational burden, has been proposed based on a novel adaptive estimation method for the unknown parameter (density function) in the Preisach-typed hysteresis nonlinearity. Furthermore, the inverse compensation error, the nonlinearities and uncertainties appeared in the controlled plant are accommodated by the innovative adaptive fuzzy feedback controller. With our scheme, it can ensure that the closed-loop stability, predefined steady-stated tracking performance and the convergence of algorithms including inverse algorithm and adaptive updating laws. In addition to theoretical analysis, we have validated the effectiveness of the proposed control scheme through simulation comparisons and experimental results conducted by the real-life piezoelectric actuator.

Multilayer neuroadaptive constraint-handling control architecture for a family of nonlinear systems with uncertainty compensation

In practical applications, there are some requirements for time-varying constraints on full system states. Currently, Barrier Lyapunov Function is a popular tool for constraint control. However, how to handle various uncertainties while satisfying constraint requirements is worth further research. Accordingly, a high-performance multilayer neuroadaptive constraint-handling controller for a class of nonlinear systems with uncertainty compensation will be developed. Significantly, asymmetric time-varying constraints for full system states can be implemented. Furthermore, a set of novel multilayer neuroadaptive disturbance observers will be proposed to address modeling uncertainties. Moreover, by introducing a set of nonlinear command filters, the intelligent control algorithm will be designed via the command filtered backstepping method. The stability of the whole closed-loop system is strictly proved. Additionally, the proposed algorithm is applied to different nonlinear systems including a hydraulic robotic manipulator system to verify its feasibility.

Observer-based robust servomechanism control of a three-phase induction motor drive

Induction motors (IMs) are widely used in industrial applications, but harmonic distortion in IM drives can lead to inefficiencies and reduced lifespan. Traditional control strategies and filtering methods have limitations in mitigating lower-order harmonics, particularly the 5th harmonic, which can generate reverse torque and increase overheating risk. Existing solutions often struggle to fully address these issues, especially in high-power applications with dynamic loading conditions. This paper proposes a control strategy to reduce voltage and current harmonics in a Z-source inverter (ZSI)-fed IM drive. The system incorporates an observer-based output feedback robust servomechanism controller, designed using Linear Quadratic Regulator (LQR) and Linear Matrix Inequality (LMI) techniques. It ensures closed-loop stability, precise tracking regulation, and effective disturbance rejection, while also featuring a speed adaptation mechanism for sensorless operation. Simulation results demonstrate significant harmonic mitigation, with the controller achieving 1.01% lower voltage THD and 1.03% lower current THD compared to conventional approaches. This improvement aligns with industry standards and outperforms several existing techniques. The proposed method contributes a comprehensive solution for harmonic mitigation in high-power IM drives, applicable to various industrial applications requiring high-quality power and precise speed control.

Anti-swing position control of super-twisting sliding mode for underactuated tower crane based on nonlinear marine predator algorithm

Due to the nonlinear, underactuated, and strongly coupled characteristics of tower cranes, issues such as inaccurate load positioning and severe swinging are prone to occur during transportation, making the control problem extremely complex. To address these issues, this paper has designed a super-twisting robust sliding mode controller based on the nonlinear marine predator algorithm (NMPA) to ensure the accurate positioning of the desired location during the transportation process of the tower crane while reducing the oscillation of the load. First, a nonlinear dynamic model of a four-degree-of-freedom tower crane considering friction is constructed. Second, to address the difficulty of effectively controlling the underactuated tower crane system model due to its nonlinearity and strong coupling, the super-twisting algorithm is introduced, and a super-twisting sliding mode controller for anti-swing positioning during the crane transportation process is designed. Then, the parameters of the super-twisting sliding mode controller are optimized using the NMPA to suppress sliding mode chattering and quickly achieve the system’s steady state. Finally, the stability of the nonlinear tower crane system is analyzed using Lyapunov’s theory and LaSalle’s invariance principle to ensure the closed-loop stability of the error dynamics. The simulation results show that the proposed control method exhibits excellent load anti-sway performance and robustness.

Robust fractional-order load frequency control for hybrid power system concerning high wind penetration

Hybrid power systems concerning wind farms have witnessed significant dynamic characteristic changes due to unpredicted generation output and integration mode conversion between frequency-sensitive wind plants and non-scheduled ones. This work presents a robust fractional-order load frequency control (LFC) method for a multi-area hybrid power system in the presence of wind penetration uncertainties. To characterize the injection effect of wind farms, the power system is described by a model with an uncertain wind penetration factor in a pre-estimated range. Then, an enhancement of Levy’s identification method is developed to convert this model into a fractional-order reduced structure to design the load frequency controller, which is in a form of fractional-order PID with a filter for ease of engineering implementation. The closed-loop stability is analyzed by the stability boundary locus (SBL) method under different wind penetration levels. It is shown that superior frequency response performance and system robustness can be obtained if the controller is designed in terms of the model with the worse-case wind penetration. Illustrative examples including a three-area hybrid power system under a variety of wind penetration variations are given to show the effectiveness of the proposed method.

Autonomous Underwater Vehicle (AUV) Motion Design: Integrated Path Planning and Trajectory Tracking Based on Model Predictive Control (MPC)

This paper attempts to develop a unified model predictive control (MPC) method for integrated path planning and trajectory tracking of autonomous underwater vehicles (AUVs). To deal with the computational burden of online path planning, an event-triggered model predictive control (EMPC) method is introduced by using the environmental change as a triggering mechanism. A collision hazard function utilizing the changing rate of hazard as a triggering threshold is proposed to guarantee safety. We further give an illustration of how to calculate this threshold. Then, a Lyapunov-based model predictive control (LMPC) framework is developed for the AUV to solve the trajectory tracking problem. Leveraging a nonlinear integral sliding mode control strategy, we construct the contraction constraint within the formulated LMPC framework, thereby theoretically ensuring closed-loop stability. We derive the necessary and sufficient conditions for recursive feasibility, which are subsequently used to prove the closed-loop stability of the system. In the simulations, the proposed path planning and tracking control are verified separately and integrated and combined with static and dynamic obstacles.

Fixed-time attitude control for hypersonic morphing vehicles: A dynamic memory event-triggering approach

This paper focuses on achieving fast attitude tracking and resource preservation for hypersonic morphing vehicles (HMVs) in continuous morphing stages. Firstly, the most remarkable feature of an HMV are the morphing wings, leading to dramatic aerodynamic property changes. As a result, fast tracking and excellent adaptation to various morphing statuses are necessary to guarantee the success of flight missions. Thus, this work employs the fixed-time stability theory to establish a high-performance controller, including variable exponent coefficients. Compared to the traditional constant exponent coefficient-based methods, some singularity problems are avoided, and the global fixed-time stability is ensured. Then, in order to implement the control input in a low-resource occupation, the dynamic event-triggering mechanism is presented to provide a flexible updating policy. The proposed event-triggering technology has a more concise and efficient structure than the traditional methods. In this case, the controller and the dynamic variable of the event-triggering method simultaneously adopt the exponent coefficients. Finally, the closed-loop stability is proven via the Lyapunov thesis, and simulation results show the effectiveness and the advantage of the proposed control strategy.

Resilient Self-Triggered Model Predictive Control of Cyber-Physical Systems Under Two-Channel False Data Injection Attacks

Abstract This paper presents a novel resilient self-triggered model predictive control (ST-MPC) method to alleviate potential threats of false data injection (FDI) attacks on cyber-physical systems (CPSs). First, considering that the data transmitted via the sensor-to-controller (S–C) and controller-to-actuator (C–A) channels in CPS may be tampered with by FDI attacks, a novel input reconstruction strategy combined with the ST-MPC mechanism is proposed to alleviate the threats of FDI attacks while reducing the computational and communication resources, in which key optimal control signals are selected and protected based on systematic performance inequalities. Correspondingly, a resilient ST-MPC algorithm combined with the dual-mode strategy is further proposed. Moreover, the iterative feasibility and the closed-loop stability are strictly demonstrated. Finally, the effectiveness of the proposed strategy is verified via a simulation study.

Safety-Preserving Lyapunov-Based Model Predictive Rendezvous Control for Heterogeneous Marine Vehicles Subject to External Disturbances.

This article investigates the cooperative rendezvous control problem for perturbed heterogeneous marine systems composed of an autonomous underwater vehicle (AUV) and an autonomous surface vehicle (ASV). A novel Lyapunov-based model predictive control (LMPC) framework is presented to accomplish safe and precise rendezvous under input limitations and external disturbances. First, by incorporating the prescribed performance control (PPC) technique into the LMPC framework, we transform the original ascending state of the AUV into a self-constrained state, which serves as the decision variable of the model predictive control (MPC) optimization problem. Then, PPC-aided auxiliary control laws based on disturbance observers (DOBs) are designed to establish a robust contractive constraint to provide stability margins. Combining the LMPC with the PPC technique makes the original state-constrained problem an equivalent state-constraint-free problem. By addressing the MPC problem for the equivalent unconstrained system, the proposed method preserves the rendezvous safety. With the robust contractive constraint, the proposed safety-preserving LMPC (SP-LMPC) controller can inherit robustness and stability from the robust auxiliary control laws. Furthermore, theoretical analyses are conducted to assess recursive feasibility and closed-loop stability. With comprehensive theoretical support, the proposed method provides a new framework to simultaneously address state constraints and disturbances for highly nonlinear marine systems. Finally, simulations and comparisons are conducted to demonstrate the effectiveness and advantages of the proposed algorithm.

Robust neuro-adaptive command-filtered back-stepping fault-tolerant control of satellite using composite learning

This study proposes an adaptive neural command-filtered backstepping control system for precise and fast attitude control of a satellite considering different uncertain dynamics. Mission success crucially depends on robust attitude control resilient to model uncertainties, unmodeled dynamics, external disturbances, and actuator faults. The proposed approach synergistically combines a neural network for handling model uncertainties, unmodeled dynamics, and actuator faults, with a disturbance observer for compensating external disturbances and neural network estimation errors. The command-filtered backstepping technique avoids the explosion of complexity inherent to traditional backstepping, while integrating integral action into the design results in the elimination of the steady-state tracking error. Besides, a composite learning method optimizes the update laws for the neural network and disturbance observer weights, enhancing control performance. Despite the presence of uncertainties, the closed-loop system stability is guaranteed by the Lyapunov stability theorem. Simulation results demonstrate the proposed controller’s ability to handle severe actuator faults, unmodeled dynamics, and measurement noise without requiring explicit fault detection and isolation schemes.

Adaptive complementary sliding mode control of ship course under environmental disturbance

In this paper, an adaptive complementary sliding mode control strategy based on nonlinear extended state observer (NESO) is proposed for the ship course tracking control subject to environmental disturbances. By introducing the adaptive law, the system uncertainty is estimated and adjusted, so that the boundary layer of the complementary sliding mode control can realize dynamic changes and ensure the system robustness. At the same time, the auxiliary control system is introduced to compensate the complementary sliding mode control law to guarantee the system stability under finite actuation. For the environmental disturbances of the heading process, a NESO is designed for real-time estimation and compensated to the adaptive complementary sliding mode control law to improve the robustness of the system. The closed-loop stability is proved, and simulation results show that the control strategy effectively improves the tracking accuracy and robustness of the system.