Stability Of Closed-loop System Research Articles

Mathematical modeling of an articulated flying vehicle for precise control analysis in grasping highly oscillatory objects

In this research work, a detailed mathematical modeling approach has been taken in order to develop a complete package for the investigation of phenomena associated with the flight dynamics and control of an articulated aerial robot in grasping high weight oscillatory objects such as living creatures. To this end, the origin of forces and moments generated by a moving target is analyzed and the nonlinear differential equations of the system are derived. Then, the model is verified and the effect of target oscillations on the whole system dynamics is investigated. In the next step, due to the nonlinear nature of this under-actuated system and the presence of the force-generating target with unknown dynamics and model parametric and non-parametric uncertainties, two versions of adaptive sliding mode control (A-SMC) are designed to enable the system follows the nominal trajectories in a desirable way without needing to know the upper bounds of the time-varying forces and uncertainties. In this regard, the stability of closed-loop systems is proved based on Lyapunov theory. The performance and robustness of the designed controllers are evaluated and compared through numerical and Monte Carlo simulations with some standard criteria. At the end, the conclusion of this work is presented.

Flight tracking control of mini-drone: Flower pollination algorithm based model-free control

This paper presents a novel model-free control approach, Flower Pollination Algorithm-based Model-Free Control (FPA-MFC), for trajectory tracking of mini-drone quadrotor unmanned aerial vehicles (UAVs). The proposed approach employs an adaptive estimator based on filtered signals to approximate the nonlinear dynamic functions of the system. This approximator allows the development of a robust decentralized control law able to separately manage the position and attitude dynamics of the drone. The controller design is free of any prior knowledge of the system dynamics, and the control inputs are computed solely from instantaneous input and output measurements. Indeed, this can significantly reduce the computational burden and improve the efficiency of the control algorithm while preserving its simplicity. The design gains of the control law are selected using the metaheuristic flower pollination algorithm to achieve greater trajectory tracking performance and ensure closed-loop system stability. Simulation tests conducted on the Parrot mini drone platform validate the effectiveness and superior performance of FPA-MFC, compared to similar controllers without optimization and using the particle swarm optimization algorithm.

Dynamic event-triggered fault-tolerant control for nonaffine systems with asymmetric error constraint

This paper focuses on the problem of dynamic event-triggered fault-tolerant control (FTC) for nonaffine systems with unmeasurable state and asymmetric error constrain. At first, an adaptive failure compensation observer is designed to calculate unpredictable state of the nonaffine systems. Then, a dynamic event triggering strategy (DETS) is constructed to adjust the control signal and make it more flexible in transmission. Next, a new error-dependent conversion function (EDCF) is designed to confine tracing error, which can ensure that the designed Lyapunov function is always positive definite, and extend the symmetric constraint boundary to the asymmetric constraint boundary. The tracking performance and stability of closed-loop systems are proven through Lyapunov stability analysis. Finally, the availability of this method is verified by simulation experiments.

Reinforcement learning-adaptive fault-tolerant IGC method for a class of aircraft with non-affine characteristics and multiple uncertainties

Abstract In this paper, a brand-new adaptive fault-tolerant non-affine integrated guidance and control method based on reinforcement learning is proposed for a class of skid-to-turn (STT) missile. Firstly, considering the non-affine characteristics of the missile, a new non-affine integrated guidance and control (NAIGC) design model is constructed. For the NAIGC system, an adaptive expansion integral system is introduced to address the issue of challenging control brought on by the non-affine form of the control signal. Subsequently, the hyperbolic tangent function and adaptive boundary estimation are utilised to lessen the jitter due to disturbances in the control system and the deviation caused by actuator failures while taking into account the uncertainty in the NAIGC system. Importantly, actor-critic is introduced into the control framework, where the actor network aims to deal with the multiple uncertainties of the subsystem and generate the control input based on the critic results. Eventually, not only is the stability of the NAIGC closed-loop system demonstrated using Lyapunov theory, but also the validity and superiority of the method are verified by numerical simulations.

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.

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.

Event-Triggered Adaptive Neural Impedance Control of Robotic Systems.

This article presents an event-triggered adaptive neural impedance control (ETANIC) scheme for robotic systems, where the combination of impedance control (IC) and event-triggered mechanism can significantly reduce the computational burden and the communication cost under the premise of ensuring the stability and tracking performances of the robotic systems. The IC is used to achieve the compliant behavior of the robotic systems in response to the environment. The uncertainties of the robotic systems are estimated by the radial basis function neural network (RBFNN), and the update laws for RBFNN are derived from the designed Lyapunov function. The stability of the whole closed-loop control system is analyzed by the Lyapunov theory, and the event-triggered conditions are designed to avoid the Zeno behavior. The numerical simulation and experimental tests demonstrate that the proposed ETANIC scheme can achieve better efficiency for controlling the robotic systems to perform the interaction tasks with the environment in comparison to the adaptive neural IC (ANIC).

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.

Recursive terminal sliding mode approximate optimal control strategy based on reconstructed nonlinear systems

For a class of nonlinear systems with unknown internal states and actuator failures, this paper proposes a recursive terminal sliding-mode fault-tolerant control method based on reconfigurable nonlinear systems and further designs an approximate optimal compensated controller based on adaptive dynamic programming, which employs a neural network (NN) to estimate the optimal value function. The system ensures that the tracking error converges to a small set around zero with faster speed and higher accuracy even when the actuator fails. Finally, the convergence of the expanded state observer and the single-evaluation NN weights is demonstrated based on the Lyapunov theory, and the stability of the whole closed-loop system is given. Simulation results and comparisons verify the effectiveness of the proposed control strategy.

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.

Fuzzy disturbance observer-based fuzzy swing suppression control of a ‘mooring-heavy lift crane-cargo’ coupled system

In this paper, an adaptive fuzzy disturbance observer (FDO)-based control is proposed for the swing suppression of the mooring-heavy lift crane (HLC)-cargo system in the presence of a wave disturbance. First, the dynamic model of the HLC system is determined by employing the Lagrangian method, and the wave force is modeled as an exosystem with unknown terms based on the Jonswap spectrum. Then, based on the HLC model and the wave force exosystem, an FDO is established to determine the wave disturbances, and a fuzzy approximator is developed to estimate the unknown terms. A novel disturbance estimation error observer is first developed to facilitate the parameter adaptive updating law. Subsequently, by augmenting the HLC system and disturbance estimation error system, an FDO-based fuzzy antiswing control method is proposed in terms of the linear matrix inequality technique to suppress the swing. The closed-loop system stability is examined by using the Lyapunov method. Finally, the effectiveness of the proposed method is validated by numerical simulation.

A DMPC-based three-dimensional cooperative guidance scheme with impact time and impact angle constraints

In this paper, a distributed model predictive control (DMPC)-based three-dimensional (3D) cooperative guidance scheme is proposed for multiple interceptors with controllable thrust and constrained acceleration, to simultaneously attack a maneuvering target at desired terminal angles. The cooperative guidance scheme consists of a fractional power function-based extended state observer (FPESO) for disturbance estimation, and a DMPC controller to generate the control actions. By introducing the assumed state trajectory, the DMPC controller (of each interceptor) can simultaneously employ the zebra optimization algorithm (ZOA) to solve the constrained optimization problem, and generate the real-time guidance commands with no need of any global information. For restricting the uncertain deviation between the assumed state trajectory and the actual one, a compatibility constraint is designed, and the terminal ingredients are developed for coupling and decoupling stage costs, respectively. By applying the above designed constraints and the terminal ingredients, the recursive feasibility of the resulting optimization problem and the closed-loop stability of multi-interceptor system are both ensured. Through numerical simulations, it is verified that the proposed cooperative guidance scheme can achieve cooperative interception with impact time and angle constraints in various scenarios, and has advantageous performance.

Output-feedback formation tracking control of autonomous surface vessels with collision avoidance

In this paper, a formation control problem with collision avoidance is investigated for underactuated surface vessels with position–heading measurements. Each vessels is subject to actuator magnitude and rate saturations. At first, an anti-saturation nonlinear extended state observer is developed to recover the linear velocity and yaw rate as well as unknown uncertainty and disturbances. Then, observer-based formation control laws are designed based on an artificial potential functions, obstacle avoidance yaw references and a backstepping technique. The stability of closed-loop formation control system is proved. The salient features of this paper are as follows. First, formation control with the capability of collision avoidance is achieved by using artificial potential functions and obstacle avoidance yaw references, which is more aggressive. Second, the proposed controller is able to deal with the magnitude and rate constraints of the actuator. Third, the proposed anti-saturation nonlinear extended state observer can achieve better estimation results for rapidly changing signals. Simulation results are given to substantiate the proposed formation control laws.

Tensor product model transformation-based reinforcement learning neural network controller with guaranteed stability

Despite the success of neural network (NN) controllers, the stability of closed-loop NN control systems is still a major challenge. This paper proposes a constrained reinforcement learning (RL) algorithm to design optimal NN controllers for a class of nonlinear dynamical systems while guaranteeing the stability of the control systems. By representing a controlled system as a tensor product (TP) model, a sufficient stability condition for a closed-loop NN control system is derived, which is then employed as a training constraint for the NN controller throughout the training process to ensure the stability in each training step. By showing the existence of a Lyapunov function, which is also directly obtained during the training process, the stability can be theoretically confirmed. Simulation studies on various nonlinear dynamical systems illustrate that the NN controllers trained with the proposed constrained RL algorithm outperform linear–quadratic–regulator controllers and yield roughly the same performance index values as those trained with an unconstrained RL algorithm, indicating that the imposed constraint does not significantly affect the training performance. Most importantly, while simulation results show that all controllers provide closed-loop stability, only the NN controllers trained with the proposed constrained RL algorithm theoretically guarantee stability.

Improving stability and performance in IoT-Driven networked control systems

With the widespread adoption and benefits of the Internet of Things (IoT), this technology has expanded its reach into the realm of automation and control, giving rise to a branch known as industrial networks. The use of IoT technology is on the rise due to its daily increasing advantages and ease of use. However, it has also introduced new challenges in control systems, prompting researchers to conduct numerous studies to address these challenges and propose innovative solutions. One of these challenges, for example, is the limited bandwidth of the network, which leads to challenging issues such as variable random time delays and packet loss. In light of these challenges, using networked control systems instead of many traditional control methods can significantly improve the performance and stability of closed-loop systems. In this context, this paper aims to enhance system tolerance and reliability, along with permanent state error correction, by presenting methods for designing networked controllers that are influenced by random delays. To achieve this goal, we first propose a predictive control model with reduced prediction horizons, assuming constant delays in the input. This controller not only ensures stability but also tracks the reference input. Simulation results demonstrate that this controller can tolerate some variations in delay despite being designed for constant delays. However, it is not robust against significant variations in delay inherent to network environments. Therefore, in the second approach, a controller based on the Lyapunov function and linear matrix inequalities is designed for a system with time-varying input delays. This controller, in addition to stabilizing the system, tracks the reference input by minimizing the state error.

Adaptive model predictive control scheme for partially internal thermally coupled air separation column

Partially Internal Thermally Coupled Air Separation Column (P-ITCASC) is a highly energy-efficient and cost-effective technology. However, its complex dynamics resulting from thermal coupling pose a challenge to the operating stability of this technology. This article, therefore, proposes an adaptive model predictive control (AMPC) scheme for the P-ITCASC process. The controller incorporates an auto-regressive and exogenous inputs (ARX) model, a linear time-varying Kalman filter, and a recursive polynomial model estimator (RPME) algorithm. Within RPME, ARX polynomial models are identified and utilized to estimate the time-varying parameters and update the prediction model of the process. The process states are observed through the Kalman filter, and the constrained receding horizon optimization problem is solved using quadratic programming. This control scheme ensures the closed-loop system's feasibility and stability in the presence of output/input constraints. An adaptive generic model control, model predictive control, and adaptive internal model control schemes were also designed for benchmarking study. Numerical simulations show that AMPC is more efficient in handling nonlinear dynamics and maintaining product concentration to desired set points compared to other control schemes.

Neural operators for robust output regulation of hyperbolic PDEs

The recently introduced neural operator (NO) has been employed as a gain approximator in the backstepping stabilization control of first-order hyperbolic and parabolic partial differential equation (PDE) systems. Due to the global approximation ability of the DeepONet, the NO provides approximate spatial gain function with arbitrary accuracy. The closed-loop system stability can be ensured by the backstepping controller involving the approximate gain with sufficiently small error. In this paper, the NO theory is leveraged to solve the robust output regulation problem for a class of uncertain hyperbolic PDE systems under the design framework of backstepping-based regulator. The NO is trained offline on a dataset containing a sufficient number of system parameters and corresponding prior solutions of the kernel equation, so as to generate feedback gain for the robust regulator. Once the NO is trained, the kernel equation does not need to be solved ever again, for any new system parameters that do not exceed the range of the training set. Based on the internal model principle, the regulator is inherently robust to a degree of parameter uncertainty and error in approximate gain. Therefore, the tracking error can still converge to 0 if the extended regulator equations are solvable and the parameter uncertainty leads to an asymptotically stable origin. We provide a series of theory proofs and a numerical test under the approximate control and observation gains to demonstrate the robust regulation problem. It is shown that the NO is almost three orders of magnitude faster than PDE solver in generating kernel function, and the loss remains on the order of 10−4 in the test. This provides an opportunity to use the NO methodology for accelerated gain scheduling regulation for PDEs with time-varying system parameters.

Backstepping control of hypersonic vehicles under input and output constraints with model uncertainties and disturbances

In this paper, considering the physical restriction of hypersonic vehicle systems in a practical flight environment, the altitude tracking problem is studied with input magnitude, input rate, output constraints, system parameter uncertainties and disturbances, which expands the traditional considerations of control methods in the hypersonic vehicle field. The hyperbolic tangent function is employed to address the system input constraints. Furthermore, the incorporation of barrier Lyapunov function serves to ensure that the system output is limited in the prescribed limitations. In particular, two extended state observers are integrated to eliminate errors from model uncertainties and disturbances. Based on the effective combination of these techniques and auxiliary variable designs, a novel backstepping controller is proposed to simultaneously handle problems of input and output constraints, model uncertainties and disturbances. The closed-loop system stability is demonstrated using the Lyapunov theory. Simulation results show the effectiveness and superiority of the proposed controller compared with the traditional backstepping controller.

On robustification of digital event-based controllers for control-affine nonlinear systems

In this paper, the robust digital stabilization problem of nonlinear systems is investigated. In particular, a methodology for the design of robust quantized sampled-data stabilizers updated via an event-triggered mechanism is provided for time-varying control-affine nonlinear systems affected by actuation disturbances and measurement noises. The notion of time-varying steepest descent feedback (TSDF), continuous or not, and the Input-to-State Stability (ISS) redesign methodology are used for the development of the proposed robust event-based digital controller. Under the assumption that the actuation disturbances and measurement noises are bounded with a-priori known bounds and that the amplitude of the measurement noises satisfies a certain condition related to the new added robustification term, the following result is proved: there exist a suitably fast sampling and an accurate quantization of the input/output channels such that the digital implementation of robustified TSDF controllers, updated through a proposed event-triggered mechanism, ensures semi-global practical stability of the related closed-loop system regardless of the above uncertainties. In the methodology here proposed, time-varying sampling periods and the non-uniform quantization of the input/output channels are allowed. Moreover, the theory here developed includes the analysis of the intersampling system behaviour. Possible discontinuities in the function describing the TSDF at hand are also managed. The provided results are validated through a numerical example.

Adaptive Visual Control for Robotic Manipulators with Consideration of Rigid-Body Dynamics and Joint-Motor Dynamics

A novel cascade visual control scheme is proposed to tailor for electrically driven robotic manipulators that operate under kinematic and dynamic uncertainties, utilizing an uncalibrated stationary camera. The proposed control approach incorporates adaptive weight radial basis function neural networks (RBFNNs) to learn the behaviors of the uncertain dynamics of the robot and the joint actuators. The controllers are designed to nullify the approximation error and mitigate unknown disturbances through an integrated robust adaptive mechanism. A major advantage of the proposed approach is that prior knowledge of the dynamics of the robotic manipulator and its actuator is no longer required. The controller autonomously assimilates the robot and actuator dynamics online, thereby obviating the need for fussy regression matrix derivation and advance dynamic measurement to establish the adaptive dynamic parameter update algorithm. The proposed scheme ensures closed-loop system stability, bounded system states, and the convergence of tracking errors to zero. Simulation results, employing a PUMA manipulator as a testbed, substantiate the viability of the proposed control policy.