Time-varying Parameter Uncertainties Research Articles

Feedback Control Design Strategy for Stabilization of Delayed Descriptor Fractional Neutral Systems with Order 0 < ϱ < 1 in the Presence of Time-Varying Parametric Uncertainty

Descriptor systems are more complex than normal systems, which are modeled by differential equations. This paper derives stability and stabilization criteria for uncertain fractional descriptor systems with neutral-type delay. Through the Lyapunov–Krasovskii functional approach, conditions subject to time-varying delay and parametric uncertainty are formulated as linear matrix inequalities. Based on the established criteria, static state- and output-feedback control laws are designed to ensure regularity and impulse-free properties, together with robust stability of the closed-loop system under permissible uncertainties. Numerical examples illustrate the effectiveness of the control methods and show that the results depend on the range of variation in the delays and on the fractional order, leading to stability analysis results that are less conservative than those reported in the literature.

Self-tuning PID feedback control method for magnetic suspension active vibration isolation system with parameters uncertainty

A self-tuning PID (Proportion-Integral-Derivative) control method based on the adaptive mechanism was proposed for the magnetic suspension active vibration isolation system with the characteristics of nonlinear, time-varying, and model parameter uncertainty. The controller identified the controlled object parameters online and solved the controller parameters in real time. To test the effectiveness of the proposed method, a six degree-of-freedom (DOF) magnetic suspension active vibration isolation system was designed and built. The six DOF dynamic model of the vibration isolation system with uncertain model parameters was derived for control. Experiments were carried out and compared with the control effects of the tradition PID control and cascade PID control algorithm. The experimental results show that the proposed self-tuning PID controller has more outstanding practicality and effectiveness in solving the model parameter uncertainty problem compared with the existing studies at home and abroad, and it also proves that the control method has a good isolation effect on the wide band disturbances.

Adaptive Control of Unmanned Aerial Vehicles with Varying Payload and Full Parametric Uncertainties

This article investigates an adaptive tracking control problem for a six degrees of freedom (6-DOF) nonlinear quadrotor unmanned aerial vehicle (UAV) with a variable payload mass. The changing payload introduces time-varying parametric uncertainties into the dynamical model, rendering a static control strategy no longer effective. To handle this issue, two adaptive schemes are developed to maintain the uncertainties in the translational and rotational dynamics. Initially, a virtual proportional derivative (PD) is designed to stabilize the horizontal position; however, due to an unknown and time-varying mass, an adaptive controller is proposed to generate the total thrust of the UAV. Furthermore, an adaptive controller is designed for the rotational dynamics, to handle parametric uncertainties, such as inertia and external disturbance parameters. In both schemes, a standard adaptive scheme using the certainty equivalence principle is extended and designed. A stability analysis was conducted with rigorous analytical proofs to show the performance of our proposed controllers, and simulations were implemented to assess the performance against other existing methods. Tracking fitness and total control efforts were calculated and compared with closed-loop adaptive tracking control (CLATC) and adaptive sliding mode control (ASMC). The results indicated that the proposed design better maintained UAV stability.

Finite-Time Disturbance Observer-based New Fast Terminal Sliding Mode Control for Systems with Uncertainties in Dynamics and Disturbances: Application to Three-DOF Hover Quadrotor

This paper proposes a Finite-Time Disturbance Observer-based new Fast Terminal Sliding Mode Control (FTDO–FTSMC) for systems under disturbances and parametric uncertainties with input saturation. Our approach begins with the design of a finite-time observer to estimate disturbances, in which we show that the errors in disturbance estimation converge to zero in finite time. Then, a new fast terminal sliding surface is proposed for the fast and finite-time convergence of the tracking errors. The closed-loop system under the proposed control scheme has been proved to be asymptotically stable by using the Lyapunov theory. Finally, the proposed FTDO–FTSMC framework is applied to the attitude control of a three-DOF hover quadrotor under time-varying disturbances and parametric uncertainties. Simulation results show that the proposed control strategy achieves excellent performance in terms of trajectory tracking, disturbance rejection and robustness, even in the presence of external disturbances and model uncertainties, compared with the existing control approaches.

Event-Triggered Quantized Quasisynchronization of Uncertain Quaternion-Valued Chaotic Neural Networks With Time-Varying Delay for Image Encryption.

In this article, a class of quaternion-valued master-slave neural networks (NNs) with time-varying delay and parameter uncertainties was first established by conducting the extension from real-valued chaotic NNs to the quaternion field. Then, based on logarithmic quantized output feedback, the quasisynchronization issue of the NNs was investigated via devising a neoteric dynamic event-triggered controller. In virtue of the classical Lyapunov method and a generalized Halanay inequality, not only corresponding synchronization criteria were obtained to realize the quasisynchronization of master-slave NNs but also a precise upper bound was provided. Moreover, Zeno behavior can be eliminated under the presented scheme in this article. The accuracy of the theoretical outcomes was demonstrated by means of Chua's circuit. Ultimately, some experimental results of pragmatic application in image encryption/decryption were exposed to substantiate the feasibility and efficacy of the current algorithm for the proposed quaternion-valued NNs.

Simultaneous Estimation of Vehicle Sideslip and Roll Angles Using an Integral-Based Event-Triggered H$_{\infty }$ Observer Considering Intravehicle Communications

In recent years, several technological advances have been incorporated into vehicles to ensure their safety and ride comfort. Most of these driver-assistance technologies aim to prevent skidding, whereas less attention has been paid to the avoidance of other dangerous situations such as a rollover. Since knowledge of slip and roll angles is critical to the control and safety of vehicle handling, their estimation remains of great interest when addressing emerging constraints in modern technologies involving networked communications and distributed computing. This paper presents an integral-based event-triggered H <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$_{\infty }$</tex-math></inline-formula> observer to simultaneously estimate the sideslip and roll angles, considering intravehicle communications with a networked-induced delay. As the longitudinal velocity and tire cornering stiffness of a vehicle can vary significantly during driving and have a strong influence on vehicle lateral stability, these time-varying parameter uncertainties are considered in the design of the observer. The simulation and experimental results demonstrate the effectiveness of the proposed observer.

Finite Time State-of-Charge Observer With Robustness Against Unknown Parameter Uncertainties

Accurate state of charge (SOC) is of great engineering significance to relieve the range anxiety, avoid safety accidents, and prolong the battery lifetime. This brief proposes an SOC observer with finite-time stability and robustness against unknown and time-varying parameter uncertainties. First, an equivalent circuit model (ECM) is employed to describe the battery dynamic characteristic with full consideration of time-varying parameter uncertainties and unknown noises, which are only assumed to be bounded. Second, a hybrid method combined with off-line and on- line identifications is proposed to estimate the battery model parameters. It means that the change of the battery parameters can be well traced and the estimation error in the early stage can be effectively diminished. Third, a finite-time observer is designed to estimate SOC, which can achieve faster error convergence rate. Finally, sufficient criteria and rigorous proof are given to ensure the convergence of the estimation errors in finite time. Extensive simulations and experiments are conducted to assess the effectiveness of the proposed method as well. Results illustrate the high accuracy, strong robustness, and fast convergence speed of the proposed method with the estimation errors bounded by 1% and the convergence time limited in 20 s.

Distributed Robust Partial State Consensus Control for Chain Interconnected Delay Systems

Partial state consensus (PSC) is investigated for chain interconnected systems with time-varying delays and parameter uncertainties. A novel design philosophy of PSC control is proposed and a sequential calculation method is presented to guarantee the robustness of the controller. A sufficient condition based on linear matrix inequalities (LMIs) is derived and the stability is proven by the Lyapunov method. The proposed approach can ensure that the states which are subject to a consensus constraint achieve consensus, while those without a consensus constraint track their own set points. Finally, numerical simulations and a solution proportioning experiment are developed to validate the effectiveness of the proposed method.

Cooperative driving of heterogeneous uncertain nonlinear connected and autonomous vehicles via distributed switching robust PID-like control

In this work, the leading-tracking control problem for heterogeneous and uncertain nonlinear autonomous vehicles is addressed. These latter communicate their status information over a wireless communication network and engage in cooperative movements in extra-urban traffic environment. The nonlinear vehicle dynamics are affected by time-varying parameter uncertainties, and the air-drag reduction caused by platooning is explicitly considered. The variation of V2V links as a result of cooperative manoeuvres is modelled by incorporating switching into the communication network topology. To this aim, we develop a novel robust distributed Proportional-Integral-Derivative (PID)-like control protocol which ensures that all vehicles within the platoon robustly track the behaviour of the leader, despite the presence of both unknown parameters uncertainties and network switching. The analytical stability of the proposed control strategy is demonstrated using Lyapunov theory. Sufficient stability conditions are expressed as a set of feasible Linear Matrix Inequalities (LMIs) whose solution allows the robust control gains to be properly tuned. The effectiveness of the approach is evaluated via the Mixed Traffic Simulator (MiTraS) co-simulation platform, which combines MATLAB/Simulink with SUMO microscopic traffic simulator. The exhaustive simulation analysis, involving the Monte Carlo method, is carried out considering different cooperative platooning manoeuvres, and confirms the theoretical derivation.

Disturbance Observer-Based Robust Control Design for Uncertain Periodic Piecewise Time-Varying Systems With Disturbances

With the aid of disturbance observer strategy, this article aims to investigate the disturbance rejection and stabilization problems for periodic piecewise time-varying systems that are subject to time-varying delays, parameter uncertainties, nonlinear perturbations and exogenous disturbances. To be more specific, the periodic piecewise time-varying systems are built by segmenting the fundamental period of periodic systems into a limited number of subintervals. Further, the disturbances engendered from an exogenous system are estimated by deploying the disturbance observer and subsequently, on the premise of disturbance that is esimated, a robust controller protocol is constructed for the considered system. Moreover, by bridging the time-varying periodic piecewise Lyapunov-Krasovskii functional with a matrix polynomial lemma, a set of adequate criteria is framed, which confirms the asymptotic stability of the system that is being addressed. Subsequently, on the premise of established criteria, the design of periodic piecewise gain matrices of devised controller and configured observer are presented. Eventually, the importance and potential of the presented theoretical concepts are evidenced through offering a numerical illustration with the simulation results.

Finite-time stabilization for uncertain nonlinear systems with impulsive disturbance via aperiodic intermittent control

This paper ensures finite-time stabilization (FTS) and finite-time contractive stabilization (FTCS) for impulsive systems with time-varying parametric uncertainties by investigating the design of an aperiodic intermittent controller, where uncertain impulsive disturbance is generated at the instants caused by the control action to the plant. Based on the Lyapunov methods, several sufficient conditions are proposed to guarantee the FTS and FTCS. In the framework of finite-time, two relationships between impulsive disturbance, aperiodic control periods, and aperiodic control widths are established to guarantee the FTS and FTCS for the system, respectively. Moreover, such two relationships can potentially increase the freedom of the designed control periods and control widths. Finally, two numerical simulations and a practical application are given to show the validity of the aperiodic intermittent controller.

Distributed time-varying formation optimal tracking for uncertain Euler–Lagrange systems with time-varying cost functions

This article studies the distributed formation optimal tracking problems for Euler–Lagrange systems, where each agent only has access to local cost function and other relative state information with its neighbors. Different from existing works, the effects of time-varying formation, parametric uncertainties, external disturbances and optimal performance of Euler–Lagrange systems are all considered simultaneously. Under the proposed distributed formation optimal tracking protocol, all agents are able to asymptotically track an optimal reference trajectory, while maintain the given time-varying formation. Firstly, a dynamic system is introduced for each agent to generate optimal reference signal, which uses only the individual's own state and the neighboring relative measurements with no extra exchange of virtual states needed. Then, an optimal tracking control strategy is proposed, with which zero optimum-tracking error can be achieved. Thirdly, sufficient conditions are given to guarantee that the agents' states asymptotically converge to the optimal solution in the desired formation under the proposed algorithm. At last, numerical simulation is designed to verify the strategies.

NLS Based Hierarchical Anti-Disturbance Controller for Vehicle Platoons With Time-Varying Parameter Uncertainties

Cooperative adaptive cruise control (CACC) is a promising technology for vehicle platoons to increase roadway capacity. This paper proposes a networked Lagrange system (NLS) based CACC dynamic model based on which a hierarchical anti-disturbance controller is developed to solve the stability problem of CACC in vehicle platoons with time-varying parameter uncertainties, external disturbances, and directional dynamic communication topology. First, a hierarchical anti-disturbance controller for NLS is constructed which comprises three layers, these are, the adaptive smooth estimator-control layer, the distributed classifying amplitude-related layer, and the anti-disturbance control layer, in which the parameter uncertainties are estimated in the adaptive smooth estimator-control layer, the disturbance classification and distribute control are executed in the distributed classifying amplitude-related layer and the anti-disturbance control layer respectively. In addition, the proposed controller is extended to address the stability problem of CACC in vehicle platoons with time-varying parameter uncertainties, external disturbances, and directional dynamic communication topology conditions, which shows the versatility of the controller. Finally, comparison studies and simulation results are provided to demonstrate the effectiveness, significance, and advantages of the presented controllers.

Finite-Time Neuro-Sliding-Mode Controller Design for Quadrotor UAVs Carrying Suspended Payload

Due to the quadrotor’s underactuated nature, suspended payload dynamics, parametric uncertainties, and external disturbances, designing a controller for tracking the desired trajectories for a quadrotor that carries a suspended payload is a challenging task. Furthermore, one of the most significant disadvantages of designing a controller for nonlinear systems is the infinite-time convergence to the desired trajectory. In this paper, a finite-time neuro-sliding mode controller (FTNSMC) for a quadrotor with a suspended payload that is subject to parametric uncertainties and external disturbances is designed. By constructing a finite-time sliding mode controller, the quadrotor can follow the reference trajectories in finite time. Furthermore, despite time-varying nonlinear dynamics, parametric uncertainties, and external disturbances, a neural network structure is added to the controller to effectively reduce chattering phenomena caused by high switching gains, and significantly reduce the size of the control signals. Following the completion of the controller design, the system’s stability is demonstrated using the Lyapunov stability criterion. Extensive numerical simulations with various scenarios are run to demonstrate the effectiveness of the proposed controller.

Stability analysis of discrete-time cyclic switched systems under improved cyclic switching regularity

The stability issue of discrete-time switched systems governed by cyclic switching laws is discussed in this paper. By establishing inverse-timer-based multiple Lyapunov functions (ITBMLFs), which are less conservative than traditional MLFs, limitations of the existing findings on discrete-time cyclic switched systems (DTCSSs) are well relaxed. Furthermore, from the perspective of computational complexity adjustment, the proposed ITBMLFs are confirmed to be more flexible than the previous ones, which is especially meaningful for the DTCSSs consisting of a large number of subsystems. Based on the cycle-dependent average dwell time (CD-ADT) concept and the ITBMLF approach, newly enhanced stability conditions are launched for DTCSSs where subsystems can be entirely or partially stable, or even completely unstable. Moreover, robust stability of DTCSSs can be achieved when norm-bounded and time-varying parameter uncertainties (NBTVPUs) are taken into account. Finally, the effectiveness and superiority of the proposed technologies are expounded through numerical examples.

Event-Triggered Neural Sliding Mode Guaranteed Performance Control

To solve the trajectory tracking control problem for a class of nonlinear systems with time-varying parameter uncertainties and unknown control directions, this paper proposed a neural sliding mode control strategy with prescribed performance against event-triggered disturbance. First, an enhanced finite-time prescribed performance function and a compensation term containing the Hyperbolic Tangent function are introduced to design a non-singular fast terminal sliding mode (NFTSM) surface to eliminate the singularity in the terminal sliding mode control and speed up the convergence in the balanced unit-loop neighborhood. This sliding surface guarantees arbitrarily small overshoot and fast convergence speed even when triggering mistakes. Meanwhile, we utilize the Nussbaum gain function to solve the problem of unknown control directions and unknown time-varying parameters and design a self-recurrent wavelet neural network (SRWNN) to handle the uncertainty terms in the system. In addition, we use a non-periodic relative threshold event-triggered mechanism to design a new trajectory tracking control law so that the conventional time-triggered mechanism has overcome a significant resource consumption problem. Finally, we proved that all the closed-loop signals are eventually uniformly bounded according to the stability analysis theory, and the Zeno phenomenon can be eliminated. The method in this paper has a better tracking effect and faster response and can obtain better control performance with lower control energy than the traditional NFTSM method, which is verified in inverted pendulum and ball and plate system.

Self-triggered adaptive model predictive control of constrained nonlinear systems: A min–max approach

In this paper, a self-triggered adaptive model predictive control (MPC) method is proposed for constrained discrete-time nonlinear systems subject to parametric uncertainties and additive disturbances. Firstly, a real-time zonotope-based set-membership parameter estimator is developed to refine a set-valued description of the time-varying parametric uncertainty based on the available measurements. By approximating the reachable sets for the states between two successive triggering time instants, the proposed estimator can be used for dynamic systems sampled in an aperiodic manner, including the self-triggered scheduling. We leverage this estimation scheme to design a novel self-triggered adaptive MPC (ST-AMPC) approach for uncertain nonlinear systems. Compared with the existing self-triggered robust MPC methods, the proposed ST-AMPC method can further reduce the average sampling frequency while preserving comparable closed-loop performance. We theoretically show that, under some reasonable assumptions, the proposed ST-AMPC algorithm is recursively feasible, and the closed-loop system is input-to-state practical stable (ISpS) at triggering time instants. Numerical experiments and comparisons are conducted to demonstrate the efficacy of the proposed method.

Performance improvement for large floating wind turbine by using a non‐linear pitch system based on neuro‐adaptive fault‐tolerant control

To stabilize the power out and reduce the dynamic loads in the over-rated state, the pitch system is key for regulating pitch angle to the desired one obtained from the command layer. Here, actuator failure of the pitch system is considered and a neural adaptive fault-tolerant control strategy with a rate function is proposed. More specifically, a non-linear model of the pitch system considering time-varying parameter uncertainties and unknown disturbances is established firstly. Then, the neural network is used to counteract the external disturbance and system uncertainty. The rate function with adjustable parameters is designed to transform the error, which makes the tracking error decrease at a fast rate and converge to a small zero domain, and realize the control goal of accurate and fast tracking the desired pitch angle of the pitch system. A co-simulation is developed, and the merits of the proposed method are verified.

Efficient simulation of clinical target response surfaces.

Simulation of combination therapies is challenging due to computational complexity. Either a simple model is used to simulate the response for many combinations of concentration to generate a response surface but parameter variability and uncertainty are neglected and the concentrations are constant—the link to the doses to be administered is difficult to make—or a population pharmacokinetic/pharmacodynamic model is used to predict the response to combination therapy in a clinical trial taking into account the time‐varying concentration profile, interindividual variability (IIV), and parameter uncertainty but simulations are limited to only a few selected doses. We devised new algorithms to efficiently search for the combination doses that achieve a predefined efficacy target while taking into account the IIV and parameter uncertainty. The result of this method is a response surface of confidence levels, indicating for all dose combinations the likelihood of reaching the specified efficacy target. We highlight the importance to simulate across a population rather than focus on an individual. Finally, we provide examples of potential applications, such as informing experimental design.

Robust dissipativity and passivity of stochastic Markovian switching CVNNs with partly unknown transition rates and probabilistic time-varying delay

&lt;abstract&gt;&lt;p&gt;This article addresses the robust dissipativity and passivity problems for a class of Markovian switching complex-valued neural networks with probabilistic time-varying delay and parameter uncertainties. The main objective of this article is to study the proposed problem from a new perspective, in which the relevant transition rate information is partially unknown and the considered delay is characterized by a series of random variables obeying bernoulli distribution. Moreover, the involved parameter uncertainties are considered to be mode-dependent and norm-bounded. Utilizing the generalized It$ \hat{o} $'s formula under the complex version, the stochastic analysis techniques and the robust analysis approach, the $ (M, N, W) $-dissipativity and passivity are ensured by means of complex matrix inequalities, which are mode-delay-dependent. Finally, two simulation examples are provided to verify the effectiveness of the proposed results.&lt;/p&gt;&lt;/abstract&gt;