Unknown Time-varying Parameters Research Articles

Synchronization of Bidirectionally Coupled Fractional-Order Chaotic Systems with Unknown Time-Varying Parameter Disturbance in Different Dimensions

In this article, the synchronization of bidirectionally coupled fractional-order chaotic systems with unknown time-varying parameter disturbance in different dimensions is investigated. The scale matrices are designed to address the problem of the synchronization for fractional-order chaotic systems across two different dimensions. Congelation of variables is used to deal with the unknown time-varying parameter disturbance. Based on Lyapunov’s stability theorem, the synchronization controllers in different dimensions are obtained. At the same time, adaptive laws of the unknown disturbance can be designed. Benefiting from the proposed methods, we verify all the synchronization errors can converge to zero as time approaches infinity, regardless of whether in n-D or m-D synchronization, simultaneously ensuring that both control and estimation signals are bounded. Finally, simulation studies based on fractional-order financial systems are carried out to validate the effectiveness of the proposed synchronization method.

Saturated adaptive control for high-order fully actuated systems with an extended state

ABSTRACT The present study focuses on controller design for high-order fully actuated systems that experience input saturation and are affected by bounded disturbances, such as nonlinear uncertainties and time-varying unknown parameters. A saturated adaptive controller is developed via the fully actuated system approach and the Lyapunov stability theory to achieve output control and reject disturbances. The disturbances are treated as an extended state and then estimated by introducing an extended state observer. An adaptive variable is used to handle the estimation error between the actual and estimated values of the disturbances. An auxiliary system is designed to mitigate the saturation effect. Lyapunov's direct method verifies that the estimation error, the tracking error, the adaptive state, and the auxiliary system state will eventually stabilise within a bounded ellipsoid. An illustration of spacecraft attitude control demonstrates the effectiveness of the proposed controller.

An adaptive internal model control approach for unmanned surface vehicle based on bidirectional long short-term memory neural network: Implementation and field testing

This paper investigates a practical adaptive internal model control (IMC) for an unmanned surface vehicle (USV) with unknown time-varying nonlinear model parameters and environmental disturbances. Firstly, an internal model of the USV is presented using the Bidirectional Long Short-Term Memory (BiLSTM) neural network. Then, an adaptive neural IMC controller is designed for the trajectory tracking of USV by using the IMC method. The internal model and the controller are updated by an error threshold algorithm. The proposed control scheme comprises of a trajectory guidance module via the Line-of-Sight (LOS) guidance method and a tracking control module designed by IMC theory. Under the proposed control scheme, the development processes of the vehicle platform and the control algorithms are described, and accurate tracking control can be achieved. Finally, the results of simulation and field experiments are presented and discussed to validate the effectiveness of the proposed control scheme.

A Multifilters Approach to Adaptive Event-Triggered Control of Uncertain Nonlinear Systems With Global Output Constraint.

This article focuses on the problem of adaptive event-triggered output feedback control for a class of uncertain nonlinear systems under the output constraint. Different from the existing works, the time-varying parameters and the global output constraint are taken into account. First, by means of multifilters, the unmeasurable state variables are reconstructed, under which the unknown time-varying parameters and sensor sensitivity are transformed into the estimation problem of unknown parameters. Second, based on a barrier function, a novel constraint algorithm is established to make the output enter into asymmetric time-varying constraint boundaries, which is independent of the initial value of the output. To avoid continuous sampling of the controller, an event-triggered mechanism is proposed without the Zeno phenomenon. By means of the Lyapunov stability theory, it is strictly proved that the output enters into the pregiven asymmetric constraint boundaries, and never exceeds. Finally, the validity of our proposed control algorithm is illustrated by a numerical simulation.

Adaptive Exponential Convergence State-Constrained Control for Interconnected Nonlinear Systems With Time-Varying Unknown Parameters

Adaptive Exponential Convergence State-Constrained Control for Interconnected Nonlinear Systems With Time-Varying Unknown Parameters

Global asymptotic fault-tolerant tracking for time-varying nonlinear complex systems with prescribed performance

This paper investigates the global adaptive asymptotic fault-tolerant control of time-varying complex nonlinear systems with prescribed performance. The considered system simultaneously involves both mismatched intrinsic unknown time-varying parameters and nonvanishing external disturbances as well as possible actuator faults, which make the underlying problem challenging. By introducing a special kind of funnel functions, together with fusing a barrier Lyapunov function technique and a bound estimation approach, a novel prescribed performance fault-tolerant control scheme is proposed, which, as compared with the existing results, exhibits the following appealing features: (1) it is capable of dealing with nonlinear systems with high relative degree and serious unmatched time-varying uncertainties; (2) it can guarantee a global prescribed transient performance such that the performance specifications in terms of settling time and the tracking accuracy can be off-line preassigned according to task requirements, without dependence on initial conditions and any design parameters; (3) it can realize asymptotic output tracking, where no knowledge about the high-order derivatives of the reference trajectory is required. In the end, a simulation example is provided to attest the efficiency of the designed scheme.

Adaptive backstepping fault-tolerant control for hypersonic aircraft with unknown control direction under actuator and sensor faults

Abstract In this paper, an adaptive backstepping controller of hypersonic flight vehicle (HFV) system is investigated in the presence of unknown actuator and sensor faults, unknown control direction and varying external disturbance, which expands traditional fault-tolerant control (FTC) approaches in HFV field. The control-oriented model is established with reasonable and comprehensive analysis of various fault types. Compared with the previous FTC research on HFV system, the time-varying and fixed fault types are simultaneously designed for actuator and sensors, and the control direction is unknown, which can more accurately simulate the real fault situations in the hypersonic flight environment. To avoid singularity problems caused by the unknown control direction, the Nussbaum gain function technique is adopted in the control algorithm, which is also capable of overcoming the influence of unknown time-varying fault parameters. The boundness and stability of system under the designed control scheme are theoretically verified. Finally, numerical simulation results demonstrate the effectiveness and superiority of the proposed control strategy.

Event-triggered adaptive prescribed performance tracking for nonlinear time-varying systems with unknown control directions

This article deals with the adaptive prescribed performance tracking for nonlinear time-varying systems. To handle multiple unknown control directions, a novel lemma is established by using a general class of Nussbaum functions. To handle unknown time-varying parameters, the congelation of variables method is employed. Different novel functions are introduced to achieve prescribed performance tracking and finite-time prescribed performance tracking, respectively. Meanwhile, the problem of explosion of complexity is avoided by utilizing the command filter and the compensation mechanism. For reasons of saving network resources and reducing communication burden, a new event-triggered mechanism is proposed, which can circumvent the Zeno behavior. Then, an event-triggered adaptive prescribed performance tracking control scheme is constructed and is extended to event-triggered finite-time adaptive prescribed performance tracking, both of which guarantee that all closed-loop signals are bounded and the trajectory of the tracking error can be limited to the prescribed region. Finally, the availability of the control scheme is demonstrated by two examples.

Non-uniform Trajectory Tracking AILC for Nonlinear Time-varying Parameter System with Multiple Unknown Control Directions

In this paper, a new iterative learning controller is presented for nonlinear time-varying parameter system to solve the tracking problem of different target trajectories. Based on Nussbaum function and the Lyapunov-like synthesis design the learning controller to handle system dynamics with multi-unknown control directions. Over a finite time interval, the unknown time-varying parameter is considered to be periodic, so it is expanded using a Fourier series expansion, and the remaining terms are treated with a canonical series. The controller designed in this paper can ensure that all signals of the closed-loop system are bounded in a finite time interval [0,T], and can complete non-uniform target tracking. Finally, a simulation example is given to verify the effectiveness of the designed controller.

Adaptive Control of Quadrotor Unmanned Aerial Vehicle With Time-Varying Uncertainties

This paper studies the real-time parameter estimation and adaptive tracking control problem for a six degrees of freedom (6-DOF) of quadrotor unmanned aerial vehicle (UAV) as an under-actuated system. A virtual proportional derivative (PD) is proposed to maintain position dynamics. Two adaptive control schemes are designed and compared to maintain the attitude dynamics of UAV while several parameters of UAV are unknown. In the first scheme, a classical adaptive scheme using the certainty equivalence principle is extended and designed for tracing control of the systems with unknown time-varying parameters. To improve the performance of the first scheme, a new control scheme is designed in the second scheme by proposing additional continuous function to handle the unknown parameters. An additional robust term is designed in both schemes to handle the perturbation caused by unknown time-varying parameters. The rigorous analytical proof and numerical simulation analysis are provided to support the efficacy of the proposed controller.

Adaptive observer for a nonlinear system with partially unknown state matrix and delayed measurements

Problem of an adaptive state observer design for nonlinear system with unknown time-varying parameters and under condition of delayed measurements is considered. State observation problem was raised by many researchers (see for example Sanx et al. (2019)). In this paper the results proposed in Bobtsov et al. (2021b), Bobtsov et al. (2021a), Bobtsov et al. (2022a), Bobtsov et al. (2022b) are developed. The problem is solved under assumption that the state matrix can be represented as sum of known and unknown parts. The output vector is measured with a known constant delay. An adaptive observer which reconstructs unmeasured state and unknown time-varying parameter is proposed.

Distributed Containment Control for Human-in-the-Loop MASs With Unknown Time-Varying Parameters

This paper considers the distributed containment control problem for human-in-the-loop (HiTL) multiagent systems (MASs) subject to unknown time-varying parameters and input saturation. A smooth function containing positive integrable time-varying function is embedded in the controller to compensate for the negative effects of unknown time-varying parameters and uncertain disturbances. Meanwhile, an auxiliary system with the same order as the considered system is skillfully introduced into the backstepping control method to overcome the problem of input saturation. By constructing an adaptive command filter with error compensation mechanism, the problems of the computation burden and filtering errors are solved simultaneously. Moreover, the output signals of followers can converge into the convex hull spanned by multiple dynamic leaders which are controlled by a human operator. Based on the Lyapunov stability theory, it is shown that the containment errors can asymptotically converge into the prescribed bounds. Finally, two simulation examples evaluate the effectiveness of the presented control scheme.

An adaptive observer for uncertain linear time-varying systems with unknown additive perturbations

In this paper we are interested in the problem of adaptive state observation of linear time-varying (LTV) systems where the system and the input matrices depend on unknown time-varying parameters. It is assumed that these parameters satisfy some known LTV dynamics, but with unknown initial conditions. Moreover, the state equation is perturbed by an additive signal generated from an exosystem with uncertain constant parameters. Our main contribution is to propose a globally convergent state observer that requires only a weak excitation assumption on the system, which is satisfied in the present context of regulation.

Adaptive Time-Varying Parameter Estimation via Weak Measurement

Extending quantum sensing to time-varying parameter estimation is a potential and challenging task in practical application. To achieve this goal, we propose an adaptive method to estimate an unknown time-varying parameter through light-intensity split detection and the insertion of reference phases in the weak measurement. Theoretical analysis and numerical simulation are applied to illustrate the feasibility and practical applications of our method. The results demonstrate that the method has adjustable sensitivity and linear dynamic range, and is robust to nonideal measurement conditions. Moreover, we analyze the precision of our method and show that its precision limit can surpass the standard quantum limit and approach the Heisenberg scaling when using a squeezed light of optimal Gaussian state.

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.

Adaptive Control with Switched Reference Models: Application to Learn-to-Fly

Learn-to-Fly (L2F) is a new framework that aims to replace the traditional iterative development paradigm for aerial vehicles with a combination of real-time aerodynamic modeling, guidance, and learning control. To ensure safe learning of the vehicle dynamics on the fly, this paper presents an adaptive control ()-based scheme, which actively estimates and compensates for the discrepancy between the intermediately learned dynamics and the actual dynamics. First, to incorporate the periodic update of the learned model within the L2F framework, this paper extends the architecture to handle a switched reference system subject to unknown time-varying parameters and disturbances. The paper also includes analysis of both transient and steady-state performance of the architecture in the presence of nonzero initialization error for the state predictor. Second, the paper presents how the proposed scheme is integrated into the L2F framework, including its interaction with the baseline controller and the real-time modeling module. Finally, flight tests on an unmanned aerial vehicle validate the efficacy of the proposed control and learning scheme.

Adaptive fuzzy finite‐time fault‐tolerant control design for non‐linear systems under sensor faults

In this article, an adaptive fuzzy finite-time fault-tolerant control (FTC) scheme for uncertain non-linear systems under sensor faults is proposed. Compared with the existing methods, the considered system contains unknown time-varying fault parameters, uncertain non-linear functions, and can guarantee the performance of the system in finite time. The coupling between fault parameters and actual states is solved by the fault parameters separation method. The fuzzy logic system (FLS) is used to approximate the unknown functions, and combining the backstepping technology an adaptive fault-tolerant controller is designed. The finite-time stability of the closed-loop system is proved by the Lyapunov theory. At last, the numerical simulation and the real physical system simulation verified the effectiveness of the proposed scheme.

Command Filter Adaptive Asymptotic Tracking of Uncertain Nonlinear Systems With Time-Varying Parameters and Disturbances

This article is devoted to the adaptive asymptotic tracking for a class of uncertain nonlinear systems. The presence of unknown time-varying parameters and uncertain disturbances makes the systems in question essentially different from those in the related works. By skillfully combining adaptive technique and command filter-based backstepping, a novel command filter adaptive tracking controller is successfully designed to achieve asymptotic tracking. The typical feature of the proposed controller lies in the introduction of a smooth function with positive integrable time-varying function, which makes the controller powerful enough to compensate the unknown time-varying parameters and uncertain disturbances. Remarkably, a novel Lyapunov function by incorporating the lower bounds of control gains is used to prove the stability of the closed-loop system. Compared with some existing command filter-based backstepping, the conditions on the virtual control coefficients and disturbances are relaxed. Finally, the effectiveness of the proposed method is shown by a simulation example.

Global stabilisation of nonlinear systems with unknown time-varying delay and measurement uncertainty

ABSTRACT Based on a new constructive solution of a couple of matrix inequalities containing an unknown time-varying parameter, this paper proposes a novel dual-gain scaling approach including a dynamic-gain observer and an output feedback controller with static and dynamic gains. In particular, our control approach is applicable to a class of nonlinear time-delay systems with nonlinear growth constraint and large unknown measurement sensitivity that may be non-differentiable. With the help of the Razuminkhin theorem, it is shown that the global adaptive stability of the resulting closed-loop system is achieved and our controller is robust to arbitrary bounded time-varying delay. In addition, the control approach proposed is non-backstepping and has low computing complexity.

Adaptive control for full-states constrained nonlinear systems with unknown control direction using Barrier Lyapunov Functionals

In this paper, a new adaptive back-stepping (BS) control technique based on barrier Lyapunov functions (BLFs) is proposed to manage a class of full-state constrained nonlinear systems subject to totally unknown directions and uncertain time-varying parameters. BLFs guarantee that all the system states are constrained in a predefined compact set and the tracking error can converge to a small zero neighborhood. Nussbaum’s gain technique is utilized to tackle the unknown control direction issue. Besides, a sufficiently smooth projection algorithm is adopted to estimate the unknown time-varying parameters, so as to ensure that the adaption laws are differentiable and bounded. The developed controller not only makes all the system states restrained in the compact set but also assures the smoothness and boundedness of all the signals of the closed-loop system. In addition, the sufficiently smooth projection algorithm and Nussbaum gain technique are combined with the BLF-BS control method for the nonlinear systems. Finally, the simulation example results verify the effectiveness and feasibility of the proposed control scheme.