Time-varying Scaling Research Articles

Adaptive practical prescribed-time control for uncertain nonlinear systems with time-varying parameters

In this paper, adaptive practical prescribed-time (PPT) control is proposed for a class of uncertain nonlinear systems with time-varying parameters and unmodeled dynamics. By constructing a novel time-varying scaling function and utilizing nonlinear mapping, the PPT control is successfully resolved. The dynamical uncertainties resulting from unmodeled dynamics are estimated by employing an auxiliary available signal, and the unknown continuous terms are handled by the aid of radial basis function neural networks (RBFNNs). A novel adaptive control method is developed by introducing the compensating signals and dynamic surface control as well as practical prescribed-time control. All the signals involved are proved to be semi-globally uniformly ultimately bounded, and the tracking error could enter the pre-specified convergence region within a pre-specified time. The robotic manipulator system is used to demonstrate the effectiveness of the proposed control approach.

A Novel Event-triggered Practical Prescribed-Time Control for four Complex coupled Duffing-type MEMS resonators with Prescribed Performance

This paper explores the dynamic characteristics and a novel event-triggered practical prescribed-time controller for four complex coupled Duffing-type MEMS resonators. Initially, the effects of mechanical coupling stiffness, electrostatic coupling stiffness, and internal system parameters on the system's dynamic behavior are examined. The analysis results provide guidance for selecting system parameters. Furthermore, the dynamic analysis reveals that chaotic oscillations may occur in the system without input, significantly affecting system performance. To mitigate these chaotic oscillations, a novel event-triggered practical prescribed-time controller with prescribed performance is proposed, utilizing interval type-3 fuzzy system (IT3FS) to estimate unknown nonlinear functions. By employing a more relaxed practical prescribed-time stability (PPTS) criterion and a novel time-varying scale transformation function (STF), the designed controller ensures that all signals converge within a prescribed time. Additionally, a prescribed performance function (PPF) is employed, allowing for more flexible convergence boundary settings. A dynamic event-triggered mechanism is implemented to reduce the frequency of control signal updates. The stability analysis demonstrates that all signals converge within a prescribed time, and the tracking errors remain within their prescribed boundary. Finally, simulations validate the effectiveness of the proposed scheme.

Enhancing prescribed-time trajectory tracking control for a stratospheric airship with prescribed performance

This paper studies the tracking control problem for stratospheric airships with user-specified performance. Dealing with the infinite gain phenomenon in the prescribed-time stability, a new stability criterion with bounded gain is proposed by using a new time-varying scaling function. Moreover, a same-side performance function and a novel barrier Lyapunov function are incorporated into the control algorithm, which can compress the feasible domain of tracking error to minimize the overshoot and solve the difficult in tracking error not converging to zero simultaneously. The proposed scheme guarantees the airship capable of operating autonomously with satisfactory transient performance and tracking accuracy, where the performance parameters can be designed artificially and link to the physical process directly. Finally, the effectiveness of the proposed control scheme is verified by theoretical analysis and numerical simulation.

Neural Network-Based Fixed-Time Tracking and Containment Control of Second-Order Heterogeneous Nonlinear Multiagent Systems.

This study concentrates on the fixed-time tracking consensus and containment control of second-order heterogeneous nonlinear multiagent systems (MASs) with and without measurable velocity under directed topology. By defining a time-varying scaling function and approximating the unknown nonlinear dynamics with radial basis function neural networks (RBFNNs), a novel distributed protocol for solving the fixed-time tracking consensus and containment control problems of second-order heterogeneous nonlinear MASs with full states available is proposed based on a nonsingular sliding-mode control method constructed by designing a prescribed-time convergent sliding surface. For the scenario of immeasurable velocity, a fixed-time convergent states' observer is designed to reveal the velocity information when the unknown linearity is bounded. Subsequently, a distributed fixed-time consensus protocol based on observed velocity information is proposed for the extended results. Ultimately, the acquired results are verified by three simulation examples.

State-feedback control for full-state constrained nonlinear systems in a prescribed time

This study focuses on the unresolved control problems pertaining to full-state constrained nonlinear systems within a prescribed time. Initially, two Lyapunov theorems are established using a time-varying scaling function. These theorems facilitate the achievement of prescribed-time stability while ensuring that constraints are not violated. Building upon these theorems and incorporating completely known nonlinear terms, a state-feedback controller is developed and analyzed by employing an asymmetric barrier Lyapunov function (BLF). The analysis demonstrates that the resulting controller enables the tracking error to converge to the origin within a prescribed time while subsequently maintaining it at the origin without violating any constraints. Additionally, as an extension of the proposed prescribed-time control approach, the adaptive control problem for parameterized constrained nonlinear systems is addressed. The designed adaptive controller ensures boundedness of all signals, maintains the states within the specified constraints, and achieves convergence of the tracking error to the origin within an arbitrarily prescribed time. Finally, simulation examples are presented to validate the effectiveness of the proposed control scheme.

Fuzzy prescribed-time self-triggered consensus control for nonlinear multi-agent systems with dead-zone output

This paper investigates the fuzzy prescribed-time self-triggered consensus control for nonlinear multi-agent systems (MASs) with dead-zone output. First, by proposing a dead-zone output approximation model and utilizing Nussbaum-type functions, an adaptive compensation mechanism is developed to alleviate the effect of unknown dead-zone output. Meanwhile, the fuzzy logic systems are incorporated to approximate the unknown functions of the nonlinear MASs. Next, by adopting a time-varying scaling function, a consensus control method is recursively established to steer the consensus errors into a small range within the prescribed time. Furthermore, a self-triggered scheme is established to conserve communication resources while avoiding continuously monitoring trigger conditions. It is illustrated that boundedness of all signals and practical prescribed-time leader-following consensus can be achieved. Finally, the simulation results show the effectiveness of the proposed method.

Adaptive fault-tolerant control for ascent HSV with wing damage and function constraints on states

In this article, a fault-tolerant tracking control technique is developed for the ascent of hypersonic vehicles (HSV) experiencing wing damage and time-varying state constraints. The difficulty of control problem lies in handling state constraints associated with both state and time, while determining the unknown control directions of the multi-input multi-output (MIMO) nonlinear system. The presence of constraints in both state and time complicates the design of the control algorithm. This paper proposes the construction of a novel state transition function to establish a new unconstrained system, thereby eliminating the conservative feasibility conditions of Barrier Lyapunov Function (BLF) and integral BLF methods when dealing with time-varying constraints. The fusion of time-varying scaling functions and Nussbaum-type functions not only resolves the issue of unknown control directions in the MIMO nonlinear system but also enhances the transient and steady-state performance of the closed-loop system. Neural Networks are employed to approximate the unknown nonlinear functions. Using Lyapunov stability theory, it is proven that state constraints are not violated, and all signals in the closed-loop system are bounded. Simulation results demonstrate the merits of the designed fault-tolerant control (FTC) algorithm.

A scaling-based model to describe temporal variability in soil hydraulic properties

Accurate knowledge of temporal variability in soil hydraulic properties (SHPs) can improve the prediction capability of flow and transport models. Lab and field measurements for determining SHPs at multiple timescales are expensive and time-consuming. Further, the existing Fokker-Plank equation (FPE) based numerical and analytical models for describing temporal variation in SHPs require parameterization. In this study, a scaling model is proposed to describe temporal variation in SHPs of four different soils. As field studies related to temporal variation in SHPs are limited, first synthetic temporally varying SHPs, soil water characteristic curves and hydraulic conductivity curves are generated using the analytical solution of FPE. Functional normalization approach is then used to develop reference curves and to obtain scale factors at different time-steps. The time-varying scale factors and the initial SHPs are related by two-step regression equations. The reference curves and the regression equations together can be used to estimate SHPs at any time given the initial SHPs. The developed model is validated using a 5-fold cross validation method and with experimental data at two study sites. The average percentage error in predicted van Genuchten parameters (θs,n and Ksat) except for α are mostly less than 10 %. The performance of the proposed model is comparable to that of FPE analytical model for experimental data. The proposed method holds promise for describing temporal variation in SHPs using only the initial SHPs.

Global Prescribed Performance Control for Strict Feedback Systems Pursuing Uncertain Target.

In this work, an online solution for reconstructing and predicting the uncertain target trajectory in real-time is proposed based on general regression neural network (GRNN). On this basis, an adaptive tracking control scheme guaranteeing prescribed performance is suggested for a class of strict-feedback systems with unknown control directions. In contrast to existing trajectory reconstruction methods, the one presented in this note does not require prior modeling of the uncertain target or offline training. Contrary to most current state-of-the-art prescribed performance control (PPC) technology, a novel time-varying scaling function and its corresponding translation function are introduced such that no strict constraints on initial conditions are needed, that is, global stability is achieved. The proposed control scheme allows the output of the system to chase the predicted value of the uncertain target, and the tracking error converges to a prescribed small set within a preassigned time, despite unmatched uncertainties and unknown control directions. The benefits of the proposed control scheme are confirmed by numerical simulations.

Observation-driven filtering of time-varying parameters using moment conditions

We develop a new and flexible semi-parametric approach for time-varying parameter models when the true dynamics are unknown. The time-varying parameters are estimated using a recursive updating scheme that is driven by the influence function of a conditional moments-based criterion. We show that the updates ensure local improvements of the conditional criterion function in expectation. The dynamics are observation driven, which yields a computationally efficient methodology that does not require advanced simulation techniques for estimation. We illustrate the new approach using both simulated and real empirical data and derive new, robust filters for time-varying scales based on characteristic functions.

Prescribed-Time Fractional Order Control of DWR via Time-Varying Scaling Function

This study focuses on a differential wheeled robot’s (DWR) prescribed-time fractional order position control. Firstly, based on the kinematic model of DWR, a distance-related orientation error is designed using the inverse sine function. Based on this, an improved linear velocity constraint function is proposed. Compared with existing methods, while ensuring the correlation between velocity and orientation error, the multibalance point risk caused by large angle errors is avoided. Then, a prescribed-time fractional order position controller based on a time-varying scaling function is proposed to stabilize the kinematic system of DWR in the prescribed time. This controller can stabilize the position control system of the DWR in a prescribed time by adjusting the prescribed-time parameter, avoiding the infinite gain risk in traditional prescribed-time controllers. Finally, through numerical simulation, we verify that the proposed control law can converge the system status of DWR to the bounded interval in the prescribed time.

Neuroadaptive tracking control of uncertain nonlinear systems with spatiotemporal constraints

This study investigates the neuroadaptive tracking control problem for a class of strict-feedback nonlinear systems with spatiotemporal constraints. An adaptive neural network-based control system is developed to alleviate the effects of modeling uncertainties and external disturbances. In particular, the proposed method ensures that the system tracking error has a predefined performance boundary (spatial constraint). Moreover, using a novel time-scale transformation method, uncertain nonlinear systems can achieve a prescribed finite-time convergence to a time-varying scaling function in the pointing position (temporal constraint). Finally, the efficiency of the proposed method is verified with two simulation examples.

A varying-parameter fixed-time gradient-based dynamic network for convex optimization

We focus on the fixed-time convergence and robustness of gradient-based dynamic networks for solving convex optimization. Most of the existing gradient-based dynamic networks with fixed-time convergence have limited ability to resist interferences of noises. To improve the convergence of the gradient-based dynamic networks, we design a new activation function and propose a gradient-based dynamic network with fixed-time convergence. The proposed dynamic network has a smaller upper bound of the convergence time than the existing dynamic networks with fixed-time convergence. A time-varying scaling parameter is employed to speed up the convergence. Our gradient-based dynamic network is proved to be robust against bounded noises and is able to resist the interference of unbounded noises. The numerical tests illustrate the effectiveness and superiority of the proposed network.

Energy consumption prediction and optimization of industrial robots based on LSTM

Due to wide distribution and low energy efficiency, the energy-saving of industrial robots draws more and more attention, and a large number of methods have emerged to predict or optimize the energy consumption (EC) of robots. However, many dynamic and electrical parameters are unavailable due to the commercial limitations of industrial robots, which constrains the application of those model-based methods. Therefore, this paper proposes a data-driven method for the prediction and optimization of robot EC. Initially, the cause-and-effect relationship between robot EC and joint motion variables, such as the joint position, velocity, and acceleration, is qualitatively analyzed based on the influence of the capacitive and inductive components in the drive system. And a deep neural network based on long short-term memory (LSTM) is proposed to reveal the nonlinear mapping between the industrial robot EC and the joint motion variables, which can predict EC without the parameters of the industrial robot. Based on the proposed neural network, the adaptive genetic algorithm is adopted to optimize the time-variant scaling function, which can optimize the scaled trajectory to reduce EC without hardware modification. To validate the accuracy and efficacy of the proposed method, experiments are conducted on a KUKA KR60-3 six degree-of-freedom (DOF) industrial robot. The results demonstrate that the proposed neural network can predict EC with a mean absolute percentage error less than 4.21% and the proposed method reduces the EC by 22.35%.

Prescribed-time containment control of high-order nonlinear multi-agent systems based on distributed observer

This paper investigates the prescribed-time containment control problem for multi-agent systems with high-order nonlinear dynamics under a directed communication topology. Firstly, in view of the fact that only some follower agents can directly access the state information of multiple leader agents, a prescribed-time distributed observer is put forward to estimate the convex hull spanned by these leaders. Then, with the help of the distributed observer, a novel containment control method is developed for each follower based on a time-varying scaling function, so that all followers can converge to the convex hull spanned by the states of multiple leaders within a prescribed time. The comparison with the finite-time and fixed-time control methods differs in that the convergence time of the method proposed in this paper is independent of the initial conditions and control parameters and can be arbitrarily preassigned according to actual needs. Finally, an example is given to demonstrate the usefulness of the prescribed-time containment control method.

Heating up Peccei-Quinn scale

We discuss production of QCD axion dark matter in a novel scenario, which assumes time-varying scale of Peccei-Quinn symmetry breaking. The latter decreases as the Universe's temperature at early times and eventually stabilises at a large constant value. Such behavior is caused by the portal interaction between the complex field carrying Peccei-Quinn charge and a Higgs-like scalar, which is in thermal equilibrium with primordial plasma. In this scenario, axions are efficiently produced during the parametric resonance decay of thecomplex Peccei-Quinn field, relaxing to the minimum of its potential in the radiation-dominated stage. Notably, this process is not affected by the Universe's expansion rate and allows to generate the required abundance of dark matter independently of an axion mass. Phenomenological constraints on the model parameter space dependon the number density of radial field fluctuations, which are also generically excited along with axions, and the rate of their thermalization in the primordial plasma.For the ratio of radial field and axion particles number densities larger than ∼ 0.01 at the end of parametric resonance decay, the combination of cosmological and astrophysical observations with the CAST limit confinesthe Peccei-Quinn scale to a narrow range of values ∼ 108 GeV, —this paves the way for ruling out our scenario with the near future searches for axions.

Application of an Intensive Longitudinal Functional Model with Multiple Time Scales in Objectively Measured Children’s Physical Activity

This study proposes an intensive longitudinal functional model with multiple time-varying scales and subject-specific random intercepts through mixed model equivalence that includes multiple functional predictors, one or more scalar covariates, and one or more scalar covariates. An estimation framework is proposed for estimating a time-varying coefficient function that is modeled as a linear combination of time-invariant functions with time-varying coefficients. The model takes advantage of the information structure of the penalty, while the estimation procedure utilizes the equivalence between penalized least squares estimation and linear mixed models. A number of simulations are conducted in order to empirically evaluate the process. In the simulation, it was observed that mean square errors for functional coefficients decreased with increasing sample size and level of association. Additionally, sample size had a greater impact on a smaller level of association, and level of association also had a greater impact on a smaller sample size. These results provide empirical evidence that ILFMM estimates of functional coefficients are close to the true functional estimate (basically unchanged). In addition, the results indicated that the AIC could be used to guide the choice of ridge weights. Moreover, when ridge weight ratios were sufficiently large, there was minimal impact on estimation performance. Studying two time scales is important in a wide range of fields, including physics, chemistry, biology, engineering, economics, and more. It allows researchers to gain a better understanding of complex systems and processes that operate over different time frames. Consequently, studying physical activities with two time scales is critical for advancing our understanding of human performance and health and for developing effective strategies to optimize physical activity and exercise programs. Therefore, the proposed model was applied to analyze the physical activity data from the Active Schools Institute of the University of Northern Colorado to determine what kind of time-structure patterns of activities could adequately describe the relationship between daily total magnitude and kids’ daily and weekly physical activity.

Distributed Fixed-Time Tracking and Containment Control for Second-Order Multi-Agent Systems: A Nonsingular Sliding-Mode Control Approach

This paper focuses on distributed fixed-time tracking consensus and containment control problems of second-order multi-agent systems (MASs) with directed topology. To make the offline design and convergence time estimation of the consensus protocol for second-order MASs possible, a novel nonsingular sliding-mode control method is established by introducing a time-varying scaling function in the design of the sliding surface. Subsequently, sufficient conditions ensuring fixed-time tracking consensus and containment control of the second-order MASs are obtained by using the proposed nonsingular sliding-mode control method. The results show that the estimated convergence time of considered MASs is independent of the initial values and other parameters of the system, where the convergence time on the sliding surface can be prescribed. Ultimately, two numerical examples are illustrated to verify the validity of the obtained results.

Adaptive Uniform Performance Control of Strict-Feedback Nonlinear Systems With Time-Varying Control Gain

In this paper, we present a novel adaptive performance control approach for strict-feedback nonparametric systems with unknown time-varying control coefficients, which mainly includes the following steps. Firstly, by introducing several key transformation functions and selecting the initial value of the time-varying scaling function, the symmetric prescribed performance with global and semi-global properties can be handled uniformly, without the need for control re-design. Secondly, to handle the problem of unknown time-varying control coefficient with an unknown sign, we propose an enhanced Nussbaum function (ENF) bearing some unique properties and characteristics, with which the complex stability analysis based on specific Nussbaum functions as commonly used is no longer required. Thirdly, by utilizing the core-function information technique, the non-parametric uncertainties in the system are gracefully handled so that no approximator is required. Furthermore, simulation results verify the effectiveness and benefits of the approach.

Adaptive fault-tolerant control for the ascent phase of hypersonic vehicle with time-varying full state constraints

In this paper, a novel attitude adaptive fault-tolerant control (FTC) scheme is presented for the ascent phase of hypersonic vehicle (HSV) subject to pneumatic-propulsion coupling and time-varying full state constraints, which are unique to the ascent phase of HSV and are caused by the integrated design of fuselage engine and power system switching. Compared with some existing methods for time-varying constraints, the proposed control method contains a constrained function so that constraints can be incorporated directly into the state, which asymmetric and time-varying state constraints can be handled without feasibility conditions. Moreover, by designing a time-varying scaling function matrix to transform the tracking error, the proposed method enables the practical tracking control to be achieved without any switching for a multi-input multi-output (MIMO) pure-feedback system which is transformed from the ascent phase model of HSV. Besides, to incorporate constraints into the state, an adaptive fault estimation filter is designed to estimate unknown faults and disturbances. It is proved that the proposed FTC scheme can guarantee that the closed-loop control system is stable and the time-varying state constraints are satisfied. Finally, simulation results are provided to illustrate the effectiveness of the proposed FTC scheme.