Time Base Generator Research Articles

Estimator-based multi-target tracking of networked robotic systems via predefined-time hierarchical control method

In this paper, we study the multi-target tracking problem of networked robotic systems (NRSs) within predefined time under a directed interaction topology considering disturbances and physical parameter uncertainties. On the basis of non-singular sliding-mode surface, a new predefined-time estimator-based hierarchical control algorithm is put forward so as to address the tracking problem under the case of multiple moving targets. Using the time base generator (TBG), a distributed estimator algorithm is designed to ensure that the followers can estimate different target states within a predefined-time. Certain sufficient conditions of predefined-time multi-target tracking of NRSs are presented using the Lyapunov stability and neighbor information interaction principle. In the end, numerical simulation experiments are offered to indicate the availability and correctness of the theoretical results.

Multiobjective Distributed Optimization via a Predefined-Time Multiagent Approach

In this study, we propose a predefined-time multi-agent approach for multi-objective optimization. Predefined-time optimization is an optimization approach that can converge to a state that is extremely close to an optimal solution at a given time. A time-base generator is derived and applied to the optimization approaches for achieving predefined-time optimization. The multi-objective optimization problem is reformulated as a distributed optimization problem and thus solved in a private and safe manner. For distributed optimization, a multi-agent system (MAS) with time-base generators is developed for predefined-time optimization, and its convergence and speed are proven. Several examples confirm the validity of the results.

Practical time-boundary consensus for fractional-order multi-agent systems under well-known and estimable topology

A framework for multi-agent systems with single-integrator dynamics to achieve practical fixed-time consensus has been developed under a well-known topology. However, the disagreement boundary in which is influenced by the initial values of the system. To avoid this, a practical time-boundary (PTB) consensus framework using a novel time-boundary-base generator (TBBG) is proposed in this paper, and it is extended to fractional-order multi-agent systems and estimable topology. A significant fractional differential equation is solved as the theoretical basis to achieve PTB consensus. Evolving from the time-base generator, this novel TBBG inherits the benefit of reducing the initial control input and saves energy consumption by optimizing four newly added adjustable parameters compared to the existing work. Additionally, outcomes are extended to quasi-PTB consensus and PTB-cluster consensus. The effectiveness and superiorities of the proposed approach are illustrated by two numerical examples.

Fully Distributed, Event-Triggered Containment Control of Multi-Agent Systems Based on Wireless Sensor Networks and Time Base Generators

In this study, wireless sensor networks and time base generators are used to solve the fixed-time containment control problem in multi-agent systems with fixed topologies. A new event-triggered control protocol is proposed, which combines a fully distributed method and a time base generator (TBG). The goal is to converge the states of all followers to the convex hull formed by the leader. The controller reduces communication and improves control efficiency by integrating a fully distributed control mechanism using wireless sensor networks. In addition, a time base generator (TBG) is added to ensure that the dwell time continues to be pre-specified and independent of initial conditions. Using matrix theory, the original system is transformed into an error system, and its stability is analyzed by the Lyapunov method. The necessary and sufficient conditions for solving the time consensus containment control problem in multi-agent systems are determined and Zeno behavior is avoided. The effectiveness of the proposed control algorithm is illustrated by numerical examples.

Predefined-Time Distributed Nash Equilibrium Seeking for Noncooperative Games With Event-Triggered Communication

In this paper, we investigate a predefined-time distributed Nash equilibrium seeking problem for a class of noncooperative games under an event-triggered scenario. To achieve fast convergence while reducing the communication and computation costs, a novel distributed Nash equilibrium seeking approach is proposed by applying the gradient play, a consensus-based estimator, and a time base generator (TBG). Different from existing works on Nash equilibrium computation under a bounded convergence time, the design of distributed algorithm in this paper is based on a newly developed TBG. The new TBG is more efficient and convenient than the traditional TBG. By virtue of an adaptive event-triggered rule, the distributed estimators are designed to estimate other players’ actions over strongly connected directed graphs. Moreover, the predefined-time convergence analysis of the players’ actions to the Nash equilibrium is given based on the Lyapunov stability method. Finally, simulation studies are provided to demonstrate the effectiveness of the constructed TBG and the advantages of the derived strategy.

Time Base Generator-Based Practical Predefined-Time Stabilization of High-Order Systems With Unknown Disturbance

This paper investigates a predefined-time stabilization problem for a high-order integrator chain system with an unknown disturbance by using a time base generator (TBG) method. Until now it is still a challenge to realize the TBG based predefined-time stabilization for high-order systems. In this paper, a novel TBG function is constructed for a high-order integrator system and a nonlinear coordinate transformation is proposed to facilitate the design of the predefined-time controller. The feature of this TBG function is that it is smooth and applicable to arbitrary order systems. Then the practical predefined-time stability of the closed-loop system is analyzed under the proposed TBG based controller when an unknown disturbance exists in the system. Furthermore, the settling time can be preset arbitrarily, and thus is independent of the system’s initial condition. Finally, some numerical examples are presented to validate the effectiveness of the proposed TBG based control strategy.

Predefined-Time Barrier Function Adaptive Sliding-Mode Control and Its Application to Piezoelectric Actuators

This article reports the design and validation of a novel predefined-time barrier function adaptive sliding-mode control (PTBFASMC) strategy for robust control of disturbed systems. The PTBFASMC strategy is established by integrating the time base generator along with the barrier function. Unlike existing similar works, the proposed method enables global predefined-time convergence, i.e., the system trajectory returns to the ultimate bound even if an escape occurs at a certain time instant. Besides, the convergence time can be predefined by the user, which is independent of the initial conditions and disturbance. Moreover, the reaching phase is eliminated and the magnitude of initial control output is zero. Another attractive feature of the proposed method lies in that the ultimate bound can be predefined, i.e., the ultimate bound is independent of the upper bound of disturbance. To avoid large control magnitude, a modified control strategy is provided, which extends the proposed scheme to different scenarios. The stability of the control system is demonstrated, and its superiority is verified through numerical simulations and experimental investigations on a piezoelectric actuator.

Fully distributed practical bipartite formation tracking of networked Lagrangian systems with actuator faults and bounded inputs

This paper investigates the bipartite formation tracking (BFT) problem of networked Lagrangian systems (NLSs) with signed directed graphs. Each system suffers from actuator fault with bounded input. Firstly, the unknown input of the leader is estimated for all the followers based on an observer in the prescribed time, which is constructed by employing a time base generator (TBG). Then, a hierarchical fully distributed controller is proposed to achieve BFT without using the global information with respect to the communication graphs. Then, the related sufficient condition for the system stability is derived by means of the Lyapunov theory. Finally, a simulation example is proposed to demonstrate the performance of the hierarchical fully distributed controller for achieving BFT.

Cancellation of Inertial Effects in 1 Degree of Freedom Mechanisms Applying Sliding Mode Control with Response in Finite Time

Canceling the effects generated by inertia in the mechanisms is a complicated task with great benefits, such as reducing the Chattering effect and, in turn, energy consumption. In this article, a methodology is proposed for the cancellation of the effects produced by inertia in 1 degree of freedom mechanisms. As a solution, a control system is proposed with the application of a Time Base Generator (TBG), merged with a Proportional-Integral-Derivative (PID) controller and to limit the error, a sliding surface (SMG), to finally reach the desired position in the mechanism. The main contribution of this work is to develop the algorithm to cancel the effects produced by inertia when exist a dynamic change in the mechanism, thus obtaining a decrease in the Chattering effect presented in the rotary actuators. As a secondary contribution in this work, speed has a Gaussian campaign behavior similar to the curves drawn by the extremities of the human body, thus guaranteeing the decrease of the Chattering effect and in turn reducing the energy consumption demanded by the actuator (torque) to move the mechanism. The work has as an experimental object a 1 DOF mechanism, whose task is to lift loads vertically. In the analysis the controller reaches the desired position in a finite time, eradicates the speed fluctuations that give rise to an over acceleration when the mechanism changes from rest to a state of movement. The controller compensates the disturbances generated by the loads applied to it. The results show a functional and safe controller, capable of bringing the mechanism to a desired position in a defined time, eliminating the effects of inertia (Slinky effect).

Three-dimensional integrated guidance and control with input saturation and impact angle constraints

Considering the problem of a skid-to-turn (STT) interceptor attacking maneuvering targets in the three-dimensional space, a new integrated guidance and control (IGC) law with the constraints of impact angles and input saturation is developed. To achieve the finite-time convergence and satisfactory input characteristics, a time-varying sliding mode control (TVSMC) method is presented based on a time base generator function. To this end, the IGC scheme is developed based on the TVSMC and the back-stepping. At each step, the derivative of the virtual signal is approximated by a tracking differentiator. Meanwhile, an auxiliary compensation system is designed to reduce the adverse effect raised from the saturation error. Moreover, the modeling uncertainties and disturbances are attenuated effectively by using fractional power extended state observers to estimate them. The closed-loop system states are proved to be uniformly ultimately bounded and the controlled states are proved to converge into small neighborhoods of the origin at the interception time. Finally, the performance of the presented IGC law is verified through numerical simulations.

Distributed dynamic event-triggered and practical predefined-time resource allocation in cyber–physical systems

Resource allocation is a typical problem in cyber–physical systems. However, how to achieve the fast allocation in a distributed way while saving the communication resources is still a challenging problem. In this paper, a novel resource allocation strategy is proposed by applying a dynamic event-triggered scheme and a time base generator. Different from the existing works, the proposed strategy simultaneously enjoys three advantages: (1) It can be implemented in a fully distributed manner; (2) The convergence time can be predesigned by the user; (3) The communication resources can be economized by the event-triggered mechanism. These advantages are shown by our theoretical analysis and numerical simulations.

Pen-point Trajectory Analysis During Trail Making Test Based on a Time Base Generator Model.

The Trail Making test (TMT) is a widely used neuropsychological test to assess the cognitive function of patients. This paper presents the analysis method of pen-point trajectory during the TMT based on a time base generator (TBG). In the proposed method, the movement segments between targets are first extracted from pen-point trajectories, which are measured during performance of the TMT on an iPad. By fitting the extracted trajectories with a TBG-based trajectory generation model, the proposed method can then calculate quantitative indices representing the shape and collapse of the velocity profile. In the experiment, we analyzed TMT data from 25 stroke patients who were classified into three groups according to their scores on the Mini-Mental State Examination (MMSE). The results revealed that most of the measured inter-target trajectories had unimodal bell-shaped velocity profiles, as seen in reaching movements. Furthermore, we found that the degree of collapse in the velocity profile shape increased significantly when the cognitive function decreased.

Predefined-time distributed optimization of general linear multi-agent systems

In this paper, we consider the predefined-time distributed optimization problems of homogeneous and heterogeneous linear multi-agent systems under undirected and connected communication topologies, in which, all agents share coupled equality constraint. In order to make all agents converge to the optimal output at predefined-time cooperatively, we propose two distributed algorithms for homogeneous and heterogeneous multi-agent systems according to time-base generator technology and output feedback, therein, the optimal output can make the global cost function reach minimum. In the design of the algorithms, the control gains are not required, which can avoid the requirement of some global information in advance. Furthermore, all agents converge to the optimal output with exponential speed, and we can set the convergence time arbitrarily. Finally, we provide examples to illustrate the effectiveness of the proposed distributed algorithms.

Three-dimensional time-varying sliding mode guidance law against maneuvering targets with terminal angle constraint

This paper deals with the problem of intercepting maneuvering targets with terminal angle constraints for missiles subjected to three-dimensional non-decoupling engagement geometry. To achieve the finite-time interception and satisfactory overload characteristics, a time varying sliding mode control methodology is developed based on a time base generator function. The main feature of the proposed guidance law guarantees the Line-of-Sight (LOS) angles to converge to small neighborhoods of the desired values at the interception time. First, a fractional power extended state observer is used to estimate the unknown target acceleration, which can significantly reduce the adaptive switching gain. The fractional power extended state observer enjoys the advantage of better noise tolerance. Then, a newly designed sliding mode surface is constructed by introducing a time base generator function and the time-varying sliding mode guidance law is developed based on this time-varying sliding surface. The proposed guidance law significantly reduces the overload magnitudes. Numerical simulations are carried out to verify the performance of the proposed guidance law.

Predictor-based practical fixed-time adaptive sliding mode formation control of a time-varying delayed uncertain fully-actuated surface vessel using RBFNN

This paper focuses on fixed-time formation control (FTFC) of a fully-actuated surface vessel (FASV) considering complex unknowns, including fully unknown dynamics and disturbances, input saturation and time-varying delays. First, using prediction idea to address time delay, a novel state predictor (SP) strategy combining with state transformation (ST) technique is devised for each FASV to predict the evolution of system states such that fixed-time stability can be ensured while solving the delay problem. Besides, the uncertainties in the transformed system are attentively considered. In addition, aiming to distinctly identify complex unknowns, predictor-based neural network is injected into the foregoing delay processing method. Finally, using time base generator (TBG), a new adaptive terminal sliding mode (ATSM) is incorporated into FTFC strategy which in turn contributes to decreasing control inputs and acquiring smooth convergence process. Simulation results and comparisons are thoroughly provided to testify the effectiveness and superiority of the designed FTFC scheme.

A predefined‐time first‐order exact differentiator based on time‐varying gains

AbstractRecently, a first‐order differentiator based on time‐varying gains was introduced in the literature, in its nonrecursive form, for signals having a second‐order derivative bounded by a known time‐varying function, where such time‐varying bound has a logarithmic derivative bounded by a known constant. It has been shown that such differentiator is globally finite‐time convergent. In this article, we redesign such an algorithm, using time base generators (a class of time‐varying gains), to obtain a differentiator algorithm for the same class of signals, but with guaranteed convergence before a desired time, that is, with fixed‐time convergence with an a priori user‐defined upper bound for the settling time. Thus, our approach can be applied for scenarios under time‐constraints. We present numerical examples exposing the contribution with respect to related state‐of‐the‐art algorithms.

Model-Free High Order Sliding Mode Control with Finite-Time Tracking for Unmanned Underwater Vehicles

Several strategies to deal with the trajectory tracking problem of Unmanned Underwater Vehicles are encountered, from traditional controllers such as Proportional Integral Derivative (PID) or Lyapunov-based, to backstepping, sliding mode, and neural network approaches. However, most of them are model-based controllers where it is imperative to have an accurate knowledge of the vehicle hydrodynamic parameters. Despite some sliding mode and neural network-based controllers are reported as model-free, just a few of them consider a solution with finite-time convergence, which brings strong robustness and fast convergence compared with asymptotic or exponential solutions and it can also help to reduce the power consumption of the vehicle thrusters. This work aims to implement a model-free high-order sliding-mode controller and synthesize it with a time-base generator to achieve finite-time convergence. The time-base was included by parametrizing the control gain at the sliding surface. Numerical simulations validated the finite-time convergence of the controller for different time-bases even in the presence of high ocean currents. The performance of the obtained solution was also evaluated by the Root Mean Square (RMS) value of the control coefficients computed for the thrusters, as a parameter to measure the power consumption of the vehicle when following a trajectory. Computational results showed a reduction of up to 50% in the power consumption from the thrusters when compared with other solutions.

Practical Bipartite Tracking for Networked Robotic Systems via Fixed‐Time Estimator‐Based Control

In this paper, the fixed‐time practical bipartite tracking problem for the networked robotic systems (NRSs) with parametric uncertainties, input disturbances, and directed signed graphs is investigated. A new fixed‐time estimator‐based control algorithm for the NRSs is presented to address the abovementioned problem. By applying a sliding surface and the time base generator (TBG) approach, a new stability analysis method is proposed to achieve the fixed‐time practical bipartite tracking for the NRSs. We also derive the upper bound of the convergence time for employing the presented control algorithm to solve the practical bipartite tracking problem and further demonstrate that the convergence time is independent of the initial value. Finally, the simulation examples are given to verify the effectiveness of the presented algorithms.

Constant Speed Control of Slider-Crank Mechanisms: A Joint-Task Space Hybrid Control Approach

In this paper, a constant speed control of slider-crank mechanisms for machine tools is proposed. A joint-task space hybrid controller based on a second-order sliding mode control and time-base generator was used to guarantee a constant speed trajectory tracking and a complete turn of the mechanism crank. A switching criterion was implemented in order to avoid the singularities located at the two extreme positions of the slider stroke. A trapezoidal speed profile with parabolic blends was designed directly over task space slider trajectory considering a constant cutting speed, the workpiece dimensions and the slider stroke length. Stability of the second-order sliding mode control was validated with the Lyapunov stability theory. Simulations were carried out to verify this approach.

Predefined-Time Distributed Optimal Allocation of Resources: A Time-Base Generator Scheme

In this article, we present a novel predefined-time distributed optimization protocol for the resource allocation problem (RAP). Different from the existing finite/fixed-time distributed optimal algorithms, the proposed protocol is built on the time-varying time-based-generator scheme. The settling time is independent of the initial values of the agents and any designed parameters, which implies that the settling time can be predesigned by the user. To address the inequality constraints, the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\epsilon $ </tex-math></inline-formula> -exact penalty function method is introduced to solve the RAP within a predefined-time. In addition, the designed optimization protocol can be implemented in an initialization-free manner, which makes the algorithms feasible under arbitrary initial states. Finally, several numerical simulation results are provided to demonstrate the effectiveness of the proposed algorithms.