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Proximal policy optimization (PPO) is a deep reinforcement learning algorithm based on the actor-critic (AC) architecture. In the classic AC architecture, the Critic (value) network is used to estimate the value function while the Actor (policy) network optimizes the policy according to the estimated value function. The efficiency of the classic AC architecture is limited due that the policy does not directly participate in the value function update. The classic AC architecture will make the value function estimation inaccurate, which will affect the performance of the PPO algorithm. For improvement, we designed a novel AC architecture with policy feedback (AC-PF) by introducing the policy into the update process of the value function and further proposed the PPO with policy feedback (PPO-PF). For the AC-PF architecture, the policy-based expected (PBE) value function and discount reward formulas are designed by drawing inspiration from expected Sarsa. In order to enhance the sensitivity of the value function to the change of policy and to improve the accuracy of PBE value estimation at the early learning stage, we proposed a policy update method based on the clipped discount factor. Moreover, we specifically defined the loss functions of the policy network and value network to ensure that the policy update of PPO-PF satisfies the unbiased estimation of the trust region. Experiments on Atari games and control tasks show that compared to PPO, PPO-PF has faster convergence speed, higher reward, and smaller variance of reward.

We approach the problem of stabilizing a dynamical system while optimizing a cost and satisfying safety and control constraints. For affine control systems and quadratic costs, it has been shown that Control Barrier Functions (CBF) guaranteeing safety and Control Lyapunov Functions (CLF) enforcing convergence can be used to reduce the optimal control problem to a sequence of Quadratic Programs. In this paper, we propose High Order CBFs (HOCBF), which can accommodate systems of arbitrary relative degree. We construct a set of controls that renders the intersection of a set of sets forward invariant for the system, which implies the satisfaction of the original safety constraint. Our notion of HOCBF is more general than the recently proposed exponential CBF. We formulate optimal control problems with constraints given by HOCBF and CLF, and propose two methods - the penalty and the parameterization methods - to address the feasibility problem. Finally, we show how our methodology can be extended for safe navigation in unknown environments with long-term feasibility. We illustrate the proposed framework on a cruise control system and on a robot control problem.

This paper considers a privacy-concerned distributed optimization problem over multi-agent networks, in which malicious agents exist and try to infer the privacy information of the normal ones. We propose a novel dual averaging algorithm which involves the use of a correlated perturbation mechanism to preserve the privacy of the normal agents. It is shown that our algorithm achieves deterministic convergence under arbitrary initial conditions and the privacy preservation is guaranteed. Moreover, a probability density function of the perturbation is given to maximize the degree of privacy measured by the trace of the Fisher information matrix. Finally, a numerical example is provided to illustrate the effectiveness of our algorithm.

Differential dynamic programming (DDP) is a well-recognized method for trajectory optimization due to its fast convergence characteristics. However, the original DDP requires a predefined final time and cannot handle nonlinear constraints in optimization. This prohibits the application of DDP for autonomous vehicles due to the heuristic nature of setting a final time beforehand and the existence of inherent physical limits. This paper revisits DDP by dynamically optimizing the final time via the first-order optimality condition of the value function and using augmented Lagrangian method to tackle the issue of nonlinear constraints. The resultant algorithm is termed as Flexible Final Time Constrained Differential Dynamic Programming (FFT-CDDP). Extensive numerical simulations for a three-dimensional guidance problem are used to demonstrate the working of FFT-CDDP. The results indicate that the proposed FFT-CDDP provides much higher computational efficiency and stronger robustness against the initial solution guess, compared with the off-the-shelf GPOPS algorithm.

In this article, recursive filtering is investigated for time-varying discrete sequential systems (DSSs) under weighted try-once-discard (WTOD) protocols, which are employed to govern the access authorization of a shared network in order to remit the communication burden. A transmission model, dependent on a Bernoulli distributed white sequence, is developed to describe the phenomenon of deception attacks. In light of the adopted protocol and the attack model, a recursive algorithm with the form of Riccati-like difference equations is developed to optimize the filtering performance in the mean square sense. Furthermore, by resorting to the mathematical induction, the convergence of the proposed recursive algorithm is discussed profoundly. Finally, a simulation example is presented to verify the availability of the designed recursive filter.

Iterative learning control (ILC) aims to improve a system's performance by learning from previous iterations in repetitive operations. Traditional ILC requires the system to operate in a strictly repetitive way and the learning process is within the confines of one single system. This paper proposes an iterative learning method that extends traditional ILC from a temporal learning process within one single system to a spatial learning process between two heterogeneous systems. This learning mechanism is made viable by designing learning filters which bridge the dynamics of different systems. To design such learning filters, firstly, a dynamic system that consists of two heterogeneous systems and two learning filters is constructed; secondly, the two learning filters are decoupled from the known dynamics step by step. Each filter is successfully placed in the feedback loop of a reconstructed system consecutively, which enables us to transfer the filter design problem into a controller design problem that can be solved by leveraging the H-infinity optimal control theory. Meanwhile, the solvability of the learning filters, the stability of the system, and the learning convergence are rigorously analyzed. The proposed new algorithm is applied to the trajectory tracking problem of quadrotor drones. Both numerical and experimental studies have been conducted to validate the effectiveness of the proposed iterative learning method for multiple heterogeneous systems.

The learning control strategy is studied for networked stochastic systems, where the output and input data are transmitted through multiple independent fading channels. The traditional P-type learning control scheme is revised according to the specific fading positions, where the constant learning gain is replaced by a variable one to suppress the effect of various uncertainties. Strong convergence of the proposed scheme is established under random fading phenomena and system noise. The input error is shown convergent to zero as the cycle number increases. Two numerical examples demonstrate the applications of the proposed scheme.

We consider a gradient-like system for real-time implementation of multivariable algebraic loops arising in input-constrained control problems. Using results from mathematical programming, we establish global asymptotic convergence under a less stringent condition as compared to existing techniques. We comment on the application of the gradient-like system in anti-windup control implementation where the closed loop can also be interpreted within the framework of singularly perturbed systems. The proposed system can easily be realized for practical circuit implementation and may be prototyped using fast analog processors.

Convergence, diversity and feasibility are three important issues when solving constrained multiobjective optimization problems (CMOPs). To deal with the balance among convergence, diversity and feasibility well, this article proposes a cooperative multiobjective evolutionary algorithm with propulsive population (CMOEA-PP) for solving CMOPs. CMOEA-PP has two populations, including propulsive population and normal population, and these two populations work cooperatively. Specifically, propulsive population focuses on convergence. Normal population gives priority to feasibility and is obligated to maintain diversity. To cross through the infeasible region and reach the Pareto front (PF), propulsive population does not consider constraints in the early stage and only considers constraints in the later stage. To further accelerate the speed of convergence, propulsive population only searches for corner solutions and center solutions, while normal population searches for the whole PF. As a result, propulsive population can cross through the infeasible region because of the lack of attention to feasibility. In addition, propulsive population also can guide and accelerate the convergence of the evolutionary process. Comprehensive experiment results on several sets of benchmark problems demonstrate that CMOEA-PP is better than existing state-of-the-art competitors.

The design of binary sequences with low autocorrelation sidelobes is critically important to diverse applications including, radar and sonar as well as communications. Many computational methods have been proposed recently to design binary sequences through optimizing the integrated sidelobe level (ISL, which is a commonly used optimization metric. However, due to the high computational complexities, few of them can be used for long binary sequence designs, which are needed in, for example, low-cost commercial automotive radar systems. To improve the performance of the recently introduced FFT-based CANARY algorithm for long aperiodic binary sequence designs, we introduce a new penalty function into the ISL metric and also propose a new framework of double-loop iterations. These new ideas are also extended to design long periodic binary sequences with low autocorrelation sidelobes and long aperiodic and periodic binary sequences with low correlation zones (LCZs . The associated cost functions are still optimized efficiently via FFT-based iterations, making the proposed algorithms computationally efficient and hence suitable for long binary sequence designs. Moreover, the convergence properties and the computational complexities of these algorithms are analyzed. Numerical examples are provided to demonstrate the effectiveness of the proposed algorithms.

This paper proposes an improved noniterative fault location method on untransposed transmission lines without utilizing line parameters. Two-end three phase voltage and current phasor measurements before and during the fault are typically required. First, the parameter-free fault location problem is formulated through multi-section transmission line models, and the necessary condition of noniterative solutions is carefully investigated to determine the maximum possible section number of the multi-section line model. Afterwards, with the determined section number, the analytical solution of the fault location is derived with full utilization of the inherent characteristics of the line parameter matrices. Instead of solving all the parameters, two key variables inside the parameter matrices are extracted and the fault location is obtained by analytically solving a polynomial equation. The method provides a closed-form analytical solution, and therefore avoids convergence issues of iterative algorithms. In addition, line asymmetry of untransposed transmission lines are fully considered to minimize fault location errors. Extensive numerical experiments show that the proposed method has improved fault location accuracy compared to the existing method, with different fault types, locations and impedances.

The heat-electricity integrated energy system (HEIES) with energy hubs (EHs) and prosumers is the typical form of future energy system, EH can efficiently model the integration of different energy carriers and coordinate an integrated energy sharing system of multiple prosumers in HE-IES. In this paper, a closed-loop framework is designed to integrate the contract theory and consensus algorithms for a bi-level heat-electricity energy sharing system. First, the energy sharing scheme between prosumers and an EH in the lower-level energy system is formulated. Contract theory is utilized to maximize the profits of EH under the information asymmetry scenario, and different contract items are designed for the electric and thermal networks. In particular, a set of new bi-directional contract items is proposed in the electrical network. Furthermore, a consensus-based energy sharing framework among various EHs and utility grid in the upper-level system is developed and network constraints is considered. Two types of Lagrange multipliers are defined to decouple the electric and thermal network, and an interactive mechanism is designed to solve the problem. Finally, the simulation results verify the convergence of the bi-level closed-loop framework and the feasibility and performance of the scheme.

For distributed estimation arising in the nonlinear least squares (NLLSs) problems over adaptive networks, where every node has the abilities of data processing and learning, only the incomplete local data are exploited by the traditional noncooperative method, thereby resulting in the degradation on estimation performance. In this article, a cooperative diffusion strategy is proposed by using a Gauss-Newton (GN) method in order to fully utilize the diversity of temporal-spatial data on local updates. The proposed algorithm includes two steps, i.e., aggregate then update (ATU), where the aggregating step collects in real time the global information instead of local information due to the diffusion strategy, and the updating step implements the local GN iteration. The resulting ATU diffusion algorithm is a distributed and cooperative system without any increase on communication cost, as compared with the noncooperative version. Based on the detailed convergence analysis for ATU, which is fundamental to the promotion of this algorithm, the sufficient conditions for convergence are derived and the evidences of faster convergence than the noncooperative version are provided. The simulation results confirm the obtained theoretical derivations by applying the ATU algorithm to an NLLS-based target localization problem and show the cooperation gains in many aspects, such as the convergence rate, steady-state accuracy, and robustness to noisy range, step size, node, and link failures.

A model-free optimal tracking controller is designed for discrete-time nonlinear systems through policy gradient adaptive critic designs (PGACDs) with experience replay (ER). By using system transformation, optimal tracking control problems are converted into optimal regulation problems. An off-policy PGACD algorithm is developed to minimize the iterative Q-function and improve the tracking control performance. The proposed method is realized based on the critic network and the actor network (AN), which are applied to approximate the iterative Q-function and the iterative control policy, respectively. Then, the policy gradient technique is introduced to derive a novel weight updating law of the AN explicitly by using measured system data only. The convergence of the iteration is established through theoretical analysis, and the uniform ultimate boundedness is demonstrated for the closed-loop system under the PGACD-based controller by using Lyapunov's direct method. To guarantee the stability and increase the data usage efficiency of the learning process, an ER-based learning framework is designed to improve the realizability of the proposed method. Finally, simulation results of two examples are provided to demonstrate the performance of the off-policy PGACD algorithm.

In this paper, we study the problem of trajectory planning for a class of nonlinear systems with convex state/control constraints and nonconvex state constraints with concave constraint functions. This corresponds to a challenging nonconvex optimal control problem. We present how to convexify the nonlinear dynamics without any approximation via a combination of variable redefinition and relaxation. We then prove that the relaxation is exact by designing an appropriate objective function. This exact relaxation result enables us to further convexify the nonconvex state constraints simply by linearization. A a result, an algorithm is designed to iteratively solve the obtained convex optimization problems until convergence to get a solution of the original problem. A unique feature of the proposed approach is that the algorithm is proved to converge and it does not rely on any trust-region constraint. High performance of the algorithm is demonstrated by its application to trajectory planning of UAVs and autonomous cars with obstacle avoidance requirements.

In this paper, a varying-gain neural bi-criterion velocity minimization self-motion (VGN-BCVM-SM) approach is proposed to solve the self-motion problem for a redundant robot manipulator. Firstly, based on quadratic programming method and neural dynamic method, the proposed approach is derived in detail. For comparisons, a traditional fixed-parameter neural bi-criterion velocity minimization self-motion (FPN-BCVM-SM) approach is also presented. Then, the convergence and robustness of the proposed method is analyzed theoretically. Theoretical analysis shows that the proposed approach has global convergence and can overcome the errors of kinematics measurements. Computer simulations based on a six degrees-of-freedom manipulator demonstrate that the proposed approach can effectively avoid the robot manipulator exceeding the physical limits of joints. Meanwhile, the proposed VGN-BCVM-SM has higher efficiency and accuracy than fixed-parameter approach for solving self-motion problem of a redundant robot manipulator.

Federated learning is a new paradigm to support resource-intensive and privacy-aware learning applications. It enables the Internet-of-Things (IoT) devices to collaboratively train a global model to accomplish a machine learning task without sharing private data. In practice, the IoT devices powered by batteries finish the local training and interact with the central server via wireless links. However, the repeated interaction between IoT devices and the central server would consume considerable resources. Motivated by the emerging technology of intelligent reflecting surface (IRS), we propose to leverage the IRS to reconfigure the wireless propagation environment to maximize the utilization of the available resources. Specifically, we consider the critical energy efficiency issue in the reconfigurable wireless communication network. We formulate an energy consumption minimization problem in an IRS-assisted federated learning system subject to the completion training time constraint. An iterative resource allocation algorithm is proposed to jointly configure the parameters with proven fast convergence. Simulation results validate that the proposed algorithm converges fast and can achieve significant energy savings, especially when the number of reflecting elements is large and when the IRS is properly configured.

This article considers the problem of designing robust event-triggered functional observers for linear interconnected systems with disturbances. The considered system comprises $N$ interconnected subsystems where each subsystem is subject to unknown-but-bounded input disturbances that do not necessarily satisfy the observer matching condition. First, novel Zeno-free event-triggered mechanisms (ETMs) for $N$ subsystems of the considered interconnected system are proposed. Then, robust distributed functional observers are designed based on the proposed ETMs. The designed event-triggered functional observers are robust such that the observer error for each subsystem is $\epsilon _i$ -convergent. This ensures that the $i$ th estimated state vector of the $i$ th subsystem converges robustly within an $\epsilon _i$ -bound of the true state vector of the $i$ th subsystem. Numerical examples are given to illustrate the effectiveness of the proposed design method.

In this paper, we present a gliding efficiency optimization strategy based on deep reinforcement learning (DRL) for a gliding robotic fish. For the gliding motion in shallow waters, the non-steady motion strongly impacts the gliding range and also reduces efficiency. This paper presents a concept of transient gliding motion and illustrates its importance for small-scale gliding robotic fish. For better gliding performance of active fins, several pectoral fins with different sizes are designed and their hydrodynamics and optimizing capabilities are analyzed by computational fluid dynamics (CFD) simulation. Then, a double deep Q network (DQN) based optimization strategy is proposed to improve gliding efficiency by active pectoral fins, in which an adversarial model and a two-stage reward function are presented for the adequate calculation of gliding range. Simulations are conducted to validate the convergence and effectiveness of the proposed strategy. The aquatic experiments are carried out to further verify the proposed strategy. The results reveal that the optimization strategy can save about 4.88% of energy and 19.45% of travel time. This study provides clues to the design of active control surfaces and improvement of gliding efficiency for underwater vehicles. Remarkably, the proposed strategy can significantly improve the duration and endow the robot with the potential to perform complex tasks.

This paper presents a simple control method for the fully automatic parking of an unmanned vehicle. This method is based on the switching control algorithm and backstepping theory. The fully automatic parking is hard to accomplish since it cannot converge to a specified norm, guarantee the convergence rate, and large uncertainties. Global exponential convergence to any prescribed norm bound (e-convergence) is guaranteed, and the convergence rate is explicitly given. For the design of steering laws, a method based on backstepping is proposed and analyzed in detail. The backstepping-based design of a multichain system is obtained. Moreover, an exponentially e-convergent control algorithm is adopted to guarantee both converge norm and convergence rate. Real road experiment results are presented and the results show the effectiveness of the control strategies.

Ensuring Quality of Service (QoS) in next-generation networks would be challenging because of the expected manifolds increase in network traffic volume and the massive number of connected Internet of Things (IoT) devices. The increased resources on end-devices have made it possible to make decisions on the client-side for Access Point (AP) selection. On the other hand, due to power constraints on the client-side, energy efficiency is also essential. This paper presents a client-side energy-efficient AP selection approach for QoS provisioning in hybrid Wireless Fidelity (WiFi) and Light Fidelity (LiFi) networks. Compared to conventional WiFi and LiFi approaches, the proposed technique outperforms them in energy efficiency at any data rate and in QoS provisioning at data rates higher than 10 Mbps for a network of 50 nodes. It is also shown that adapting the uplink transmission power improves the IoT node’s energy efficiency by transmitting at minimal transmission power required to satisfy the throughput QoS constraint. This paper’s contributions include the proposed algorithm, complexity and convergence analyses of the algorithm, simulation-based evaluation, and analysis of the uplink transmission power adaption. The results show that the presented technique could be integrated into next-generation networks for QoS provisioning and improving energy efficiency.

The deployment of access points (APs) imposes a great impact on the performance of wireless local area networks (WLANs). Although there have been plenty of works on the optimal AP deployment (OAD), however, the issue remains open that how to deploy APs energy-savingly in 3-D environments while considering some practical demands. Therefore, this article investigates the OAD with the objective of minimizing the total AP transmission power while guaranteeing the effective coverage by jointly optimizing the transmission power and location of each AP. Different from existing works, our article fully considers not only real 3-D environments with various obstacles but also the differentiated coverage demand and the restrictions on AP locations. To solve this NP-hard optimization problem, this article first proposes a novel hybrid swarm intelligence optimization algorithm, named PSO-Levy-DFOA. The computational results on 16 benchmark functions and comprehensive comparisons with other algorithms demonstrate the superior global convergence performance of PSO-Levy-DFOA. The proposed PSO-Levy-DFOA-based OAD method is then applied to WLAN planning in a two-story building. It has been shown that the total AP transmission power can be considerably reduced compared to the current deployment while still fulfilling the effective coverage.

This paper designs a novel finite-time extended state observer (FTESO) based super-twisting sliding mode (STSM) control scheme to promote the anti-disturbance property and tracking performance of permanent magnet synchronous motor (PMSM). Firstly, a FTESO combined with generalized super-twisting technique is constructed to estimate the unknown lumped disturbance and compensate the estimated value to the STSM speed controller. Compared with the conventional extended state observer (ESO), the proposed FTESO can make the estimation error converge to the origin in finite time, which provides a faster convergence speed and higher estimation accuracy. Moreover, in order to tackle the problem of performance deterioration caused by inertia mismatch, particularly for PMSM speed control, an inertia identification method is employed to calculate the true value of inertia online to tune the parameters of FTESO and STSM controller automatically. Comprehensive simulation and experimental results demonstrate that the proposed control method can improve the robustness of PMSM system in the presence of load torque and inertia variations.

The power voltage (P-V) characteristics of photovoltaic (PV) systems exhibit multiple power peaks under partially shaded conditions. Several global maximum power point tracking (GMPPT) algorithms in the literature recognize the irradiance change, only after the convergence of operating point to global peak, or use additional hardware to call GMPPT subroutine at definite time intervals to detect any insolation change, and thus track the global peak. However, during fast changing partial shading conditions, these methods are less effective, as they do not detect any irradiance change during the tracking phase of any shading pattern. This paper proposes a novel modified current control approach that uses current as a parameter to detect the insolation change during the tracking phase and track the global peak under fast changing partial shading conditions without any additional hardware. The proposed technique improves the tracking efficiency by as much as 39%, thus proving to be effective under fast changing partial shading conditions. The superior tracking performance of the proposed algorithm over the existing techniques in terms of its tracking efficiency, dynamic tracking capability, tracking speed, and convergence to the global peak is demonstrated with extensive simulations using MATLAB/Simulink and experimental results.

In this paper, we consider stochastic master equations describing the evolution of a multi-qubit system interacting with electromagnetic fields undergoing continuous-time measurements. By considering multiple z-type (Pauli z matrix on different qubits) and x-type (Pauli x matrix on all qubits) measurements and one control Hamiltonian, we provide general conditions on the feedback controller and the control Hamiltonian ensuring almost sure exponential convergence to a predetermined Greenberger-Horne-Zeilinger (GHZ) state, which is assumed to be a common eigenstate of the measurement operators. We provide explicit expressions of feedback controllers satisfying such conditions. We also consider the case of only z-type measurements and multiple control Hamiltonians. We show that local stability in probability holds true, however, the reachability of a neighborhood of a predetermined GHZ state is not clear. In this case, we provide a heuristic discussion on some conditions which may ensure asymptotic convergence toward the target state. Finally, we demonstrate the effectiveness of our methodology for a three-qubit system through numerical simulations.

This article is mainly concerned with the fixed-time tracking control problem for multiple uncertain mechanical systems with actuation dead zones. As the dead zones and control gains are time varying and completely unknown, the control impact on mechanical system becomes completely unknown, making the achievement of fixed-time tracking control nontrivial. The existing studies on fixed-time tracking control cannot effectively estimate and compensate such dead zones, resulting in the upper bound of convergence time being uncertain and even system becoming unstable. To compensate the dead zones in a fixed time, we introduce a bound estimation method to estimate the impact of dead zones and design two fixed-time adaptive laws. Two cases on system uncertainties are considered. By introducing distributed control method, adaptive control method, neural networks and some skillful treatments, two novel distributed adaptive neural fixed-time tracking control schemes are proposed. It is confirmed that, with the proposed control schemes, all followers which are uncertain mechanical systems with completely unknown dead zones track the leader with sufficient precision in a predefined time.

Feature selection is an important pre-processing technique for improving the quality of feature sets in many practical applications. Particle swarm optimisation (PSO) has been widely used for feature selection due to being efficient and easy to implement. However, when dealing with high-dimensional data, most of the existing PSO-based feature selection approaches face the problems of falling into local optima and high computational cost. Evolutionary multitasking is an effective paradigm to enhance global search capability and accelerate convergence by knowledge transfer among related tasks. Inspired by evolutionary multitasking, this paper proposes a multitasking PSO approach for high-dimensional feature selection. The approach converts a high-dimensional feature selection task into several related low-dimensional feature selection tasks, then finds an optimal feature subset by knowledge transfer between these low-dimensional feature selection tasks. Specifically, a novel task generation strategy based on the importance of features is developed, which can generate highly related tasks from a dataset adaptively. In addition, a new knowledge transfer mechanism is presented, which can effectively implement positive knowledge transfer among related tasks. The results demonstrate that the proposed method can evolve a feature subset with higher classification accuracy in a shorter time than other state-of-the-art feature selection methods on high-dimensional classification.

Localization is fundamental for autonomous vehicle applications. Compared with widely developed LiDAR-based vehicle localization, vision based localization has attracted considerable attention in recent years owing to the low-cost sensor. One of the challenges for visual localization is the outlier in measurements due to the appearance changes caused by illumination, season, and weather. To address this problem, we present a real-time robust visual localization approach that achieves deterministic optimality with global convergence. The idea is to decouple the rotation and translation estimation by utilizing the fact that the pitch and roll angles of the query pose are similar to those of the map reference pose, since the vehicle motion is locally planar. Based on the decoupled formulation, we first estimate the optimal yaw angle and eliminate the majority of outliers by an efficient inlier voting method, then find the optimal translation by maximum clique search. The two subproblem estimators are embedded into a prioritized search paradigm to guarantee deterministic optimality. In the experiments, the simulation demonstrates that the proposed method can achieve superior robustness even dealing with extreme outlier rates (95%). Results on both public and self-collected real-world vehicle datasets validate the effectiveness of the proposed method in the real application.

Position estimation error caused by the cross-saturation effect seriously affects the performance of signal injection based sensorless control, especially for the surface permanent-magnet synchronous motor (SPMSM) with load. In this paper, a position estimation error compensation method is proposed to improve the accuracy and stability of sensorless control for a dual three-phase SPMSM. Based on the space vector signal injection, the initial position is obtained by the demodulation of high-frequency current response. By analyzing the relationship between the stator flux and stator current, the optimal compensation angle can be achieved. The position estimation error can be dynamically compensated under load conditions with the combination of initial position and compensation angle. Due to the convergence of compensation angle, the compensation process has weak dependence on prior knowledge of the motor. Simulation and experimental results are presented to validate the proposed method.

In this paper, a nonsingular fast terminal sliding mode (NFTSM) control strategy is proposed based on the high-order super-twisting observer (HOSTO) to acquire a fast and precise tracking performance for position regulation of permanent magnet linear synchronous motor. First, the NFTSM control is introduced to achieve fast convergence of the position tracking error. However, the lumped disturbances result in incompleteness of the system state information, the robustness of the system is guaranteed through a large switching gain for the NFTSM, which causes system chattering. Therefore, the HOSTO is utilized to estimate the state information. Then, the NFTSM controller is designed base on the estimated state variables. The system's stability under the proposed control is demonstrated using Lyapunov stability theory. Finally, real-time experiments are carried out to illustrate the efficiency and superiority of the proposed control strategy.

The future distribution systems expose to an unprecedented level of uncertainties due to renewable resources, nontraditional loads, aging infrastructure, etc., posing potential risks to secure operation of the system.This article proposes a new technique to estimate the voltage stability margin of the distribution systems with high penetration of renewables.Its convergence and robustness under complex and stressed working conditions are guaranteed in theory. This technique is handy for the operation as it features self-adaptive step size and is applicable to general system topology. It leverages a newly derived analytical solvability certificate based on the Kantorovich fixed-point theorem. A fast version of the proposed technique is duly proposed to speed up the computation up to 8 times while maintaining high accuracy, which lends itself to online and time-sensitive emergency tasks. Numerical simulations with various IEEE test feeders verify the performance of the techniques. Ministry of Education (MOE) Nanyang Technological University National Research Foundation (NRF) This work was supported in part by NTU SUG, MOE AcRF TIER 1- 2019-T1-001-119 (RG 79/19), and in part by EMA & NRFEMA-EP004-EKJGC-0003.

This paper proposes a discrete-time differentiation algorithm of arbitrary order inspired by the continuous-time uniform robust exact differentiator and the continuous-time arbitrary order robust exact differentiator. As the well-known explicit Euler method is not suitable for discretizing algorithms with the fixed-time convergence property, a semi-implicit approach is proposed. The discrete-time differentiators of order 2 and 3 are studied in detail and it is proven that the estimation errors vanish independent of their initial condition in the unperturbed case. In the presence of perturbations it is shown that the origin of the estimation errors is surrounded by an attractive invariant set. Furthermore the performance of the proposed algorithm is evaluated via simulation studies.

Intelligent driving system requires more precise and reliable steering control, and steering-by-wire (SBW) technology can better adapt to the development of autonomous driving. The permanent magnet synchronous motor (PMSM) servo system is the actuator of the SBW. Aiming at the uncertainties of the PMSM servo system, a new adaptive control method for PMSM servo system is proposed. Parameter adaptive laws are designed for each slowly varying parameter and unknown parameter, and robust terms are introduced to the adaptive laws for the parameter uncertainties. The convergence speed of the parameter adaptive law proposed can be improved by adjusting the parameters related to convergence rate. To reduce the scope of disturbance uncertainties, the steering load disturbances are divided into a bounded unknown time-varying part and a predictable time-varying disturbance. Based on Luenberger observer, the prediction term of load torque is estimated by the current of PMSM in real time. By introducing boundary estimation and robust term of unknown disturbance into the control law and parameter adaptive law respectively, the uncertainties of parameters and unknown external disturbance can be compensated. Simulation and hardware-in-the-loop test are carried out on SBW platform. Experiments show that the control strategy of PMSM servo system designed in this paper has good tracking accuracy and stability.

This paper investigates the event-triggered adaptive fuzzy fixed-time secure control problem for a class of nonlinear cyber-physical systems (CPSs) subject to unknown deception attacks and backlash-like hysteresis. Based on an improved fractional-order command filtered backstepping (FOCFB) method, fuzzy approximation technique, and Nussbaum gain technique, a novel adaptive practical fixed-time secure control scheme is proposed. Theoretical analysis proves that the fixed-time stability of the resulting control system and boundedness of all signals in the closed-loop system can be guaranteed by using the presented resilient controller. Especially, the given convergence time is independent of the initial states of the system and better system performance consisting of higher control accuracy and faster convergence rate can be ensured. Finally, a chemical reaction system is carried out to show the validity and superiority of the developed secure control scheme.

Zeroing neural network (ZNN) is an effective neural solution to time-varying problems including time-varying complex Sylvester equations. Generally, a ZNN model involves a convergence design parameter (CDP) that influences its convergence rate. In traditional fixed-parameter ZNNs (FP-ZNNs), the CDPs are set to be constant, which is not realistic since the CDPs are actually time-varying in practical hardware environments. By considering this fact, varying-parameter ZNNs (VP-ZNNs) with time-varying CDPs have been researched in the literature. Although these VP-ZNNs have been demonstrated to deliver superior convergence as compared with FP-ZNNs, they have one drawback that is their CDPs usually keep increasing with time, meaning that the CDPs tend to be infinity large with time progresses. Evidently, infinity large CDPs are unacceptable in practice. Moreover, computing resources will be wasted by growing the CDPs with time after the VP-ZNNs become convergent. To tackle the above issues, this paper for the first time proposes an arctan-type VP-ZNN (ATVP-ZNN) with finite-time convergence for solving time-varying complex Sylvester equations. The ATVP-ZNN is able to adjust its CDPs that finally converge to be constant when the ATVP-ZNN becomes convergent in finite time. In theory, the finite-time convergence of the ATVP-ZNN and the upper bound of the CDPs are mathematically analyzed. Numerical studies are comparatively performed with the superior convergence of the ATVP-ZNN substantiated.

In this paper, a quantized control capable of appointed-time performances for quadrotor attitude tracking is investigated. A continuous and piecewise behavior boundary, rather than an exponential decaying function employed in traditional pre-scribed performance control (PPC), is devised using error transformation to enforce attitude convergence to pre-assigned transient and steady zones in an appointed time. To circumvent the inertia moment uncertainties and external perturbations, an extended state observer (ESO) with only one parameter to be tuned is introduced to precisely estimate the total disturbances acting on angular rate subsystem. Addi-tionally, a hysteretic quantizer (HQ) capable of converting continuous control behaviors to finite discrete scalars is es-tablished in controller to actuator channel to reduce the transmission burden and amount of sampling data. With a novel quantization decomposition, an attitude quantized con-troller is integrated in terms of a guaranteed tracking. The prominent feature is that a prescribed appointed-time attitude response can be preserved with a decreased demand of communication bandwidth, despite of uncertainties. Theoreti-cal analysis shows that all error signals are ultimately uni-formly bounded. Eventually, the superiority of explored con-trol strategy is demonstrated through experimental results.

The extended state observer (ESO) used to estimate the unknown model for nonlinear systems has been widely applied in model-free control. In the ESO, three factors: 1) nonderivative structure; 2) insufficient usage of innovation; and 3) no compensation of the unknown character of a nonlinear function, causing low type and low accuracy of observation are identified. The convergence problem of the ESO is also raised. A simple linear compensation function observer (CFO) is proposed. The CFO adopts the derivative form overcoming the structure problem of the ESO, fully uses the available innovation, and then introduces a compensator to replace the unknown function. The filtering compensator counteracts the effect of the time-varying nonlinear unknown model to make the error equation behave with desired poles. The convergence of the CFO is theoretically proved. The CFO is the Type-III system, whereas the ESO is a Type-I system; therefore, the CFO has a qualitative leap over the ESO in accuracy improvement of observation. The CFO can observe nonlinear functions, including lumped disturbances, uncertainties, and unmodeled parts for nonlinear systems. The CFO decouples the multi-input and multioutput (MIMO) systems. Five unknown typical nonlinear functions are tested and demonstrates that the CFO qualitatively prevails over the ESO. The MIMO chaotic attitude system of a small-scale unmanned aerial vehicle (UAV) helicopter is conducted with results that CFO performance of function observation is highly improved over that of ESO about 29 times.

We propose an approach to solving the AC network-constrained unit commitment problem (AC-NCUC) of large-scale power systems. This approach relies on solving convex (continuous and mixed-integer) optimization problems. First, we formulate a second-order conic relaxation of the original optimization problem, which renders a mixed-integer second-order conic optimization problem. To solve this problem, we use Benders' decomposition, which decomposes it into a master problem, which is mixed-integer linear, and a subproblem, which is continuous and second-order conic. To improve the convergence of the Benders' algorithm, we add several linear feasibility constraints to the master problem. Since the second-order relaxation of the original problem cannot guarantee AC feasibility of the solution found, we ensure such feasibility by solving a sequence of continuous convex optimization problems. We numerically validate the proposed approach using a Texas 2000-bus system.

This article considers the practical fixed-time self-triggered consensus tracking problem of delayed multiagent networks (MANs) subject to external disturbances under undirected topology and directed topology. The fixed-time consensus implies that the consensus is reached in a finite time and the convergence time is independent of initial conditions under the nonlinear consensus protocols. A self-triggered control (STC) strategy is developed based on the event-triggered control (ETC) strategy. For the ETC strategy, the nonlinear controllers and the measurement errors are designed based on the hyperbolic tangent function to avoid a nondifferential problem and Zeno behavior. To avoid continuous monitoring, the STC strategy is presented. Furthermore, the minimal interevent interval is strictly positive, which implies that no Zeno behavior occurs in the STC strategy. Finally, a numerical example is presented to verify the availability of the algorithms.

This article considers the third-order connected vehicle systems (CVSs) to implement cooperative formation control for autonomous vehicles. The error dynamics is modeled based on the proposed distributed control protocols for two large classes of general network topologies. The performance indices, such as stability, scalability, speedability, and string stability (4S) indices, are investigated. The necessary and sufficient conditions of stability for CVSs are derived and properties of characteristic roots are discussed. These roots are dependent on information of the given network topology. The sufficient conditions of stability, which are independent of network topology, are given by analyzing the range of eigenvalues of the Laplacian matrix of the corresponding network topology, so scalability is guaranteed. To guarantee fast convergence speed, the upper boundary of stability margin is derived, which is also independent of the size of the network topology and can be conveniently tuned by the controller gains and model parameter. The necessary and sufficient conditions of stability are also achieved for the bidirectional-leader following (BLF) network topology. The conditions of string stability are further derived to ensure that spacing errors (caused by disturbances) decay along the vehicle platoon. Furthermore, combining the conditions of stability, speedability, and string stability, the CVSs are proven to be not only stable but also string stable and quickly convergent. Thus, the 4S indices can be guaranteed. Numerical simulations are provided to validate the theoretical results.

In recent years, most of the studies have shown that the generalized iterated shrinkage thresholdings (GISTs) have become the commonly used first-order optimization algorithms in sparse learning problems. The nonconvex relaxations of the l₀-norm usually achieve better performance than the convex case (e.g., l₁-norm) since the former can achieve a nearly unbiased solver. To increase the calculation efficiency, this work further provides an accelerated GIST version, that is, AGIST, through the extrapolation-based acceleration technique, which can contribute to reduce the number of iterations when solving a family of nonconvex sparse learning problems. Besides, we present the algorithmic analysis, including both local and global convergence guarantees, as well as other intermediate results for the GIST and AGIST, denoted as (A)GIST, by virtue of the Kurdyka-Łojasiewica (KŁ) property and some milder assumptions. Numerical experiments on both synthetic data and real-world databases can demonstrate that the convergence results of objective function accord to the theoretical properties and nonconvex sparse learning methods can achieve superior performance over some convex ones.

This paper proposes a finite-time event-triggered secondary frequency and voltage control for islanded AC microgrids (MGs) in a distributed fashion. The proposed control strategy can effectively perform frequency restoration and voltage regulations, while sharing the active and reactive power among the distributed generators (DGs) based on their power ratings. The finite-time control enables a system to reach consensus in a finite period of time enhanced from the asymptotic convergence. The event-triggered communication is utilized to reduce the communication burden among the DG controllers by transmitting data among DGs if an event-triggering condition is satisfied. The performance of the proposed finite-time event-triggered frequency control is verified utilizing a hardware-in-the-loop experimental testbed which simulates an AC MG in Opal-RT.

Complex-valued neural network is a kind of learning model which can deal with problems in complex domain. Fully complex extreme learning machine (CELM) is a much faster training algorithm than the complex backpropagation (CBP) scheme. However, it is at the cost of using more hidden nodes to obtain the comparable performance. An upper-layer-solution-aware algorithm has been proposed for training single-hidden layer feedforward neural networks, which performs much better than its counterparts, pseudo-inverse learning (PIL)/extreme learning machine and gradient decent-based backpropagation neural networks. Consequently, there exist two challenges that need to be dealt with: 1) How to combine the advantages of CBP and CELM to develop a novel complex learning algorithm? and 2) What is the convergent behavior of the presented algorithm? In this article, an input weights dependent complex-valued (IWDCV) learning algorithm based on Wirtinger calculus has been proposed, which effectively solves the nonanalytic problem of the common activation functions during training neural networks. In addition, the monotonicity of the error function and the deterministic convergence of the proposed model have been strictly proved, which theoretically guarantee the efficiency and effectiveness of the given model, IWDCV. Finally, for real and complex-valued problems, a variety of simulations have been done to demonstrate the comparable performance of the proposed algorithm which support the theoretical observations as well.

Structured Support Vector Machines (structured SVMs) are a fundamental machine learning algorithm, and have solid theoretical foundation and high effectiveness in applications such as natural language parsing and computer vision. However, training structured SVMs is very time-consuming, due to the large number of constraints and inferior convergence rates, especially for large training data sets. The high cost of training structured SVMs has hindered its adoption to new applications. In this article, we aim to improve the efficiency of structured SVMs by proposing a parallel and distributed solution (namely FastSSVM ) for training structured SVMs building on top of MPI and OpenMP. FastSSVM exploits a series of optimizations (e.g., optimizations on data storage and synchronization) to efficiently use the resources of the nodes in a cluster and the cores of the nodes. Moreover, FastSSVM tackles the large constraint set problem by batch processing and addresses the slow convergence challenge by adapting stop conditions based on the improvement of each iteration. We theoretically prove that our solution is guaranteed to converge to a global optimum. A comprehensive experimental study shows that FastSSVM can achieve at least four times speedup over the existing solutions, and in some cases can achieve two to three orders of magnitude speedup.

This article investigates the tracking problem of an uncertain n-link robot manipulator with guaranteed safety and performance. To tackle parametric uncertainties, the torque filtering-augmented concurrent learning (CL) method is introduced for online identification of the unknown system without requirements of joints acceleration. By using CL, the parameter convergence is guaranteed by exploiting the current and historical data simultaneously. This technique enjoys practicability compared with common methods that need to incorporate external noises to satisfy the persistence of excitation condition for the parameter convergence. Based on the estimated model, we design a barrier Lyapunov function (BLF)-based adaptive control law by the backstepping technique and Lyapunov analysis. By ensuring the boundness of the BLF, the system output and the tracking error are proved to lie in the safety set and performance set, respectively. Numerical simulation results and experiment tests validate the proposed strategy.

Fixed-time stability (FXTS) and fixed-time control (FXTC) of dynamic systems are reconsidered in this article based on special functions from the view of improving the estimate accuracy of settling time (ST) and reducing the chattering caused by the sign function. First, by means of the idea of contradiction and variable transformations, some generic FXTS criteria are established and some upper bounds of ST are directly calculated and expressed by several special functions. It is further proved that these estimates are the most accurate compared with the existing results. Besides, to suppress the chattering caused by the sign function, some saturation functions are constructed to replace the sign function and the FXTS of the new system obtained by replacing is ensured by rigorous theoretical analysis. As applications, the problem of stabilization for chaotic systems in fixed or preassigned time is explored. Especially, an innovative saturation controller is developed to realize preassigned-time stabilization, where the convergence time is prescribed in advance according to actual requirement and the control gains are finite, the existing control methods with time-varying infinite gains are essentially improved. Lastly, three numerical examples are provided to verify the improved estimates of ST and the chattering reduction.

The extended Kalman filter (EKF), one of the most popular state estimators for nonlinear uncertain dynamic systems, is considered here in its continuous-discrete (CD) form. The CD version enhances the EKF's accuracy but requires robust and computationally efficient numerical integration methods. The purpose of this paper is to present several new efficient integration methods suited to the implementation of the CD EKF and to compare them to classical implementations such as the Dormand-Prince and Euler methods. They are first applied on two proposed nonlinear parameter estimation testbenches and to the stiff Curtiss and Hirschfelder model for state and parameter estimation. Then they are applied on the estimation of the iron losses of a high speed synchronous machine. The results show that for highly nonlinear dynamic systems or for a low to medium sampling frequency, the implicit implementation of the EKF provides better accuracy and convergence safety. For less nonlinear functions and for a higher sampling frequency, classical explicit methods obviously give similar results for a lower computation time.

A new time-varying adaptive dynamic programming (ADP) algorithm is developed for finite-horizon optimal control problems for a class of discrete-time affine nonlinear systems in this paper. Inspired by the pseudo-linear method, the nonlinear system can be approximated by a series of time-varying linear systems. In each iteration of the time-varying ADP algorithm, the optimal control law for the time-varying linear system is obtained. Convergence analysis is provided for the time-varying ADP algorithm. For an arbitrary initial state, it is proven that states of the time-varying linear systems converge to the states of discrete-time affine nonlinear systems if the convergence criterion is satisfied. It is shown that the iterative value functions and the iterative control laws converge to the optimal value function and the optimal control law, respectively. Finally, numerical results are presented to verify the effectiveness of the present method.

The measurement algebraic connectivity plays an important role in many graph theory-based investigations, such as cooperative control of multiagent systems. In general, the measurement is considered to be centralized. In this article, a distributed model is proposed to estimate the algebraic connectivity (i.e., the second smallest eigenvalue of the corresponding Laplacian matrix) by the approach of distributed estimation via high-pass consensus filters. The global asymptotic convergence of the proposed model is theoretically guaranteed. Numerical examples are shown to verify the theoretical results and the superiority of the proposed distributed model.

This article investigates the distributed average tracking (DAT) problem for disturbed second-order multiagent systems, where a crowd of agents is required to track the average of the multiple time-varying signals. First, a new kind of distributed average estimator is developed for each agent to estimate the average of the multiple time-varying signals in finite time. The protocol possesses the distinguished feature of robustness to initialization errors, which can recover from network alterations. Then, an observer-based finite-time tracking protocol is proposed to make each agent exactly track the average of the multiple time-varying signals in finite time in the absence of velocity measurement. By carefully analyzing the dynamic properties of the tracking error system, a suitable Lyapunov function is constructed to estimate the settling time for convergence of the tracking error system theoretically. Furthermore, an adaptive DAT protocol is proposed, which is a fully distributed protocol because it can solve the DAT problem without using any global information. Finally, two simulation examples are provided to verify the effectiveness of the methods.