Performance Index Function Research Articles

Variable Gain Prescribed Performance Control for Dynamic Positioning of Ships with Positioning Error Constraints

In this paper, a variable gain prescribed performance control law is proposed for dynamic positioning (DP) of ships with positioning error constraints, input saturation and unknown external disturbances. The error performance index functions are designed to preset the prescribed performance bounds and the error mapping functions are constructed to incorporate the prescribed performance bounds into the DP control design. The variable gain technique is used to limit the output amplitude of the control law to avoid input saturation of the system by dynamically adjusting the control gain of the DP control law according to the positioning errors, and the error mapping function replaces the positioning error as a recursive sliding-mode surface to realize the prescribed performance control of the system and guarantee the stability of the closed-loop system with variable control gains. It has been proved that the proposed DP control law can make the uniformly ultimately boundedness of all signals in the DP closed-loop control system. The numerical simulation results illustrate that the proposed control law can make the ship’s position and heading maintain at the desired value with positioning error constraints, enhance the non-fragility of the DP control law to the perturbation of system’s parameters and improve the system’s rejection ability to external disturbances.

Optimal consensus model-free control for multi-agent systems subject to input delays and switching topologies

In this paper, the optimal consensus control problem of the discrete-time multi-agent systems with switching topologies and input delays is investigated by adopting the adaptive dynamic programming method. Through introducing a new state variable, the original input-delayed system can be transformed into a delay-free one. Then, a novel local performance index function is designed for each agent to eliminate the impact of switching topologies, which does not explicitly rely on the information of neighbors. Based on Bellman optimality principle, Lyapunov stability theorem and deep reinforcement learning method, the stability of the error system and the optimality of the value function are proved. In order to solve the consensus problem of the unknown systems, we propose a new value iteration algorithm based on the input and output data of the system, which can not only guarantee the achievement of consensus but also minimize the performance index function. Finally, two numerical simulations based on actor-critic neural networks are given, including the following two cases: periodic switching topologies and Markov switching topologies, to verify the effectiveness of the proposed optimal control scheme.

Particle-Swarm-Optimization-Based 2D Output Feedback Robust Constraint Model Predictive Control for Batch Processes

For the input and output constraints and uncertainties in batch processes, a 2D output feedback robust constrained model predictive control (MPC) method is designed by combining iterative learning control (ILC), MPC and output feedback. Firstly, an equivalent 2D-FM closed-loop prediction model is established by combining with the proposed output feedback controller. Then an optimization performance index function with terminal constraint is constructed to study its control optimization. According to the designed optimization performance index and Lyapunov stability theory, the feasible MPC problem is obtained by solving the linear matrix inequalities (LMIs). At the same time, the gain of the new output feedback control law is given to ensure that the performance index reaches the minimum upper bound under the constraints of input and output. In order to solve the manual adjustment problem of some parameters in the performance index function, the particle swarm optimization (PSO) algorithm is introduced, and a better solution is found near the controller by using the search optimization method. Finally, taking the injection molding process as an example and comparing with the existing method without using PSO algorithms, it is proved that the above method is more feasible.

Optimal Configuration Based on Lever Arm Effect Rejection Performance Index for Redundant Inertial Sensors

Redundant inertial sensor systems improve navigation performance and guarantee fault detection or fault isolation functions. However, they may cause unexpected side effects owing to their enlarged size. The misalignment between the center of gravity of the sensor system and the rotational origin of the vehicle results in the lever arm effect inducing significant acceleration errors. To minimize the lever arm effect error, the configuration of redundant sensors should be carefully considered, as their performance is highly dependent on its configuration. Thus, the figure-of-merit (FOM), which is considered a performance index or cost function, is proposed to obtain the optimal configuration for minimizing the lever arm effect error. Further, to define an FOM the angular velocity and angular acceleration are considered as random variables and to quantify them, they were replaced as variances. The lever arm effect error was found to be completely eliminated when a redundant inertial measurement unit (RIMU) with more than eight single-axis inertial sensors was configured using the proposed FOM. Further, a case study and simulation were conducted to verify the proposed FOM and configuration, and it was found that the proposed FOM can be used to obtain the optimal configuration of the RIMU and as an indicator of the lever arm effect error.

Design and HIL Realization of an Online Adaptive Dynamic Programming Approach for Real-Time Economic Operations of Household Energy Systems

Stochastic, nonlinear and time-varying factors bring great challenges to accurate modeling and design of real-time (RT) energy management systems (EMSs) for modern energy systems with intermittent renewable energy sources. In this paper, we propose a novel model-free RT-EMS based on the predictive adaptive dynamic programming (ADPredictive) algorithm for energy scheduling problems in a home EMS environment. The proposed RT-ADPreditive EMS can minimize the total cost of electricity, reduce battery life loss, and maximize the utilization of renewable energy generation. In the proposed RT-ADPredictive EMS, the gated recurrent unit (GRU) neural network (NN) is employed to perform online prediction of renewable energy generation and load consumption of the household based on RT data. The RT-ADPreditive algorithm can approximate the performance index function and the optimal control law based on the RT data and predicted data for the next time step. Convergence of the proposed method is mathematically proven, and a hardware-in-the-loop (HIL) experimental platform comprising dSPACE and RT-lab is built to verify the effectiveness of the proposed RT-ADPreditive home EMS.

Adaptive Event-Triggered Near-Optimal Tracking Control for Unknown Continuous-Time Nonlinear Systems

This paper studies the event-triggered optimal tracking control (ETOTC) problem of continuous-time (CT) unknown nonlinear systems. In order to solve the ETOTC problem, an augmented system composed of the error system dynamics and the reference dynamics is used to introduce a new discounted performance index function (DPIF). A novel event-triggered (ET) adaptive dynamic programming (ADP) method is developed to solve the ET Hamilton-Jacobi-Bellman equation (HJBE). The presented method is implemented via an identifier-critic architecture, which consists of two neural networks (NNs): an identifier NN is applied to estimate the unknown system dynamics, and a critic NN is constructed to obtain the approximate solution of the ET HJBE. The augmented closed-loop system and the critic estimation error are proved to be ultimately uniformly bounded (UUB) by the Lyapunov direct method. Finally, two simulations illustrate the effectiveness of the developed method.

A new ‐gain analysis framework for discrete‐time switched systems based on predictive Lyapunov function

AbstractThe work proposes the pre‐‐gain analysis framework based on the newly raised nonweighted pre‐‐gain performance index and predictive Lyapunov function, which is devoted to nonweighted ‐gain analysis and relevant control of discrete‐time switched systems under mode‐dependent average dwell time. This also provides new ideas for other disturbance‐related studies. To begin with, the predictive Lyapunov function is established for switched nonlinear systems in the sense of better reflecting future system dynamics and future external disturbances. Hence, it is achievable to develop less conservative stability and nonweighted pre‐‐gain criteria for switched linear systems. Further, a new disturbance‐output expression is devised to match with the nonweighted pre‐‐gain, whose function is to estimate and optimize the traditional nonweighted ‐gain of the underlying system through discussions. Then, a solvable condition is formulated to seek the piecewise time‐dependent gains of switching controller in a convex structure, ensuring the global uniform exponential stability with nonweighted pre‐‐gain and thereby attaining much smaller non‐weighted ‐gain. Finally, the simulation comprised of a circuit system and a numerical example manifests the impressive potential of the obtained results for the purpose of preferable disturbance attenuation performances.

Optimal Control Problem for Cholera Disease and Cost-Effectiveness Analysis

Cholera is a disease that continues to be a threat to public health globally and is an indicator of inequity and lack of social development in countries. For this reason, strategies for its control need to be investigated. In this work, an optimal control problem related to cholera disease was formulated by introducing personal protection, drug treatment and water sanitation as control strategies. First, the existence and characterization of controls to minimize the performance index or cost function was proved by using classic control theory. Then, the theoretical results were validated with numerical experiments by using data reported in the literature. Finally, the effectiveness and efficiency of the proposed controls were determined through a cost-effectiveness analysis. The results showed that the use of the three controls simultaneously is the cheapest and most effective strategy to control the disease.

Optimization of Energy Saving and Fuel Cell Durability for Range-Extended Electric Vehicle

For the fuel cell-range extended electric vehicle (FC-REEV), the fuel cell system can work at a fixed output power point and have a good durability. However, the differences in output power and start-stop threshold can lead to a significant difference in energy loss and degradation of power sources. Based on the thermostat control strategy (TCS), the economy of vehicle is considered in the evaluation function. Furtherly, the artificial bee colony (ABC) optimization algorithm is used to increase driving range, the conventional ABC-TCS(CABC-TCS) was proposed. However, the CABC-TCS leads to a large number of start-stop times for fuel cell. In order to improve the durability of fuel cell, a penalty factor is added in the performance index function, and a novel optimized ABC-TCS (OABC-TCS) is proposed. Different strategies are tested under FTP-72 and WLTC drive cycle respectively, result shows that compared with TCS, the optimized driving range proportion of OABC-TCS is about 10.59% and 10.3%. Compared with CABC-TCS, the start-stop times of OABC-TCS conditions is decreased by 27.55times/h and 46.47 times/h respectively.

A Novel DSP-Based MPPT Control Design for Photovoltaic Systems Using Neural Network Compensator

In this study, based on the slope of power versus voltage, a novel maximum-power-point tracking algorithm using a neural network compensator was proposed and implemented on a TI TMS320F28335 digital signal processing chip, which can easily process the input signals conversion and the complex floating-point computation on the neural network of the proposed control scheme. Because the output power of the photovoltaic system is a function of the solar irradiation, cell temperature, and characteristics of the photovoltaic array, the analytic solution for obtaining the maximum power is difficult to obtain due to its complexity, nonlinearity, and uncertainties of parameters. The innovation of this work is to obtain the maximum power of the photovoltaic system using a neural network with the idea of transferring the maximum-power-point tracking problem into a proportional-integral current control problem despite the variation in solar irradiation, cell temperature, and the electrical load characteristics. The current controller parameters are determined via a genetic algorithm for finding the controller parameters by the minimization of a complicatedly nonlinear performance index function. The experimental result shows the output power of the photovoltaic system, which consists of the series connection of two 155-W TYN-155S5 modules, is 267.42 W at certain solar irradiation and ambient temperature. From the simulation and experimental results, the validity of the proposed controller was verified.

Modified Model Free Adaptive Control for a Class of Nonlinear Systems with Multi-threshold Quantized Observations

This paper addresses a pattern-moving-based modified model free adaptive control (PMFAC) scheme and illustrates the convergence of its tracking error for a class of nonlinear systems with unknown model and multi-threshold quantized observations. The basic idea is to consider the system’s quantization error as an external disturbance and an improved performance index function of control law is proposed from the perspective of two-player zero-sum game (TP-ZSG) based on the existed MFAC algorithms. The PMFAC scheme is established which mainly includes an improved tracking control law and a pseudo-partial derivative (PPD) estimation algorithm. Under certain conditions, the bounded convergence of system tracking error and the stability of PMFAC system with quantization errors can be guaranteed. The theoretical results are demonstrated by two numerical examples.

Finite-time fuzzy game-based attitude control for on-orbit cooperative transporting

Substructure transporting is an important phase for on-orbit assembly. This paper investigates a problem of designing a control approach for multiple transporting agents attached to one substructure, so as to complete the task of attitude tracking and stabilization of the substructure in the transportation process. A finite-time fuzzy game control method is developed to solve this problem. Using the framework of differential game, a finite-time nonlinear game is formulated based on the individual performance index functions of agents and attitude dynamics of the combination consisting of transporting agents and the substructure, which can reflect the cooperation and coordination between agents. In order to realize finite-time convergence which is more suitable for engineering requirement, a speed function is introduced to transfer finite-time game into infinite-time game. Considering the limited computational ability of agents, Takagi-Sugeno (T-S) fuzzy is incorporated to divide the nonlinear game problem into weighted average of multiple linear games which are easy to get the Nash equilibrium. Numerical simulations validate the efficiency of the proposed method for attitude control and the advantage in less calculation and better performance in dynamics and steady state than the existing methods.

Tracking control of transition window for aerospace vehicles based on robust preview control

The transition window of aerospace vehicles (ASVs) is defined as the connection point of different flight phases or the engine mode transition point. For ASVs, one of the critical problems is the precise tracking of transition window that would enable the engine to implement the mode transition successfully. Since the engine of ASVs is independently controlled, it is required that ASV eliminates both velocity and position tracking errors within a specified time to reach the transition window accurately. In addition, the tracking control of ASVs is affected by uncertain aerodynamic parameter, initial deviation, and control constraint. Therefore, an innovative tracking control of transition window (TWTC) scheme is developed, which is composed of transient reference trajectory generation and control modules. A dynamic transient trajectory is generated to modify the tracking command to expand the initial feasible region. A piecewise robust preview control algorithm is presented for the control module design, which fuses the preview information of the reference signal, control constraint, equality constraint of ASV dynamics, and performance index function. Simulation results of a nonlinear ASV model show the effectiveness of TWTC scheme under uncertain aerodynamic parameters and initial deviations.

Compensator-critic structure-based event-triggered decentralized tracking control of modular robot manipulators: theory and experimental verification

This paper presents a novel compensator-critic structure-based event-triggered decentralized tracking control of modular robot manipulators (MRMs). On the basis of subsystem dynamics under joint torque feedback (JTF) technique, the proposed tracking error fusion function, which includes position error and velocity error, is utilized to construct performance index function. By analyzing the dynamic uncertainties, a local dynamic information-based robust controller is designed to engage the model uncertainty compensation. Based on adaptive dynamic programming (ADP) algorithm and the event-triggered mechanism, the decentralized tracking control is obtained by solving the event-triggered Hamilton–Jacobi–Bellman equation (HJBE) with the critic neural network (NN). The tracking error of the closed-loop manipulators system is proved to be ultimately uniformly bounded (UUB) using the Lyapunov stability theorem. Finally, experimental results illustrate the effectiveness of the developed control method.

Decentralized optimal tracking control for large‐scale nonlinear systems with tracking error constraints

SummaryIn this article, a decentralized optimal tracking control strategy is proposed for a class of nonlinear systems with tracking error constraints by utilizing adaptive dynamic programming (ADP). It should be noted that ADP technology cannot be directly used to solve decentralized optimal tracking problem of large‐scale interconnected nonlinear system with nonzero equilibrium points, since that an infinite domain performance index function may result in an unsolvable solution. In addition, by introducing a smooth function, the constrained tracking error is transformed into an unconstrained one. Then, the error dynamics and a new infinite domain performance index function are designed, such that ADP technology can be used. Following the designed performance index function, the tracking error can be ensured within a small neighborhood of zero. Finally, the feasibility and the effectiveness of the proposed decentralized optimal control scheme are verified through two simulation examples.

Learning‐based control for discrete‐time constrained nonzero‐sum games

A generalized policy-iteration-based solution to a class of discrete-time multi-player non-zero-sum games concerning the control constraints was proposed. Based on initial admissible control policies, the iterative value function of each player converges to the optimum approximately, which is structured by the iterative control policies satisfying the Nash equilibrium. Afterwards, the stability analysis is shown to illustrate that the iterative control policies can stabilize the system and minimize the performance index function of each player. Meanwhile, neural networks are implemented to approximate the iterative control policies and value functions with the impact of control constraints. Finally, two numerical simulations of the discrete-time two-player non-zero-sum games for linear and non-linear systems are shown to illustrate the effectiveness of the proposed scheme.

Local path optimization method for unmanned ship based on particle swarm acceleration calculation and dynamic optimal control

Dynamic local path optimization is an essential guarantee for unmanned ships to maintain navigation safety at all times. In existing studies, one noticeable limitation is the computational time, which is significantly increased with the number of obstacles, that makes it difficult to ensure the dynamic optimization of cruise paths for unmanned ships under time-varying conditions. And on this basis, a local path optimization method for unmanned ships based on particle swarm acceleration calculation and dynamic optimal control was proposed in this study. Firstly, an equation of motion of the ship was studied. The path constraints, boundary value constraints, and performance index functions were taken into account to established a mathematical model for the dynamic optimization of the local path. Secondly, based on the principles of navigation safety and timeliness of ships, the particle swarm optimization algorithm was applied to solve the model. Thirdly, the simulation results showed that the model was feasible and effective for local path optimization in dynamic navigation environments with multiple moving obstacle ships. It could provide a theoretical research foundation for studies regarding dynamic optimization of the local path for unmanned ships.

Neural-Network-Based Control for Discrete-Time Nonlinear Systems with Input Saturation Under Stochastic Communication Protocol

In this paper, an adaptive dynamic programming (ADP) strategy is investigated for discrete-time nonlinear systems with unknown nonlinear dynamics subject to input saturation. To save the communication resources between the controller and the actuators, stochastic communication protocols (SCPs) are adopted to schedule the control signal, and therefore the closed-loop system is essentially a protocol-induced switching system. A neural network (NN)-based identifier with a robust term is exploited for approximating the unknown nonlinear system, and a set of switch-based updating rules with an additional tunable parameter of NN weights are developed with the help of the gradient descent. By virtue of a novel Lyapunov function, a sufficient condition is proposed to achieve the stability of both system identification errors and the update dynamics of NN weights. Then, a value iterative ADP algorithm in an offline way is proposed to solve the optimal control of protocol-induced switching systems with saturation constraints, and the convergence is profoundly discussed in light of mathematical induction. Furthermore, an actor-critic NN scheme is developed to approximate the control law and the proposed performance index function in the framework of ADP, and the stability of the closed-loop system is analyzed in view of the Lyapunov theory. Finally, the numerical simulation results are presented to demonstrate the effectiveness of the proposed control scheme.

Guaranteed Cost Control Research for Networked Control System with Time-Varying Sampling Period

In practical industrial applications, the networked control system is often affected by external factors and internal components in operation, which leads to the fluctuation of some data transmitted by the system and reduces the system performance. Therefore, to ensure the normal operation of the system is the key, on this basis, we also need to make the system satisfy certain performance indicators. In this paper, guaranteed cost control for networked control systems with time delay and time-varying sampling period is studied. By constructing a more general system model, we give a design method of guaranteed performance controller to make the closed-loop system asymptotically stable within the allowable range and and satisfies certain performance indicators. Firstly, we construct the reasonable Lyapunov function and performance index function. According to the relevant lemma, the sufficient conditions for the stability of the system are obtained by equivalent transformation of LMI. Then, we design a guaranteed performance controller to minimize the upper bound of the system performance index. In the design process, more free variables are introduced, and the convexity of the function is used for equivalent transformation as far as possible to make the results less conservative. Finally, we use MATLAB to simulate and prove that the method is feasible.

Arthroscopic Osteocapsular Arthroplasty with Mini-Open Ulnar Nerve Decompression for Elbow Arthritis

Patients with elbow osteoarthritis present with painful limited motion and report ulnar nerve symptoms occasionally. Arthroscopic osteocapsular arthroplasty for arthritis have showed pain relief and improved range of motion. However, few studies about treatment and outcomes of concomitant ulnar neuropathy have been reported. The purpose of this study was to evaluate clinical outcomes after arthroscopic osteocapsular arthroplasty combined with ulnar nerve decompression for the treatment of elbow osteoarthritis with concomitant ulnar neuropathy. Among 45 patients with elbow osteoarthritis underwent arthroscopic osteocapsular arthroplasty, 22 patients with preoperative concomitant ulnar neuropathy were included in this study. Surgical procedures included arthroscopic debridement and capsulectomy with miniopen ulnar nerve decompression. Preoperatively, extent of ulnar nerve dysfunction was classified according to the McGowan stage. Postoperative elbow function was assessed using VAS, range of motion, and Mayo Elbow Performance Index (MEPI) and ulnar nerve function was assessed using the modified Bishop score. At a mean follow-up of 21 months, significant improvement occurred in the mean pain, from VAS 4.1 to 1.5and total arc of motion, from 95° to 115°. Average MEPI scores were 67 preoperatively and 85 at final follow-up and 81% of patients showed good to excellent results according to MEPI scores. Improvement of paresthesia and weakness were noted in 18 cases and and 16 cases respectively. According to the modified Bishop score, 10 patients had excellent, 7 good, 3 fair and 2 poor results. Arthroscopic osteocapsular arthroplasty combined with miniopen decompression of the ulnar nerve showed satisfactory outcomes in patients with elbow arthritis concomitant ulnar neuropathy. Miniopen ulnar nerve decompression was safe and effective procedure and can be indicated for ulnar neuropathy in the setting of elbow osteoarthritis.