Event-triggered Optimal Control Research Articles

Neural network-based adaptive critic control for saturated nonlinear systems with full state constraints via a novel event-triggered mechanism

This paper investigates the issue of event-triggered optimal control for saturated nonlinear systems with full state constraints. A smooth function is defined to map the constrained states, then the considered system can be transformed into a state unconstrained system with unknown approximate errors. In addition, a novel event-triggered mechanism is proposed via an adaptive dynamic programming algorithm, which can obtain the optimal control law without constructing the so-called event-triggered HJB equation. Moreover, in order to conquer the difficulty caused by the persistence of excitation conditions, the experience replay technique is utilized to design the critic update law. Meanwhile, it is demonstrated that all signals are uniformly ultimately bounded. Finally, two simulation examples are given to demonstrate the effectiveness of the control strategy.

Intermittent Event-Triggered Optimal Control for Second-Order Delayed Multiagent Systems With Input Constraints

Intermittent Event-Triggered Optimal Control for Second-Order Delayed Multiagent Systems With Input Constraints

ADP-Based Event-Triggered Constrained Optimal Control on Spatiotemporal Process: Application to Temperature Field in Roller Kiln.

The precise control of the spatiotemporal process in a roller kiln is crucial in the production of Ni-Co-Mn layered cathode material of lithium-ion batteries. Since the product is extremely sensitive to temperature distribution, temperature field control is of great significance. In this article, an event-triggered optimal control (ETOC) method with input constraints for the temperature field is proposed, which takes up an important position in reducing the communication and computation costs. A nonquadratic cost function is adopted to describe the system performance with input constraints. First, we present the problem description of the temperature field event-triggered control, where this field is described by a partial differential equation (PDE). Then, the event-triggered condition is designed according to the information of system states and control inputs. On this basis, a framework of the event-triggered adaptive dynamic programming (ETADP) method that is based on the model reduction technology is proposed for the PDE system. A critic network is used to approach the optimal performance index by a neural network (NN) together with that an actor network is used to optimize the control strategy. Furthermore, an upper bound of the performance index and a lower bound of interexecution times, as well as the stabilities of the impulsive dynamic system and the closed-loop PDE system, are also proved. Simulation verification demonstrates the effectiveness of the proposed method.

Neuro-adaptive Event-triggered Optimal Control for Power Battery Systems With State Constraints

Neuro-adaptive Event-triggered Optimal Control for Power Battery Systems With State Constraints

Fuzzy Weight-Based Reinforcement Learning for Event-Triggered Optimal Backstepping Control of Fractional-Order Nonlinear Systems

Fuzzy Weight-Based Reinforcement Learning for Event-Triggered Optimal Backstepping Control of Fractional-Order Nonlinear Systems

Neuro-Optimal Event-Triggered Impulsive Control for Stochastic Systems via ADP.

This article presents a novel neural-network-based optimal event-triggered impulsive control method. First, a novel general-event-based impulsive transition matrix (GITM) is constructed to represent the probability distribution evolving characteristics regarding all system states across the impulsive actions, rather than the prefixed timing sequence. On the foundation of this GITM, the event-triggered impulsive adaptive dynamic programming (ETIADP) algorithm and its high-efficiency version (HEIADP) are developed to deal with the optimization problems for stochastic systems with event-triggered impulsive controls. It is shown that the obtained controller design scheme can reduce the computational and communication burden caused by updating the controller periodically. By analyzing the admissibility, monotonicity, and optimality properties of ETIADP and HEIADP, we further establish the approximation error bound of the neural networks to address the connection between the ideal and neural-network-based realizations of the present methods. It is proven that the iterative value functions of both the ETIADP and HEIADP algorithms fall in a small neighborhood of the optimum as the iteration index increases to infinity. By adopting a novel task synchronization mechanism, the proposed HEIADP algorithm fully utilizes the computing resources of multiprocessor systems (MPSs), while significantly reducing the memory requirement compared to traditional ADP approaches. Finally, we carry out a numerical study to show that the proposed methods can fulfill the desired goals.

A Novel Framework for Game-Based Optimal Event-Triggered Control of Multi-Input Nonlinear Systems

A Novel Framework for Game-Based Optimal Event-Triggered Control of Multi-Input Nonlinear Systems

Prescribed performance event-triggered fuzzy optimal tracking control for strict-feedback nonlinear systems

The prescribed performance event-triggered optimal tracking control problem is considered for a class of uncertain strict-feedback nonlinear systems with external disturbances. First, the disturbance observers are constructed to estimate external disturbances. Then, the controller contains an adaptive fuzzy controller and an optimal compensation term, in which the unknown nonlinearities and cost function are approximated by the fuzzy logic systems. An adaptive fuzzy controller is established by the dynamic surface control (DSC) technique, which is addressed to handle “computation complexity” issue occurred in conventional backstepping approach. Based on adaptive dynamic programming (ADP) method, an optimal compensation term is developed by minimizing the cost function. Furthermore, communication load is reduced via embedding event-triggered mechanism. In addition, the tracking error can be restricted in the prescribed region with the aid of the prescribed performance control. Thus, the whole control scheme can not only ensure that the tracking error converges to a boundary but also achieve optimization, reduce the communication burden and avoid “computation complexity” issue. The boundedness of all signals in the closed-loop is proved. Finally, the simulation examples illustrate the validity of the designed control scheme.

Observer-based event-triggered recursive optimal tracking control for a class of strict-feedback nonlinear systems

In this paper, an innovative event-triggered optimal tracking control algorithm is proposed for input saturated strict-feedback nonlinear systems with unknown dynamics. In order to reduce the requirement of configuring a complete suit of sensors and enhance the reliability of the controlled system, a neural networks (NNs) based adaptive state observer is developed firstly to reconstruct the system states. Subsequently, based on the state estimation information, a hybrid-triggered feedforward controller is designed to transform the original tracking control problem into an equivalent regulation issue, which is then solved by developing an event-triggered optimal controller. Therefore, the final controller consists of a hybrid-triggered feedforward controller and an event-triggered optimal controller. In order to make the actual input signals of the two controllers be updated simultaneously, a synchronization-oriented triggering rule is established by using multiple triggering errors. By virtue of this unique framework, the proposed control scheme can not only minimize the predefined cost function, but also greatly reduce the data transmission. What is more, the convergence properties of the proposed control strategy are achieved by using Lyapunov theory. It is important to note that unlike the widely adopted observer-controller framework, where the separation principle holds for the design of the state observer, there is a considerable coupling relationship between the error dynamics of the state observer and the event-triggered optimal controller in this paper. The distinguishing feature of the proposed method is its ability to ensure a satisfactory level of precision in both state estimation and tracking control, even in the presence of control saturation issues. At last, the proposed control strategy is applied to the tracking control problem of a high-order robot system and marine surface vehicle to demonstrate its effectiveness.

Distributed edge-based event-triggered optimal formation control for air-sea heterogeneous multiagent systems

This paper addresses the optimal formation control problem for a class of air-sea heterogeneous multiagent systems with external disturbances and model uncertainties. Multiple unmanned aerial vehicles (UAVs) and multiple unmanned surface vessels (USVs) are considered in this system. First, a distributed adaptive state compensator is designed for each agent to estimate the state information of the virtual leader. This compensator is equipped with an edge-based event-triggered scheme to reduce the amount of communication for each edge. Second, a reinforcement learning-based optimal formation controller with the appointed-time prescribed performance is designed to obtain the formation configuration for an air-sea system. This method not only optimizes the formation controller but also ensures the steady-state accuracy and stabilization time. Additionally, an event-triggered mechanism is proposed to reduce the number of optimal formation controller communications. A self-structuring actor-critic neural network and a self-structuring radial basis function neural network are also proposed to solve the Hamilton-Jacobi-Bellman (HJB) equation and approximate the uncertainty, respectively. It can constantly adjust the number of neurons, eventually obtaining an optimal number. Finally, it is proven by Lyapunov theory that all signals are semiglobally uniform and eventually bounded, and the simulation results are provided to illustrate the effectiveness of the scheme.

Event-Triggered Adaptive Fuzzy Optimal Control for a Class of Strict-Feedback Nonlinear Systems With External Disturbances

In this paper, the problem of the event-triggered optimal control for a class of strict-feedback nonlinear systems with external disturbances is investigated. Firstly, by introducing proper low-pass filters to the steps of backstepping design, the problem of “jump of the error surfaces” is avoided. What's more, it facilitates the design of a fuzzy hybrid-mode-triggered feedforward controller, which aims to transform the original controlled nonlinear strict-feedback system into an equivalent nonlinear system in affine form. Secondly, by utilizing the adaptive dynamic programming theory, an event-triggered feedback controller is developed for the equivalent affine nonlinear system. Differing from the existing methods, the real control input consists of two event-triggered terms, which can be updated synchronously under the proposed composite error-based triggering condition. Moreover, it is proven that all the closed-loop signals are bounded. At last, by taking a second-order nonlinear system and missile integrated guidance and control system as examples, simulation results demonstrate the effectiveness of the proposed approach.

Adaptive critic learning for approximate optimal event-triggered tracking control of nonlinear systems with prescribed performances

This paper studies the approximate optimal event-triggered tracking control problem for a class of second-order nonlinear systems with prescribed performances. By employing a prescribed performances function, restrictions on tracking errors are removed for prescribed performances including convergence rate, maximum overshoot, and steady-state error. On this basis, a complex optimal tracking control problem can be transformed into an optimal stabilising control problem by constructing an augmented system. Subsequently, an event-triggered mechanism is introduced to reduce communication resources. Then, an adaptive critic learning algorithm is used to solve the Hamilton-Jacobi-Bellman equation, where the weights in the critic networks are tuned through the gradient descent approach and experience replay technology. Through the developed learning method, the persistence of excitation condition is released, and the data efficiency is improved. The Lyapunov stability theory is introduced to verify the stability of the close-loop system and the tracking errors are uniformly ultimately bounded. Finally, simulation results are presented to show the effectiveness of the proposed approach.

Finite-Time Multiparty Synchronization of T–S Fuzzy Coupled Memristive Neural Networks With Optimal Event-Triggered Control

This paper considers multiparty synchronization (MS) for coupled memristive neural networks (CMNNs) with a time delay. Some T-S type If-Then fuzzy rules are also introduced into the CMNNs. An event-triggered controller (ETC) is designed to achieve the MS in finite time, which avoids continuous control signals. Along with Lyapunov theory, differential inclusion theory, and inequalities, some criteria can be obtained to achieve the finite-time MS (FTMS), and the setting time (ST) of the FTMS can be calculated. By jointly considering ST, control inputs, error networks, and synchronization conditions, an optimization model is provided to get an optimal ETC (OETC). Further, the particle swarm optimization (PSO) algorithm is utilized to solve the optimization model. Thus, it gives a method to choose control gains and parameters of an event-triggered function (ETF). Finally, two examples are given to verify the theoretical results. Especially, two comparative experiments are proposed to demonstrate that the OETC can save more control energy and reduce the number of triggered times.

Collision-Risk-Based Event-Triggered Optimal Formation Control for Mobile Multiagent Systems Under Incomplete Information Conditions

This article deals with collision-risk-based event-triggered optimal formation control problems for mobile multiagent systems. First, several collision-risk-related definitions, such as collision-free margin, moving direction angle, collision risk angle, and collision risk level, are proposed for the moving agents. Then, a collision-risk dependent, time-varying, event-triggered heterogeneous communication network topology is developed, where the agent starts obtaining information of the neighboring agents only when collision risks occur among them. Third, an anti-collision control law, which is composed of a switch function, a control force direction function, and a control strength function, is designed to guarantee the collision avoidance formation of multiagents. Fourth, to ensure the formation quality and save control cost of the multiagent system, an optimal formation control scheme with feedforward compensation is designed. Simulation results illustrate that: 1) by using the collision risk information of mobile agents, the proposed control scheme is effective to realize the collision avoidance optimal formation task and 2) the anti-collision formation controller can be implemented with incomplete information of the agents.

Intermittent Event-Triggered Optimal Leader-Following Consensus for Nonlinear Multi-Agent Systems Via Actor-Critic Algorithm.

This article investigates the intermittent event-triggered optimal leader-following consensus for nonlinear multi-agent systems (MASs) utilizing the actor-critic algorithm. First, we propose a novel distributed intermittent event-triggered control strategy, and a sufficient criterion is obtained to guarantee the leader-following consensus of MASs by establishing a novel piecewise differential inequality. Next, the intermittent event-triggered optimal control strategy is delicately given. Remarkably, the optimality of MASs is proven based on policy iteration and the convergence of the closed-loop system is also proved based on the Lyapunov stability theory. Then, the intermittent event-triggered approximate optimal control strategy is designed via an actor-critic network whose weights are only updated at the trigger instants. Furthermore, the Zeno behavior can be excluded in this article. Finally, two simulation examples further verify the effectiveness of the proposed scheme.

Event-triggered optimal control of completely unknown nonlinear systems via identifier-critic learning

Event-triggered optimal control of completely unknown nonlinear systems via identifier-critic learning

Observer-based event-triggered optimal control for unknown nonlinear stochastic multi-agent systems with input constraints

This paper addresses the observer-based event-triggered optimal control (ETOC) for unknown nonlinear Ito^-type stochastic multi-agent systems (SMASs) with input constraints. To begin with, the event-triggered stochastic Hamilton-Jacobi-Bellman (HJB) equation with input constraints is presented, and a sufficient criterion on optimal mean-square leader-following consensus of constrained-input SMASs is derived. Next, a novel event-triggered policy iteration algorithm of constrained-input SMASs is designed to obtain the ETOC strategy. Then, an identifier-critic framework is designed where the observer-based identifier network is utilized to recover the knowledge of unknown stochastic dynamics and the constrained-input approximate event-triggered optimal controller is designed via event-triggered adaptive critic designs (ET-ACDs). Moreover, it is proved that the Zeno behavior can be excluded in the sense of expectation. Finally, we present two examples to further verify the validity of the ETOC scheme.

Event-Triggered Optimal Adaptive Control of Partially Unknown Linear Continuous-Time Systems With State Delay

Event-Triggered Optimal Adaptive Control of Partially Unknown Linear Continuous-Time Systems With State Delay

Event-triggered fault-tolerant control for input-constrained nonlinear systems with mismatched disturbances via adaptive dynamic programming

In this paper, the issue of event-triggered optimal fault-tolerant control is investigated for input-constrained nonlinear systems with mismatched disturbances. To eliminate the effect of abrupt faults and ensure the optimal performance of general nonlinear dynamics, an adaptive dynamic programming (ADP) algorithm is employed to develop a sliding mode fault-tolerant control strategy. When the system trajectories converge to the sliding-mode surface, the equivalent sliding mode dynamics is transformed into a reformulated auxiliary system with a modified cost function. Then, a single critic neural network (NN) is adopted to solve the modified Hamilton–Jacobi–Bellman (HJB) equation. In order to overcome the difficulty that arises from the persistence of excitation (PE) condition, the experience replay technique is utilized to update the critic weights. In this study, a novel control method is proposed, which can effectively eliminate the effects of abrupt faults while achieving optimal control with the minimum cost under a single network architecture. Furthermore, the closed-loop nonlinear system is proved to be uniformly ultimate boundedness based on Lyapunov stability theory. Finally, three examples are presented to verify the validity of the control strategy.

Event-Triggered Optimal Control for Temperature Field of Roller Kiln Based on Adaptive Dynamic Programming.

Temperature field control is crucial for the comprehensive performance of Ni-Co-Mn layered cathode material that is the most important part of lithium-ion batteries. Starting from the aspect of a class of distributed parameter systems described by highly dissipative partial differential equations (PDEs), an event-triggered optimal control (ETOC) method based on adaptive dynamic programming (ADP) for the roller kiln temperature field is proposed. First, we formulate the event-triggered control problem of the temperature field under the general framework of PDE systems. Then, an event-triggered condition is designed based on the stability of the closed-loop PDE system, which also guarantees the upper bound of the performance index. Subsequently, ADP technology is adopted to realize the ETOC, where the critic network is employed to approximate the optimal value function. Since the studied system can be regarded as an impulsive dynamic system with flow dynamics and jump dynamics simultaneously, the stability of the impulsive dynamic system combined with the ADP-based closed-loop PDE system is proved. Finally, simulation results on the temperature field verify the effectiveness of the proposed method.