Event-based Control Research Articles

Dynamic Event-Based Control for Stochastic Optimal Regulation of Nonlinear Networked Control Systems.

In this article, a dynamic event-triggered stochastic adaptive dynamic programming (ADP)-based problem is investigated for nonlinear systems with a communication network. First, a novel condition of obtaining stochastic input-to-state stability (SISS) of discrete version is skillfully established. Then, the event-triggered control strategy is devised, and a near-optimal control policy is designed using an identifier-actor-critic neural networks (NNs) with an event-sampled state vector. Above all, an adaptive static event sampling condition is designed by using the Lyapunov technique to ensure ultimate boundedness (UB) for the closed-loop system. However, since the static event-triggered rule only depends on the current state, regardless of previous values, this article presents an explicit dynamic event-triggered rule. Furthermore, we prove that the lower bound of sampling interval for the proposed dynamic event-triggered control strategy is greater than one, which avoids the so-called triviality phenomenon. Finally, the effectiveness of the proposed near-optimal control pattern is verified by a simulation example.

Influence of pH and dissolved oxygen control strategies on the performance of pilot-scale microalgae raceways using fertilizer or wastewater as the nutrient source

Dissolved oxygen concentration and pH are controllable and cost-effective variables that determine the success of microalgae-related processes. The present study compares different control strategies for pH and dissolved oxygen in pilot-scale microalgae production systems. Two 80 m2 raceway reactors were used, one operated with freshwater plus fertilizer and the other with wastewater as the nutrient source. Both were in semi-continuous mode at a fixed dilution rate of 0.2 day−1. A comparison between the classical On-Off and more advanced pH control strategies, such as PI and Event-based control, was performed, focusing on biomass productivity and the influence of all the process parameters on microalgae growth; "No control" of pH was also assayed. The results show that Event-based control was the best algorithm when using freshwater plus fertilizer. In contrast, no significant differences were observed using the different control strategies when wastewater was the nutrient source. These experiments were performed through selective control strategy, prioritizing pH over dissolved oxygen; however, it was demonstrated that they did not allow to achieve satisfactory dissolved oxygen removal results, especially for the fertilizer system. After modifying the gas diffuser configuration and improving the mass transfer, independent on-off strategies have been developed, permitting effective control of both variables and increasing productivity by up to 20% in both systems. Concluding, a detailed analysis of the energy demand for each strategy implemented in terms of gas consumption and gas flow to biomass ratio is provided.

Adaptive Critic for Event-Triggered Unknown Nonlinear Optimal Tracking Design With Wastewater Treatment Applications.

In this article, an event-based near-optimal tracking control algorithm is developed for a class of nonaffine systems. First, in order to gain the tracking control strategy, the costate function is established through the iterative dual heuristic dynamic programming (DHP) algorithm. Then, the event-based control method is employed to improve the utilization efficiency of resources and ensure that the closed-loop system has an excellent control performance. Meanwhile, the input-to-state stability (ISS) is proven for the event-based tracking plant. In addition, three kinds of neural networks are used in the event-based DHP algorithm, which aims to identify the nonaffine nonlinear system, estimate the costate function, and approximate the tracking control law. Finally, a numerical experimental simulation is conducted to verify the effectiveness of the proposed scheme. Moreover, in order to further validate the feasibility, the algorithm is applied to the wastewater treatment plant to effectively control the concentrations of dissolved oxygen and nitrate nitrogen.

Scalability of Cyber-Physical Systems with Real and Virtual Robots in ROS 2.

Nowadays, cyber-physical systems (CPSs) are composed of more and more agents and the demand for designers to develop ever larger multi-agent systems is a fact. When the number of agents increases, several challenges related to control or communication problems arise due to the lack of scalability of existing solutions. It is important to develop tools that allow control strategies evaluation of large-scale systems. In this paper, it is considered that a CPS is a heterogeneous robot multi-agent system that cooperatively performs a formation task through a wireless network. The goal of this research is to evaluate the system's performance when the number of agents increases. To this end, two different frameworks developed with the open-source tools Gazebo and Webots are used. These frameworks enable combining both real and virtual agents in a realistic scenario allowing scalability experiences. They also reduce the costs required when a significant number of robots operate in a real environment, as experiences can be conducted with a few real robots and a higher number of virtual robots by mimicking the real ones. Currently, the frameworks include several types of robots, such as the aerial robot Crazyflie 2.1 and differential mobile robots Khepera IV used in this work. To illustrate the usage and performance of the frameworks, an event-based control strategy for rigid formations varying the number of agents is analyzed. The agents should achieve a formation defined by a set of desired Euclidean distances to their neighbors. To compare the scalability of the system in the two different tools, the following metrics have been used: formation error, CPU usage percentage, and the ratio between the real time and the simulation time. The results show the feasibility of using Robot Operating System (ROS) 2 in distributed architectures for multi-agent systems in experiences with real and virtual robots regardless of the number of agents and their nature. However, the two tools under study present different behaviors when the number of virtual agents grows in some of the parameters, and such discrepancies are analyzed.

Event-triggered finite-time stabilization of nonlinear switched affine systems under mode-dependent and state-dependent switchings

This paper investigates the event-triggered finite-time stabilization (FTS) problem of nonlinear switched affine systems (NSASs) under mode-dependent and state-dependent switching signals, respectively. Firstly, an event-triggered control (ETC) strategy for NSASs with mode-dependent average dwell time constraint is proposed. Note that the presence of affine terms gives rise to difficulties in the exclusion of Zeno behavior for the widely-adopted triggering mechanism consisting of current state and error information. Therefore, a novel triggering mechanism including affine term threshold is proposed to exclude Zeno behavior. Secondly, an event-triggered impulsive control strategy for NSASs under autonomous state-dependent switching is studied. Some Lyapunov-based criteria and a state-dependent switching law for FTS are presented. Moreover, the established event-based control strategies are applied to FTS of boost converter to illustrate the effectiveness of the proposed results.

Approximate Optimal Control for Nonlinear Systems With Periodic Event-Triggered Mechanism.

This article investigates the approximate optimal control problem for nonlinear affine systems under the periodic event triggered control (PETC) strategy. In terms of optimal control, a theoretical comparison of continuous control, traditional event-based control (ETC), and PETC from the perspective of stability convergence, concluding that PETC does not significantly affect the convergence rate than ETC. It is the first time to present PETC for optimal control target of nonlinear systems. A critic network is introduced to approximate the optimal value function based on the idea of reinforcement learning (RL). It is proven that the discrete updating time series from PETC can also be utilized to determine the updating time of the learning network. In this way, the gradient-based weight estimation for continuous systems is developed in discrete form. Then, the uniformly ultimately bounded (UUB) condition of controlled systems is analyzed to ensure the stability of the designed method. Finally, two illustrative examples are given to show the effectiveness of the method.

Event-triggered control of leader-following and cluster consensus for MAS under directed graph with designable minimum event interval

This paper investigates the event-based consensus problems for linear multi-agent systems under directed network topology. First, a new event-triggered control method is proposed for the leader-following consensus problem of agents under directed graphs. Then this new method is applied to the cluster control problem under special topological conditions. The new event-based control scheme is better than some existing literature in the following aspects. 1) The graph only needs to contain a spanning tree instead of being required to be strongly connected graph or undirected, and the triggering function is state-dependent rather than time-dependent. 2) Some parameters are designable for the trade-off between the event interval and the performance of the controlled system. Besides, the optimization of some parameters is studied to reduce the trigger frequency. All the agents can achieve consensus with an exponential speed when communications among follower agents are intermittent, and Zeno behavior is excluded under the proposed method. 3) When applying this method to the cluster control problem, agents in the same cluster share the same form of triggering function. Cluster consensus can be achieved regardless of intra- and inter-cluster relative coupling strength under the event-triggered control framework.

Containment control for fractional order MASs with nonlinearity and time delay via pull-based event-triggered mechanism

The containment control for fractional order multi-agent systems with nonlinearity and time delay is investigated in this article. Firstly, a distributed control protocol with fixed time delay is proposed for the purpose of achieving containment control for nonlinear fractional order multi-agent systems. Secondly, by using the pull-based event-triggered mechanism, a distributed event-based control law with time delay is further given to accomplish containment control for fractional order multi-agent systems with nonlinearity. In this way, the controller of each agent is merely updated at its own trigger moments. Hence, it can decrease network correspondence congestion and lower computational cost. Thanks to the stability theory of fractional order calculus, matrix theory, and properties of Mittag-Leffler function, the feasibility of the designed control protocols is confirmed. Furthermore, the Zeno behavior is precluded by the strict proof. Ultimately, two simulation examples are used to illustrate the availability of above theoretical analysis respectively.

Sliding-mode surface-based decentralized event-triggered control of partially unknown interconnected nonlinear systems via reinforcement learning

This paper studies a sliding-mode surface (SMS)-based decentralized event-triggered control problem for a class of partially unknown interconnected nonlinear systems within an identifier-critic neural networks framework. By assigning an especial cost function associated with SMS for each nominal subsystem, the original control issue is equivalently converted into designing a number of optimal controllers updating under an event-triggered manner, which considerably saves the communication resources. To derive these optimal event-based control policies, the corresponding Hamilton-Jacobi-Bellman equations are solved via the reinforcement learning algorithm. Different from traditional reinforcement learning algorithms, the identifier-critic network framework can obviate the requirement for the knowledge of system internal dynamics, and remove the errors generated by approximating actor networks. The weight vector in the critic network is updated through the gradient descent method and the experience replay technology, such that the persistence of excitation condition is relaxed. Under the proposed SMS-based decentralized control scheme, the considered system has a faster control response while minimizing the cost function. After that, according to the Lyapunov stability theory, all signals of the interconnected nonlinear systems are strictly proved to be bounded. Finally, the validity of the proposed control scheme is demonstrated via a simulation example.

Consensus of multi-Agent systems with one-Sided lipschitz nonlinearity via nonidentical double event-Triggered control subject to deception attacks

As for the multi-agent systems (MASs) with time-varying switching subject to deception attacks, the leader-following consensus problem is studied in this article. The one-sided Lipschitz (OSL) condition is utilized for the nonlinear functions, which makes the results more general and relaxed than those obtained by Lipschitz condition. The nonidentical double event-triggering mechanisms (ETMs) are adopted for only a fraction of agents, and each agent transmits the data according to its own necessity. Semi-Markov process modeling with time-varying switching probability is adopted for switching topology and deception attacks occurring in transmission channel are considered. By using the cumulative distribution function (CDF) and the linear matrix inequality (LMI) technology, sufficient conditions for MASs to achieve consensus in mean square are obtained. An effective algorithm is presented to obtain the event-based control gains. The merits of the proposed control scheme are demonstrated via a simulation example.

Performance adjustable event-triggered policy to spacecraft attitude tracking

Plug-and-play modular design is the future of spacecraft manufacturing. The employment of wireless communication between different modules instead of wire connections can reduce weight and simplify assembly. This paper focuses on the design of spacecraft attitude tracking control policies under wireless communications. A new event-based control policy with performance adjustable functions is proposed to achieve intermittent sampling to save system resources. Under the designed policy, the sampling frequency and convergence rate of the considered system can be traded off by designing different performance adjustable functions. Based on the Lyapunov function method, it proves that the spacecraft attitude tracking errors are uniformly ultimately bounded. In comparison with the previous results, the proposed policy provides a more general triggering condition and has the property of freely adjustable performance, which is suitable for scenarios with different performance requirements. Numerical simulations support the conclusion of its effectiveness and superiority.

Resilient Event-/Self-Triggering Leader-Following Consensus Control of Multiagent Systems Against DoS Attacks

This paper focuses on the problem of resilient leader-following consensus for multi-agent systems (MAS) against denial-of-service (DoS) attacks. Two update strategies based on event/self-triggering are proposed for the control protocols to handle the leader-following consensus in unreliable shared networks. We first propose a dynamic event-triggered communication (DETC) scheme to mitigate unnecessary information transfer through energy-limited and vulnerable networks. Continuous communication between agents can be avoided. DoS attacks are supposed to be aperiodic and asynchronous at different edges. The concept of valid DoS attack interval is introduced, and the frequency and duration of attacks are analyzed. The leader-following consensus can be achieved when there exist DoS attacks using the dynamic event-based control strategy. Then to avoid continuous event detection and save computation resources, a self-triggered communication (STC) function is developed. The next triggering moment is predetermined with the latest received state information. And the Zeno behavior is eliminated for the feasibility of the event/self-triggering scheme. Finally, a simulation is provided to verify the effectiveness of the proposed update strategies and control protocols.

Event-Based EV Charging Scheduling in a Microgrid of Buildings

With the popularization of electric vehicles (EVs), EV charging demand is becoming an important load in the building. Considering the mobility of EVs from building to building and their uncertain charging demand, it is of great practical interest to control the EV charging process in a microgrid of buildings to optimize the total operation cost while ensuring transmission security between the microgrid and the main grid. We consider this important problem in this article and make the following contributions. First, we formulate this problem as a Markov decision process (MDP) to capture the uncertain supply and EV charging demand in the microgrid of buildings. Besides reducing the total operation cost of buildings, the model also considers the power exchange limitation to ensure transmission security. Second, this model is reformulated within an event-based optimization (EBO) framework to mitigate the impact of large state and action space. A randomized parametric event-based control policy is proposed for the microgrid controller to determine the charge ratio for each building. Then, a selecting-to-charging principle is implemented for each building controller to determine the charge control of each EV in the building. Third, a constrained gradient-based policy optimization method is developed to find the optimal event-based control policy. Furthermore, an adjustment mechanism is also introduced to ensure transmission security during optimization. Numerical experiments are conducted to analyze the structure and the performance of the event-based control policy for EV charging in a microgrid of three buildings.

Event-based consensus for third-order nonlinear multi-agent systems

Event-based consensus problem of third-order nonlinear multi-agent systems is considered. Event-based controllers are proposed and MASs with event-based controllers are viewed as nonlinear systems with disturbances. By a degenerate transformation, an error system is derived from multi-agent systems, and consensus for multi-agent systems is converted into stability of the error system. Based on Lyapunov theory and Kronecker product method, several sufficient conditions on event-based consensus are obtained. It is shown that multi-agent systems can reach event-based consensus if the trigger parameter is sufficiently small and the control gain is sufficiently large under some simple conditions. Furthermore, the Zeno-behavior of the controllers is abstained. An example is presented to show the effectiveness of the derived results.

Resilient Synchronization of Networked Lagrangian Systems Over Event-Based Communication With Asynchronous DoS Attacks

A wide range of actual systems can be modeled as Euler- Lagrange dynamics, its inherently complex nonlinearities present additional difficulties in the design of control algorithms. In this paper, the distributed resilient synchronization control problem of networked Euler- Lagrange (E-L) systems under event-based communication with distributed denial-of-service (DoS) attacks is considered. A novel distributed dynamic event-triggered scheme is proposed to schedule the communication source under asynchronous DoS attacks on different channels. Then, a self-triggered scheme is designed to reduce the updating number of the control signals. Under the proposed adaptive control scheme, the asymptotic synchronization of the closed-loop system is guaranteed under DoS attacks. Neither the control strategy nor the dual-terminal event-triggered scheme needs the eigenvalue information of the Laplace matrix. Also, no Zeno behavior occurs under the proposed event-based control and communication framework. Finally, case studies are provided to show the effectiveness of the proposed method.

Event-Triggered Cost-Guaranteed Control for Linear Repetitive Processes Under Probabilistic Constraints

In this article, the event-triggered cost-guaranteed control problem is investigated for a class of shift-varying linear repetitive processes (LRPs) with multiplicative noises under probabilistic constraints. First, in order to relieve the communication burden and improve the communication efficiency, the event-triggered mechanism is exploited for the shift-varying LRPs over the communication network of limited bandwidth. By constructing a novel event generator function, the order of the event triggering sequence is identified on two independent directions. Then, the probabilistic constraint is enforced onto the shift-varying LRPs under the influence of the event-triggered mechanism. With the aid of the Chi-square distribution and the completing-the-square technique, a controller design algorithm is proposed to ensure that both the probabilistic constraints and the quadratic cost index are satisfied by using the actual information at the triggering instants. Sufficient conditions are derived to guarantee the existence of event-based controllers, and the controller gains are obtained at each step by solving a series of matrix inequalities. Finally, an illustrative example is given to demonstrate the effectiveness of the proposed controller design method.

Robotic Park: Multi-Agent Platform for Teaching Control and Robotics

Multi-agent system research is a hot topic in different application domains. In robotics, multi-agent robot systems (MRS) can realize complex tasks even if the behavior of each individual agent seems simple thanks to the cooperation between them. Although many control algorithms for MRS are proposed, few experimental results are validated on real data, being essential to building new testbeds to conduct MRS research and teaching. Moreover, most existing platforms for experimentation do not offer an overall solution allowing software and hardware design tools. This paper describes the design and operation of Robotic Park, a new indoor experimental platform for research in multi-agent systems. The heterogeneity and flexibility of its configuration are two of its main features. It supports control strategies design and validation of MRS algorithms. Experiences can be carried out in a virtual environment, in a physical environment, or under a hybrid scheme, as digital twins have been developed in Gazebo and Webots. Currently, two types of aerial vehicles, the Crazyflie 2.X and the DJI Tello, are available. It also includes two types of differential mobile robots, the Turtlebot3 and the Khepera IV. Both internal and external positioning systems using different technologies such as Motion Capture or Ultra-WideBand are also available for experiences. All components are connected through ROS2 (Robot Operating System 2) which enables experiences under a centralized, distributed, or hybrid scheme, and different communication strategies can be implemented. A mixed reality experience that addresses the problem of formation control using event-based control illustrates the platform usage.

Quasisynchronization of Delayed Neural Networks With Discontinuous Activation Functions on Time Scales via Event-Triggered Control.

Almost all event-triggered control (ETC) strategies were designed for discrete-time or continuous-time systems. In order to unify these existing theoretical results of ETC and develop ETC strategies for nonlinear systems, whose state variables evolve steadily at one time and change intermittently at another time, this article investigates quasisynchronization of delayed neural networks (NNs) on time scales with discontinuous activation functions via ETC approaches. First, the existence of the Filippov solutions is proved for discontinuous NNs with finite discontinuities. Second, two static event-triggered conditions and two dynamic event-triggered conditions are established to avoid continuous communication between the master-slave systems under algebraic/matrix inequality criteria. Third, under static/dynamic event-triggered conditions, a positive lower bound of event-triggered intervals is demonstrated to be greater than a positive number for each event-based controller, which shows that the Zeno behavior will not occur. Finally, two numerical simulations are carried out to show the effectiveness of the presented theoretical results in this article.

Event-Based Bipartite Consensus of Multi-Agent Systems Subject to DoS Attacks

This paper investigates the event-triggered bipartite consensus control of multi-agent systems subject to DoS attack. Existing results of relevant issues are usually confined by an implicit assumption that the real-time information of DoS attack is available for the construction of triggering strategy. However, some practical systems may not be equipped with elaborated attack detection mechanism, which means the trigger may not be notified the emission and suspension instants of attack timely. To settle with this scenario, we develop a novel distributed hybrid event-driven strategy which schedules the ordinary and attack-affected triggering laws by judging whether the previous transmission attempt of corresponding follower is successful, rather than utilizing detailed attack information directly. Furthermore, taking antagonistic interactions among agents into consideration, a resilient event-based control scheme is developed over signed digraph. Then, based on the analysis of hybrid Lyapunov functions exhibiting discontinuous property at practical triggering instants, a set of sufficient conditions which can ensure the exponential leader-following bipartite consensus of the investigated systems are presented. We also prove that Zeno behavior is excluded for triggering attempt sequences. Besides, the developed results are further extended to a self-triggered case. Finally, simulation results are provided to verify the effectiveness of the proposed control scheme.

Event-Triggered Transmission Policies for Nonlinear Control Systems Over Erasure Channels

We investigate the scenario where a controller communicates with a nonlinear plant via a wireless erasure channel. We present an event-based control strategy to stabilize the plant while sporadically using the unreliable wireless network. In particular, control packets may be lost at any time with a certain probability. Consequently, stability is ensured in a stochastic sense. We then compare the proposed event-based policy with a baseline policy that transmits according to the age of information, i.e., the time elapsed since the last successful reception. For any given baseline policy, we show how to design an event-based policy that ensures the same guaranteed control performance while leading, on average, to a strictly smaller channel utilization. Numerical simulations suggest that the achieved channel utilization may in fact be significantly smaller.