Containment Control Algorithm Research Articles

Multi-objective distributed control of WT-PV-BESS integrated weak grid via finite time containment

This paper proposes a finite time containment control scheme to achieve distributed control of a weak grid which is integrated with photovoltaic (PV), wind turbine (WT) and battery energy storage system (BESS). Taking advantage of the containment control in multi-dimensional control, we proposed a multi-objective control scheme of the WT-PV-BESS system in a weak grid, wherein four control objectives are specified, namely, bus voltage regulation, grid frequency control, peak load shaving and economic benefits optimization for the system operator. Firstly, the sizing approach of BESSs to fulfill the operation mission requirements is proposed; meanwhile, the general coordination strategy for the PV, WT and BESS to achieve the demand–supply balance is proposed. Subsequently, the predefined four control objectives are modeled and transferred into the long/short time frame operational constraints of the BESSs. Afterwards, the finite time containment control algorithm is proposed to force the BESSs into achieving containment status within prescribed time. Simulation case studies are conducted on a modified IEEE 9-bus system to show the effectiveness and performance of the proposed scheme.

Adaptive Containment Control of Multiple Underactuated Hovercrafts Subjected to Switching and Directed Topologies

This article addresses the containment control for a group of uncertain underactuated hovercrafts with multiple leaders and switching directed topologies. The underactuated hovercrafts in question are underactuated, nonholonomic, and passively unstable. For such nonlinear systems, we apply the reduced-order method, time-varying approach, adaptive tool, and state transformation technique to derive a novel dynamic feedback control strategy that guarantees all hovercrafts in the group globally converge into the convex hull spanned by leaders. In particular, the proposed containment control algorithm allows the leader trajectories to be either feasible or nonfeasible, and either dynamic or stationary. The Lyapunov stability theory is applied to the closed-loop analysis. Numerical simulations illustrate the control design.

Bearing‐only containment control of multi‐agent systems

AbstractBearing‐only containment control means to achieve containment using only the bearing information, rather than the complete relative position information including both the bearing and the distance. Compared with the most existing relative position based containment control algorithms, the bearing‐only containment control algorithm is nonlinear due to the nonlinearity of the bearing, which renders the stability analysis challenging. In this article, the bearing‐only containment control problem of multi‐agent systems with dynamically changing topologies is investigated for two cases, where the leaders are stationary or dynamic. First, when the leaders are stationary, it is shown that the nonlinearity of the bearing leads to the unknown nonlinear time‐varying parameters in the system. Based on the boundedness of the nonlinear parameters and the connectivity of the switching directed sensing graphs, it is proven that all the followers converge to the stationary convex hull formed by the leaders asymptotically. Second, when the leaders are dynamic, a distributed estimator is proposed for each follower to keep a local estimate of the velocity of the leaders. Based on the optimality of the projection and the shift invariance of the normal cone, it is proven that all the followers converge to the dynamic convex hull formed by the leaders asymptotically under the conditions on the switching directed sensing and communication graphs. It is shown from the two cases that the distance information is not necessary for containment control, and containment can be achieved as long as the bearing information is provided. Numerical examples are presented to illustrate the theoretical results.

Containment Control With Different Constraints

This paper addresses a containment control problem for discrete-time multi-agent systems when position, velocity and input constraints coexist. A nonlinear distributed containment control algorithm is presented. The main difficulty is how to decouple the nonlinearities caused by the three kinds of constraints. To prove the convergence of the containment control problem, the distances from the followers to the convex hull spanned by the leaders are analyzed by removing the errors caused by the projection operators and the stochasticities of the equivalent system matrices are explored to show nonincreasing property of the maximum distance. It is shown that containment control can be achieved as long as the convex hull is contained in each position constraint set. Numerical simulations are given to illustrate the obtained theoretical results.

Model-Free Adaptive Containment Control for Unknown Multi-Input Multi-Output Nonlinear MASs With Output Saturation

In this work, a model-free adaptive containment control scheme is investigated for a class of multi-input multi-output nonlinear multiagent systems, where the agents’ dynamics are unknown with output saturation. Firstly, the dynamics of followers are transformed into a equivalently data model by using full form dynamic linearization technology. Secondly, the distributed containment control algorithm is proposed only using the input data and the saturated output data of followers and neighbors. Further, the boundedness of the containment error is proved by using the contraction mapping principle and mathematical induction method. It is shown that the developed scheme can ensure that the followers move into the convex hull composed of the leaders. Last, the effectiveness of the developed scheme can be verified through numerical simulations.

Neural Network-Based Adaptive Containment Control Algorithms Design for Nonlinear Multiagent Systems with Switching Topologies

Neural Network-Based Adaptive Containment Control Algorithms Design for Nonlinear Multiagent Systems with Switching Topologies

Finite-Time Containment Control for Nonlinear Second-Order Multiagent System Under Directed Topology

This article investigates the finite-time containment control for a class of second-order multiagent systems with nonlinear dynamics and external disturbances under fixed directed interaction topology. Due to the existence of nonlinear dynamics and unknown but bounded external disturbances, there is an underlying technical difficulty for the design of containment controller. Furthermore, it is a challenge for the theoretical analysis of finite-time containment control problem due to the asymmetric Laplacian matrix arising from the constraint of one-way directed communication among the agents. In response to the above-mentioned challenges, a finite-time containment control algorithm is proposed. First, the multiagent system is considered with inherent nonlinear dynamics and unknown but bounded external disturbances. Second, the desired containment control protocol is presented under a directed interaction topology. Furthermore, by adding a power-integrator technique and Lyapunov function theory, the sufficient conditions are derived for the existence of the finite-time containment controller of a class of second-order multiagent systems. Finally, a numerical example is given to verify the usefulness of the proposed finite-time containment control protocol.

Tube-based model predictive full containment control for stochastic multi-agent systems

In this paper, we develop a tube-based distributed model predictive full containment control (MPFCC) algorithm for leader-following systems with bounded disturbance under dynamic leaders. The proposed algorithm employs knowledge regarding the constraints on states and control inputs to extrapolate their admissible values in the entire predictive horizon. The Kalman filter is utilized to estimate the system states, introducing estimated error. The error and disturbance are both involved in the time-varying tubes to construct the tightened constraints. For each follower, by penalizing the control input difference from its neighbors' control inputs and the deviation of the states from the convex hull produced by its neighbors' states, the containment problem is optimized only by utilizing the local nominal state and control sequences. To overcome the problem that followers may fall slightly out of the convex hull of the leaders caused by disturbance, a full containment control algorithm is introduced by designing a tightened convex hull. Then the recursive feasibility and robust stability are proved through the design of proper distributed terminal controllers and constraints. Finally, the effectiveness and robustness of the proposed method are illustrated for both linear and nonlinear multi-agent systems by simulation examples.

Application of Distributed Linear Multi-Agent Containment Control to Robotic Systems

This article proposes the application of a distributed containment control algorithm to a team of mobile robots. This paper builds on the containment controller developed by Yuan et al. (2019) for generic linear multi-agent system and tested in simulation only. In this article, we particularize the controller for the case of multiple mobile robots by including it into a two-layer control scheme. The high-level controller computes a desired position for the mobile robots, that is then used as reference trajectory for the low-level controller. The resulting control system is implemented as a fully distributed system on a team of mobile robots and validated in simulations and experiments.

Distributed adaptive neural network constraint containment control for the benthic autonomous underwater vehicles

Multiple Autonomous Underwater Vehicles (AUV) can complete complex ocean exploration missions cooperatively. This paper proposes a containment control algorithm under time-varying constraints by using a neural network for control of multiple benthic AUVs which are called the Ocean Bottom Flying Node (OBFN) systems. The multiple OBFNs in the presence of nonlinear model uncertainties are under the directed topology. First, we define the auxiliary variable and low-order filter. The anti-windup saturation auxiliary system is constructed in presence of the input saturation. Further, the adaptive law and neural network are designed to compensate environmental disturbances and systems model uncertainties, respectively. Moreover, in order to ensure the control performance of OBFN, an exponential boundary constraint is imposed which could constrain the system error convergent rates and bounds. Lyapunov stability theorem and graph theory are used to prove that the multiple OBFN systems are uniformly ultimately bounded. Finally, simulation results for multiple OBFNs illustrate the effectiveness of the proposed algorithm.

Formation–containment control of multi-agent systems with communication delays

This paper designs formation–containment control algorithms for a class of second-order nonlinear multi-agent systems governed by Euler–Lagrange dynamics with communication delays. The formation–containment problem consists of leader agents’ formation control and follower agents’ containment control. Firstly, to make the leaders form a desired formation and move collectively with a constant velocity, a coordinated formation control algorithm is designed and the variable-gain technique is used to eliminate the effect of communication delays on the leaders’ formation control. Secondly, considering that only the leaders have access to the desired moving velocity, we propose distributed velocity estimators for followers in which the communication delays also exist in the followers’ information interaction. By using the estimated velocity information, coordinated containment control laws are designed for the followers to drive them asymptotically converge to the convex hull spanned by all leaders. Furthermore, to increase the system robustness against uncertainties and external disturbances, the adaptive updating laws are designed for all agents. Finally, simulations are given to demonstrate these obtained results.

Distributed Containment Control for Nonlinear Stochastic Multiagent Systems.

This paper addresses the output feedback distributed containment control problem for a class of nonlinear stochastic multiagent systems under a fixed directed graph. Existing works usually design the containment control protocol using backstepping design method based on a conservative Lipschitz condition on nonlinear functions, which has a tedious control design procedure. In this paper, a new output feedback distributed containment control algorithm is proposed based on a novel dynamic compensator, which can not only simplify the control design procedure but also relax the condition on nonlinear terms. The proposed distributed containment protocol for each agent depends only on the agent output and the relative outputs of its neighbor agents, and can reduce the communication burden between the agents. Based on the Lyapunov stability theory, it is proved that the outputs of the followers are driven into the convex hull spanned by the outputs of the leaders with the proposed linear controller. Finally, the effectiveness of the theoretical results is illustrated by simulation examples.

Event-Triggered Adaptive Sliding Mode Attitude Containment Control for Microsatellite Cluster under Directed Graph

In order to investigate the attitude containment control problem for a microsatellite cluster, an event-triggered adaptive sliding mode attitude containment control algorithm is proposed for the satellite cluster flight system under directed topology, so that attitude of followers asymptotically converges to the convex hull formed by the leaders’ orientations. At first, the event-triggered control strategy is introduced into the attitude containment control problem for the microsatellite cluster. The triggering condition consisting of state-dependent and time-dependent function is designed to adjust control period and avoid the Zeno behaviour. When the function value meets the triggering condition, the event is triggered, state information is sampled, control law is computed, and actuators are updated, while the control action performed in nontriggering time is the same as the previous triggering instant. Then, in the presence of model uncertainties and external disturbances, an event-triggered adaptive sliding mode attitude containment control algorithm is presented under directed topology, and sufficient and necessary conditions for the followers to enter into the target area formed by the leaders are given. Furthermore, cell partitions from graph theory are employed to investigate the influence of information topology on steady states of followers, which provides theoretical basis for orientation design of cluster satellites. Finally, simulation results show that the proposed control strategy could reduce control execution frequency, as well as ensure the similar control performance with the time-triggered one, and followers belonging to the same cell have the same steady states.

Multiagent Containment Control With Nonconvex States Constraints, Nonuniform Time Delays, and Switching Directed Networks.

This brief studies the constrained containment control problem of continuous-time multiagent systems with nonconvex states constraints, nonuniform time delays, and switching directed networks. A distributed containment control algorithm consisting of nonlinear projection, nonlinear constraints, and communication delays is proposed. Based on the model transformation technique, convex analysis method, and the Lyapunov function, we prove that all agents finally converge into the convex hull formed by the given stationary points with arbitrarily bounded communication delays and arbitrarily switching networks as long as each agent jointly has at least one path from the given points to itself. Finally, a numerical example is included to show the effectiveness of theoretical results.

Distributed Fixed-time Formation-containment Control for Multiple Euler-Lagrange Systems with Directed Graphs

In this paper, the distributed fixed-time formation-containment (DFTFC) problem of multiple Euler-Lagrange systems with parametric uncertainties and input disturbances is studied under directed graphs. First, a distributed fixed-time sliding-mode estimator is constructed to estimate the desired states of each robot with that only parts of followers can access the information of leaders. Next, based on the estimator, a distributed fixed-time formation control algorithm is developed to drive leaders to achieve a specified formation. Then, the distributed fixed-time containment control algorithm is proposed for followers with its estimated states being tracked in a fixed time. Note that an explicit upper bound of the convergence time of DFTFC control algorithm is obtained independent of initial conditions. Finally, numerical simulations are performed to show the effectiveness of the obtained theoretical results.

Sampled-data containment control for double-integrator agents with dynamic leaders with nonzero inputs

The objective of containment control in multi-agent systems is to design control algorithms for the followers to converge to the convex hull spanned by the leaders. Sampled-data based containment control algorithms are suitable for the cases where the power supply and sensing capacity are limited, due to their low-cost and energy-saving features resulting from discrete sensing and interactions. In addition, sampled-data control has advantages in performance, price and generality. On the other hand, when the agents have double-integrator dynamics and the leaders are dynamic with nonzero inputs, the existing algorithms are not directly applicable in a sampled-data setting. To this end, this paper proposes a sampled-data based containment control algorithm for a group of double-integrator agents with dynamic leaders with nonzero inputs under directed communication networks. By applying the proposed control algorithm, the followers converge to the convex hull spanned by the dynamic leaders with bounded position and velocity containment control errors, and the ultimate bound of the overall containment error is proportional to the sampling period. A numerical simulation is presented to illustrate the proposed algorithm.

Distributed Containment Control of Fractional-order Multi-agent Systems with Double-integrator and Nonconvex Control Input Constraints

This paper mainly considers the distributed containment control problem for continuous-time fractional-order multi-agent systems (FOMASs) with double-integrator, where the control input of each agent is constrained to lie in a nonconvex set. A distributed projection containment control algorithm is designed for each follower. To finish the convergence analysis, the original closed-loop system is first changed into an equivalent one by a proper model transformation and the method of the L1 interpolation approximation is introduced to deal with the projection operator. Then, by using the properties of the convex hull and the Mittag-Leffler function, it is shown that the largest distance between the followers and the convex hull spanned by leaders tends to zero asymptotically, while all agents’ control inputs are constrained to stay in their corresponding nonconvex constraint sets. Finally, numerical simulations are provided to verify the effectiveness of the theoretical results.

Orbital Containment Control Algorithm and Complex Information Topology Design for Large-Scale Cluster of Spacecraft

Orbital Containment Control Algorithm and Complex Information Topology Design for Large-Scale Cluster of Spacecraft

Spacecraft formation-containment flying control with time-varying translational velocity

This paper investigates the problem of Spacecraft Formation-Containment Flying Control (SFCFC) when the desired translational velocity is time-varying. In SFCFC problem, there are multiple leader spacecraft and multiple follower spacecraft and SFCFC can be divided into leader spacecraft’s formation control and follower spacecraft’s containment control. First, under the condition that only a part of leader spacecraft can have access to the desired time-varying translational velocity, a velocity estimator is designed for each leader spacecraft. Secondly, based on the estimated translational velocity, a distributed formation control algorithm is designed for leader spacecraft to achieve the desired formation and move with the desired translational velocity simultaneously. Then, to ensure all follower spacecraft converge to the convex hull formed by the leader spacecraft, a distributed containment control algorithm is designed for follower spacecraft. Moreover, to reduce the dependence of the designed control algorithms on the graph information and increase system robustness, the control gains are changing adaptively and the parametric uncertainties are handled, respectively. Finally, simulation results are provided to illustrate the effectiveness of the theoretical results.

Distributed Containment Control of Continuous-Time Multiagent Systems With Nonconvex Control Input Constraints

In this paper, we investigate the distributed constrained containment control problem for continuous-time multiagent systems with nonconvex control input constraints. A nonlinear projection containment control algorithm for followers with double-integrator continuous-time dynamics is proposed. We show that each follower finally stays in the convex hull formed by multiple stationary leaders, provided that for each follower, there exists at least one directed path from leaders to it in the union of the graphs in each bounded time interval. Finally, a simulation example is implemented to illustrate theoretical results.