Safety control using barrier certificates for multiagent systems with input saturation and formation constraints

This paper presents a novel leader-follower consensus control method for a special class of nonlinear multi-agent mechanical systems in the presence of control input saturation and external disturbances, and this class includes robot system dynamics with a wide range of potential applications in industry. In the innovative technique, one of the agents is selected as the leader and the other agents are guided in such a way that the entire states of the system can reach a consensus within the transient limits of the determined performance. Due to the presence of disturbance in most practical systems, the effect of limited disturbance has been evaluated in the consensus control method and actuator saturation is included in the design process of the control technique. Finally, a terminal sliding mode control method is adapted to ensure the stability of the overall system and fast finite-time leader-follower consensus control. The simulation results of the multi-agent nonlinear robot system in the MATLAB environment, in different scenarios by simultaneously considering the actuator saturation and external disturbance, show the effectiveness of the proposed control method.

Many interconnected systems like vehicle platoons or energy networks consist of similar or identical subsystems. The subsystem interconnections are either caused by the physical relations among the subsystems or have to be introduced by the controller to cope with cooperative control goals. This paper proposes strategies to reduce the complexity of the controller design problem (offline information reduction) and to reduce the amount of the system information, which is necessary for the implementation of the designed controller (online information reduction). It consists of two parts. The first part deals with the linear quadratic regulator (LQR) design problem for interconnected systems. A decomposition based on a state transformation is introduced, which allows to design the optimal controller for the interconnected system by considering modified subsystems separately. The proposed decomposition approach can be uniformly applied to multi-agent systems and physically interconnected systems.The second part of the paper introduces an event-based control strategy for multi-agent systems. The event-based control is a means to reduce the communication effort by invoking an information exchange among the subsystems only when the deviation between the estimated and current subsystem state exceeds an event threshold. An event-based controller is proposed, which mimics the continuous state-feedback controller with a desired precision. The relation between the event threshold and the approximation error is analysed.

This paper addresses the leader–follower consensus control problem for a nonlinear multi-agent robot system with control input constraint and external disturbances. Robot system is one of the most important practical systems in the industry. Due to the presence of disturbances in most practical systems, this paper considers the issue of finite-time leader–follower consensus control of the nonlinear multi-agent robot system along with actuator saturation and bounded disturbance. The modified terminal sliding mode control method is suggested for the system which is able to guarantee the stability of the overall system and fast finite-time leader–follower consensus control. For two different scenarios, the simulation of multi-agent robot system has been performed. The results show the effectiveness of the proposed control method.

This paper addresses the finite-time fault-tolerant attitude stabilization control problem for a rigid spacecraft in the presence of actuator faults or failures, external disturbances, and modeling uncertainties. First, a basic fault-tolerant controller is proposed to accommodate actuator faults or failures and guarantee local finite-time stability. When there is no a priori knowledge of actuator faults, disturbances, and inertia uncertainties, an online adaptive law is proposed to estimate the bounds of these uncertainties, and local finite-time convergence is achieved by an adaptive fault-tolerant controller. In addition, another adaptive fault-tolerant control scheme is derived that explicitly takes into account the actuator saturation. The proposed attitude controller provides fault-tolerant capability despite control input saturation and ensures that attitude and angular velocity converge to a neighborhood of the origin in finite time. Finally, simulation studies are presented to demonstrate the effectiveness of the proposed method.

This paper investigates event-triggered control strategy for the consensus problem of multi-agent systems with time-varying delays. The state of each agent is sampled and transmitted to its neighbors when a certain event condition is satisfied. Two kinds of decentralized event conditions are proposed. Sufficient conditions in terms of Linear Matrix Inequalities (LMIs) are established to ensure the consensus of the multi-agent systems with the event-triggered control feedbacks. Simulation example is given to demonstrate the effectiveness of the theoretical results.

Disturbances can significantly impact the dynamic performance and stability of a system, making them a key focus in stability analysis. However, direct measurement of disturbances is often challenging due to technological and cost limitations. These disturbances introduce uncertainties that complicate multi-agent coordination, particularly in formation control tasks. Consequently, designing effective control strategies for multi-agent systems becomes both challenging and crucial. This paper addresses the affine transformation formation control problem of multi-agent systems in the presence of unknown disturbances. We begin by using a state-space model to describe agent dynamics and employing an unknown input observer to estimate both the state and the unknown disturbances. Based on these estimates, we redesign the control law to ensure that tracking errors converge to an adjustable residual set. This distributed control approach allows agents to operate without global information, thereby reducing communication requirements. Finally, a simulation example demonstrates the feasibility and effectiveness of the proposed control law.

Event-driven strategies for distributed multi-agent systems are motivated by the future use of embedded microprocessors with limited resources that will gather information and actuate the individual agent controller updates. The event-driven control actuation updates considered in this paper are distributed, in the sense that agents require knowledge only of the states of their neighbors for the controller implementation. The proposed distributed strategy is compared with an earlier approach.

In this paper, we present a distributed hybrid control strategy for multiagent systems with contingent temporal tasks and prescribed formation constraints. Each agent is assigned a local task given as a linear temporal logic formula. In addition, two commonly seen kinds of cooperative robotic tasks, namely, service and formation, are requested and exchanged among the agents in real time. The service request is a short-term task provided by one agent to another. On the other hand, the formation request is a relative deployment requirement with predefined transient response imposed by an associated performance function. The proposed hybrid control strategy consists of four major components: 1) the contingent requests handling module; 2) the real-time events monitoring module; 3) the local discrete plan synthesis module; and 4) the continuous control switching module, and it is shown that all local tasks and contingent service/formation requests are fulfilled. Finally, a simulated paradigm demonstrates the proposed control strategy.

Finite time tracking control of higher order nonlinear multi agent systems with actuator saturation

This paper studies the finite time spacecraft attitude tracking control problem, while considering modeling uncertainty, external disturbances and control input saturation. A novel integral terminal sliding mode surface (ITSMS) is designed by combining the fast terminal sliding mode surface (FTSMS) with a low pass filter to achieve a fast finite time convergence rate for the control system, without input singularity. An auxiliary signal is used to compensate for the effects of actuator saturation. The basic controller is first formulated based on the ITSMS, fast-TSM-type reaching law and auxiliary system, in the presence of an external disturbance and input saturation. Then, an adaptive control procedure is introduced, which simultaneously handles modeling uncertainty and external disturbance, thereby creating an adaptive attitude tracking controller. The proposed controller provides a fast finite time convergence rate for the control system, based on the newly designed ITSMS, while simultaneously compensating for modeling uncertainty, external disturbances and input saturation, without restricting the parameter selection process nor requiring repeated differentiation of nonlinear functions. Finally, digital simulation results are presented and demonstrate the effectiveness of the proposed controllers.

In this paper, a method to synthesize controllers using finite time convergence control barrier functions guided by linear temporal logic specifications for continuous time multi-agent dynamical systems is proposed. Finite time convergence to a desired set in the state space is guaranteed under the existence of a suitable finite time convergence control barrier function. In addition, these barrier functions also guarantee forward invariance once the system converges to the desired set. This allows us to formulate a theoretical framework which synthesizes controllers for the multi-agent system. These properties also enable us to solve the reachability problem in continuous time by formulating a theorem on the composition of multiple finite time convergence control barrier functions. This approach is more flexible than existing methods and also allows for a greater set of feasible control laws. Linear temporal logic is used to specify complex task specifications that need to be satisfied by the multi-agent system. With this solution methodology, a control law is synthesized that satisfies the given temporal logic task specification. Robotic experiments are provided which were performed on the Robotarium multi-robot testbed at Georgia Tech.

The tracking performance of the industrial servo systems are highly affected by the inherent unstructured uncertainties (external disturbances, and/or unmodeled dynamics), which degrades the reliability of the drive. This paper presents a higher-order terminal sliding mode controller to achieve high-accuracy motion-tracking control of DC motor drives. Fractional integral terminal sliding mode (ITSM) manifold is selected to eliminate the reaching time to the sliding hyperplane, which provides fast tracking error convergence in finite-time. Further, super-twisting control is employed to reduce the chattering while compensating the unwanted unstructured uncertainties compared with the traditional sliding mode control. Experimental results on a DC motor-based industrial mechatronic drives unit (IMDU) with belt-drive load are presented to show the effectiveness of the proposed controller.

For a discrete-time linear system that has an open-loop pole outside the unit circle and is subject to actuator saturation, global asymptotic stabilization cannot be achieved. As a consequence, a discrete-time multi-agent system containing such an actuator saturating agent can only reach regional consensus, that is, the consensus can be achieved only if the initial state of each agent resides in a region of the state space. The region of all these initial states is referred to as the domain of consensus. In general, the exact characterization of the domain of consensus is impossible. In this paper, we consider the problem of estimating the domain of consensus of a discrete-time multi-agent system with an agent subject to actuator saturation. We establish a set of conditions under which an ellipsoidal set can be used as an estimate of the domain of consensus. Based on these conditions, an LMI-based optimization problem is formulated for obtaining the largest ellipsoidal estimate of the domain of consensus. Simulation results illustrate the effectiveness of the proposed approach and show the relationship between the size of the largest ellipsoidal estimate and the communication topology of the multi-agent system.

Markovian jumping systems have arisen naturally in the mathematical modeling of phenomena spanning disciplines in the social sciences, natural sciences, and engineering. This kind of stochastic dynamical systems can be employed to model the dynamics when parameters are subject to random abrupt changes due to sudden environment changes, subsystem switching, system noises, executor faults, and so forth. Much attention has been given to modeling, optimization, and real applications of such stochastic dynamical systems in the literature in recent years. As the advanced control and optimization will provide a basis for the design and application of such stochastic systems, these advanced techniques would result in substantial and sustainable benefits. The accepted papers in this special issue include stochastic stability, stabilization, stochastic control optimization, system modeling and identification methods, predictive control, signal processing, robust filtering, multiagent systems, networked control systems, time-delayed systems, neural networks, the Takagi-Sugeno fuzzy systems, simulated annealing, and fault detection methods.

In logics for strategic reasoning the main challenge is represented by their verification in contexts of imperfect information and perfect recall strategies. In this work, we show a technique to approximate the verification of Alternating-time Temporal Logic (ATL*) under imperfect information and perfect recall, which is known to be undecidable. Given a model M and a formula phi, we propose a verification procedure that generates sub-models of M in which each sub-model M' satisfies a sub-formula phi' of phi and the verification of phi' in M' is decidable. Then, we use CTL* model checking to provide a verification result of phi on M. We prove that our procedure is sound and in the same complexity class of ATL* model checking under perfect information and perfect recall. Moreover, we present a tool that uses our procedure and provide experimental results.