Second-Order Consensus of Networked Mechanical Systems With Communication Delays

In this paper, we consider the second-order consensus problem for networked mechanical systems subjected to nonuniform communication delays, and the mechanical systems are assumed to interact on a general directed topology. We propose an adaptive controller plus a distributed velocity observer to realize the objective of second-order consensus. It is shown that both the positions and velocities of the mechanical agents synchronize, and furthermore, the velocities of the mechanical agents converge to the scaled weighted average value of their initial ones. We further demonstrate that the proposed second-order consensus scheme can be used to solve the leader-follower synchronization problem with a constant-velocity leader and under constant communication delays. Simulation results are provided to illustrate the performance of the proposed adaptive controllers.Comment: 16 pages, 5 figures, submitted to IEEE Transactions on Automatic Contro

Distributed Cooperative Control of Multi-Agent Systems Under Detectability and Communication Constraints

Cooperative control of multi-agent systems has recently gained widespread attention from the scientific communities due to numerous applications in areas such as the formation control in unmanned vehicles, cooperative attitude control of spacecrafts, clustering of micro-satellites, environmental monitoring and exploration by mobile sensor networks, etc. The primary goal of a cooperative control problem for multi-agent systems is to design a decentralized control algorithm for each agent, relying on the local coordination of their actions to exhibit a collective behavior. Common challenges encountered in the study of cooperative control problems are unavailable group-level information, and limited bandwidth of the shared communication. In this dissertation, we investigate one of such cooperative control problems, namely cooperative output regulation, under various local and global level constraints coming from physical and communication limitations. The objective of the cooperative output regulation problem (CORP) for multi-agent systems is to design a distributed control strategy for the agents to synchronize their state with an external system, called the leader, in the presence of disturbance inputs. For the problem at hand, we additionally consider the scenario in which none of the agents can independently access the synchronization signal from their view of the leader, and therefore it is not possible for the agents to achieve the group objective by themselves unless they cooperate among members. To this end, we devise a novel distributed estimation algorithm to collectively gather the leader states under the discussed detectability constraint, and then use this estimation to synthesize a distributed control solution to the problem. Next, we extend our results in CORP to the case with uncertain agent dynamics arising from modeling errors. In addition to the detectability constraint, we also assumed that the local regulated error signals are not available to the agents for feedback, and thus none of the agents have all the required measurements to independently synthesize a control solution. By combining the distributed observer and a control law based on the internal model principle for the agents, we offer a solution to the robust CORP under these added constraints. In practical applications of multi-agent systems, it is difficult to consistently maintain a reliable communication between the agents. By considering such challenge in the communication, we study the CORP for the case when agents are connected through a time-varying communication topology. Due to the presence of the detectability constraint that none of the agents can independently access all the leader states at any switching instant, we devise a distributed estimation algorithm for the agents to collectively reconstruct the leader states. Then by using this estimation, a distributed dynamic control solution is offered to solve the CORP under the added communication constraint. Since the fixed communication network is a special case of this time-varying counterpart, the offered control solution can be viewed as a generalization of the former results. For effective validation of previous theoretical results, we apply the control algorithms to a practical case study problem on synchronizing the position of networked motors under time-varying communication. Based on our experimental results, we also demonstrate the uniqueness of derived control solutions. Another communication constraint affecting the cooperative control performance is the presence of network delays. To this regard, first we study the distributed state estimation problem of an autonomous plant by a network of observers under heterogeneous time-invariant delays and then extend to the time-varying counterpart. With the use of a low gain based estimation technique, we derive a sufficient stability condition in terms of the upper bound of the low gain parameter or the time delay to guarantee the convergence of estimation errors. Additionally, when the plant measurements are subject to bounded disturbances, we find that that the local estimation errors also remain bounded. Lastly, by using this estimation, we present a distributed control solution for a leader-follower synchronization problem of a multi-agent system. Next, we present another case study concerning a synchronization control problem of a group of distributed generators in an islanded microgrid under unknown time-varying latency. Similar to the case of delayed communication in aforementioned works, we offer a low gain based distributed control protocol to synchronize the terminal voltage and inverter operating frequency

Leader-following consensus for lower-triangular nonlinear multi-agent systems with unknown controller and measurement sensitivities

summary:In this paper, a novel consensus algorithm is presented to handle with the leader-following consensus problem for lower-triangular nonlinear MASs (multi-agent systems) with unknown controller and measurement sensitivities under a given undirected topology. As distinguished from the existing results, the proposed consensus algorithm can tolerate to a relative wide range of controller and measurement sensitivities. We present some important matrix inequalities, especially a class of matrix inequalities with multiplicative noises. Based on these results and a dual-domination gain method, the output consensus error with unknown measurement noises can be used to construct the compensator for each follower directly. Then, a new distributed output feedback control is designed to enable the MASs to reach consensus in the presence of large controller perturbations. In view of a Lyapunov function, sufficient conditions are presented to guarantee that the states of the leader and followers can achieve consensus asymptotically. In the end, the proposed consensus algorithm is tested and verified by an illustrative example

Pose consensus based on dual quaternion algebra with application to decentralized formation control of mobile manipulators

This paper presents a solution based on dual quaternion algebra to the general problem of pose (i.e., position and orientation) consensus for systems composed of multiple rigid-bodies. The dual quaternion algebra is used to model the agents' poses and also in the distributed control laws, making the proposed technique easily applicable to time-varying formation control of general robotic systems. The proposed pose consensus protocol has guaranteed convergence when the interaction among the agents is represented by directed graphs with directed spanning trees, which is a more general result when compared to the literature on formation control. In order to illustrate the proposed pose consensus protocol and its extension to the problem of formation control, we present a numerical simulation with a large number of free-flying agents and also an application of cooperative manipulation by using real mobile manipulators

On the Robust Control and Optimization Strategies for Islanded Inverter-Based Microgrids

In recent years, the concept of Microgrids (MGs) has become more popular due to a significant integration of renewable energy sources (RESs) into electric power systems. Microgrids are small-scale power grids consisting of localized grouping of heterogeneous Distributed Generators (DGs), storage systems, and loads. MGs may operate either in autonomous islanded mode or connected to the main power system. Despite the significant benefits of increasing RESs, many new challenges raise in controlling MGs. Hence, a three layered hierarchical architecture consisting of three control loops closed on the DGs dynamics has been introduced for MGs. The inner loop is called Primary Control (PC), and it provides the references for the DG’s DC-AC power converters. In general, the PC is implemented in a decentralized way with the aim to establish, by means of a droop control term, the desired sharing of power among DGs while preserving the MG stability. Then, because of inverterbased DGs have no inertia, a Secondary Control (SC) layer is needed to compensate the frequency and voltage deviations introduced by the PC’s droop control terms. Finally, an operation control is designed to optimize the operation of the MGs by providing power setpoints to the lower control layers. This thesis is mainly devoted to the design of robust distributed secondary frequency and voltage restoration control strategies for AC MGs to avoid central controllers and complexity of communication networks. Different distributed strategies are proposed in this work: (i) Robust Adaptive Distributed SC with Communication delays (ii) Robust Optimal Distributed Voltage SC with Communication Delays and (iii) Distributed Finite-Time SC by Coupled Sliding-Mode Technique. In all three proposed approaches, the problem is addressed in a multi-agent fashion where the generator plays the role of cooperative agents communicating over a network and physically coupled through the power system. The first approach provides an exponentially converging voltage and frequency restoration rate in the presence of both, model uncertainties, and multiple time-varying delays in the DGs’s communications. This approach consist of two terms: 1) a decentralized Integral Sliding Mode Control (ISMC) aimed to enforce each agent (DG) to behaves as reference unperturbed dynamic; 2) an ad-hoc designed distributed protocol aimed to globally, exponentially, achieves the frequency and voltage restoration while fulfilling the power-sharing constraints in spite of the communication delays. The second approach extends the first one by including an optimization algorithm to find the optimal control gains and estimate the corresponding maximum delay tolerated by the controlled system. In the third approach, the problem of voltage and frequency restoration as well as active power sharing are solved in finite-time by exploiting delay-free communications among DGs and considering model uncertainties. In this approach, for DGs with no direct access to their reference values, a finite-time distributed sliding mode estimator is implemented for both secondary frequency and voltage schemes. The estimator determines local estimates of the global reference values of the voltage and frequency for DGs in a finite time and provides this information for the distributed SC schemes. This dissertation also proposes a novel certainty Model Predictive Control (MPC) approach for the operation of islanded MG with very high share of renewable energy sources. To this aim, the conversion losses of storage units are formulated by quadratic functions to reduce the error in storage units state of charge prediction