Robust Distributed Model Predictive Control Based Consensus of General Linear Multi-Agent Systems

In this study, an approach to design robust distributed model predictive control (MPC) is proposed for polytopic uncertain networked control systems with time delays. To reduce the computational complexity and improve the flexibility, the entire system is decomposed into multiple smaller dimensional subsystems. For each subsystem, the proposed robust distributed MPC algorithm requires solving multiple linear matrix inequality optimisation problems to minimise an upper bound on a robust performance objective. An augmented polytopic uncertainty description is invoked to handle the input delays. The conservativeness of distributed MPC algorithm is reduced by utilising a sequence of feedback control laws. An iterative on‐line algorithm for robust distributed MPC is developed to coordinate the distributed MPC controllers. Convergence and robust stability of the proposed distributed MPC are investigated. A numerical example is carried out to demonstrate the effectiveness of the proposed algorithm.

ABSTRACTIn this work, synthesis of robust distributed model predictive control (MPC) is presented for a class of linear systems subject to structured time-varying uncertainties. By decomposing a global system into smaller dimensional subsystems, a set of distributed MPC controllers, instead of a centralised controller, are designed. To ensure the robust stability of the closed-loop system with respect to model uncertainties, distributed state feedback laws are obtained by solving a min–max optimisation problem. The design of robust distributed MPC is then transformed into solving a minimisation optimisation problem with linear matrix inequality constraints. An iterative online algorithm with adjustable maximum iteration is proposed to coordinate the distributed controllers to achieve a global performance. The simulation results show the effectiveness of the proposed robust distributed MPC algorithm.

Robust distributed model predictive control of linear systems: Analysis and synthesis

A robust distributed model predictive control algorithm

This paper investigates the problem of event-triggered distributed model predictive control (DMPC) for continuous-time nonlinear multi-agent systems (MASs) subject to bounded disturbances, input and communication delays simultaneously. The compensation schemes for input and communication delays are proposed, respectively. A new optimal control problem (OCP) to achieve consensus among all agents is formulated under the proposed delay compensation schemes. To alleviate the communication burden and sensing cost, a novel input delay-related periodic event-triggering condition is proposed based on the state error to determine when to calculate the new control input. Sufficient condition guaranteeing the feasibility of the OCP is achieved with the proposed event-triggered control scheme. In stability analysis, a novel time-varying Lyapunov function is constructed, and the input-to-state practical stability (ISpS) of the MASs is derived by using the quasi-Lipschitz continuous property of the Lyapunov function. Numerical results related to vehicle platooning demonstrate the effectiveness of the proposed event-triggered DMPC.

A tube-based distributed model predictive control (DMPC) scheme is proposed for dynamically coupled linear systems. The control scheme is designed to guarantee local performance even when neighboring controllers are not complying with the requirements of the algorithm (e.g., they are malicious or faulty). The resulting conservativeness is minimized, for controllers aim to minimize their state and input constraint sets to reduce mutual disturbances. Also, sufficient conditions for feasibility and exponential stability are given. Finally, these ideas are illustrated and assessed with respect to other robust DMPC via a simulated example.

Collective behaviors of multi-agent systems over signed graphs find applications in a variety of scenarios including social networks, predator-prey dynamics, which however have not been adequately addressed as their counterparts with nonnegative graphs. This paper studies bipartite consensus problem of general linear multi-agent systems over signed digraphs. First, we show that for general linear agents, bipartite consensus over signed graphs and ordinary consensus over nonnegative graphs are equivalent. This indicates that prevailing consensus controllers for nonnegative graphs can be adopted to solve bipartite consensus problems. Based on this observation, an existing Riccati equation based cooperative tracking controller is extended to solve the bipartite consensus problem for general linear systems.

Containment control of discrete-time general linear multi-agent systems under dynamic digraph based on trajectory analysis

In this manuscript, the problem of event-triggered consensus for fractional general linear multi-agent systems is investigated, which include integer-order general linear multi-agent systems as the special case. A distributed event-triggered strategy is proposed to utilize in fractional multi-agent systems, under which the network can achieve consensus. Also, Zeno behavior can be precluded to ensure the feasibility of the devised event-triggered strategy. Furthermore, in order to avoid keeping track of the measurement errors continuously, a self-triggered strategy is designed, in which the next update time instant of each agent can be computed by using its local history state information. Finally, some numerical simulations are presented to indicate the validity of the devised control strategies.

On distributed model predictive control for vehicle platooning with a recursive feasibility guarantee

In this work, stochastic consensus of linear multi-agent systems with multiplicative measurement noises is investigated under undirected graphs. Based on the algebraic graph theory and the matrix theory, the consensus problem is converted into the stochastic stability problem of stochastic differential equations (SDEs) driven by multiplicative noises. Then by stochastic stability theorem for SDEs, the stochastic consensus conditions are given for the multi-agent systems. For the general linear multi-agent systems, the sufficient conditions for the mean square and the almost sure consensus are obtained based on the solution to an algebraic Riccati equation, where the consentability condition on the algebraic connectivity and the channel uncertainties is revealed. For the case of second-order integrator dynamics, by choosing some appropriate Lyapunov functions, the sufficient conditions for the mean square and the almost sure consensus, and the necessary conditions for the mean square consensus are derived. Moreover, it is shown that for any bounded noise intensities, the mean square and the almost sure consensus can be achieved by carefully choosing the control gain.

This paper addresses the event-triggered consensus tracking for general linear multi-agent systems with nonlinear uncertainty dynamics under directed communication topology. The proposed event-triggered consensus strategy relaxes the assumptions in existing works that the control gain and local inputs must be continuous. With the consensus tracking condition being satisfied, the cooperative control law with bounded parameter is developed based on the intermittent samples. It shows that if the sampling condition, in terms of LMIs, is satisfied, the resulting closed-loop general linear multi-agent uncertain systems will achieve the consensus. Simulation results are provided to verify the proposed approach.

This paper presents a self-triggered model predictive control (MPC) algorithm for constrained linear discrete-time systems in the presence of bounded state and output disturbances, when only the system output can be measured at triggering instants. The proposed algorithm mainly relies on a state estimator whose estimation error is bounded by an invariant set, and on the self-triggered robust model predictive control of a nominal system, in which the cost function penalizes the nominal system state and control effort as well as the triggering interval. The proposed algorithm is proved to drive the system to an invariant set with respect to the disturbances. Numerical examples are also provided to validate the proposed algorithm and to further illustrate better performance compared with the periodic MPC.

A unified approach for the influences of negative weights on system consensus

In this paper, an observer‐based event‐triggered distributed model predictive control method is proposed for a class of nonlinear interconnected systems with bounded disturbances, considering unmeasurable states. First of all, the state observer is constructed. It is proved that the observation error is bounded. Second, distributed model predictive controller is designed by using observed value. Meanwhile, the event‐triggered mechanism is set by using the error between the actual output and the predicted output. The setting of event‐triggered mechanism not only ensures the error between the actual output and the predicted output within a certain range, but also reduces the calculation amounts of solving the optimization problem. The states of each subsystem enter the terminal invariant set by distributed model predictive control, and then are stabilized in the invariant set under the action of output feedback control law. In addition, sufficient conditions are given to ensure the feasibility of the algorithm and the stability of the closed‐loop system. Finally, the numerical example is given, and the simulation results verify the effectiveness of the proposed algorithm.