Distributed Receding Horizon Control Research Articles

Distributed RHC stabilization for discrete‐time large‐scale systems with imposed constraints

SummaryThis paper is concerned with finite horizon distributed stabilization of linear discrete‐time large‐scale systems with imposed constraints. Firstly, by constructing the performance index with two terminal weighted matrices, the necessary and sufficient conditions for stabilizing the system are derived. It is shown that distributed receding horizon control (RHC) can stabilize the discrete time large system with constraints if and only if two novel Lyapunov inequalities on the terminal weighting matrix are satisfied. Secondly, the finite horizon optimal control problem is solved by using the maximum principle (necessary condition), and the Riccati equation satisfying the corresponding distributed control system is derived. Based on the Riccati equation, the explicit optimal distributed RHC controller is obtained. Finally, simulation examples are used to verify the feasibility of distributed RHC to stabilize the system.

Synchronous distributed receding horizon control for uncertain networked systems with time delays

This study investigates the problem of distributed receding horizon control (DRHC) for constrained networked systems with polytopic uncertainty description, subject to time delays. Considering the limited communication capacity of the network and computational complexity, the approach of this study is based on a synchronous and non-iterative structure. Thus, for each subsystem, assumed predictive state evolutions of the neighbours are used. To restrict the assumed evolutions not deviating much from the true ones, the compatibility condition is derived concerning global stability. Time delays are handled by introducing an augmented polytopic uncertainty description, and the local optimisation problem is properly formulated by means of the robust receding horizon control technique. Applying the DRHC approach of this study, the recursive feasibility of the optimisation problem and exponential stability of the global system are guaranteed. An example is provided to illustrate the effectiveness of the proposed approach.

Event-triggered distributed receding horizon control for tracking and formation of homogeneous multi-agent systems

This paper proposes an event-triggered distributed receding horizon control (DRHC) approach for the formation and tracking problems of homogeneous multi-agent systems. For each agent, an event-triggering condition, based on assumed predictive information of the neighbours, is derived from stability analysis. Considering the uncertain deviation between the assumed and true predictive information, we design a time-varying compatibility constraint for the individual optimization problem. In the event-triggered DRHC algorithm, each agent solves the optimization problem and communicates with its neighbours only when the event-triggering condition is satisfied, so the communication and computation burden are reduced. Moreover, guarantees for the recursive feasibility and asymptotic stability of the overall system are proved. A simulation example is provided to illustrate effectiveness of the proposed approach.

Distributed receding horizon control of constrained nonlinear vehicle formations with guaranteed [formula omitted]-gain stability

This paper investigates the distributed receding horizon control (RHC) problem of a vehicle platoon with nonlinear dynamics and subject to system constraints, where each vehicle can communicate with its immediate predecessor and follower. A novel optimization problem and detailed distributed RHC algorithm are designed in order to keep a platoon formation, and further to ensure neighbor γ-gain stability (which is a new notion proposed in this paper and generalizes the string stability). The sufficient conditions on ensuring closed-loop stability and neighbor γ-gain stability are established, respectively. Finally, simulation studies are provided to verify the theoretical results. It is shown that it is possible to achieve certain control performance (i.e., γ-gain stability) and keep a formation simultaneously for the nonlinear vehicle platoon using distributed RHC.

Periodic event-triggering in distributed receding horizon control of nonlinear systems

How to efficiently use limited system resources in distributed receding horizon control (DRHC) is an important issue. This paper studies the DRHC problem for a class of dynamically decoupled nonlinear systems under the framework of event-triggering, to efficiently make use of the computation and communication resources. To that end, a distributed periodic event-triggered strategy is designed and a detailed DRHC algorithm is presented. The conditions for ensuring feasibility of the designed algorithm and stability of the closed-loop system are developed, respectively. We show that the closed-loop system is input-to-state stable if the energy bound of the disturbances, the triggering condition and the cooperation matrices fulfill the proposed conditions.

Distributed receding horizon control of large-scale nonlinear systems: Handling communication delays and disturbances

This paper studies the robust distributed receding horizon control (DRHC) problem for large-scale continuous-time nonlinear systems subject to communication delays and external disturbances. A dual-mode robust DRHC strategy is designed to deal with the communication delays and the external disturbances simultaneously. The feasibility of the proposed DRHC and the stability of the closed-loop system are analyzed, and the sufficient conditions for ensuring the feasibility and stability are developed, respectively. We show that: (1) the feasibility is affected by the bounds of external disturbances, the sampling period and the bound of communication delays; (2) the stability is related to the bounds of external disturbances, the sampling period, the bound of communication delays and the minimum eigenvalues of the cooperation matrices; (3) the closed-loop system is stabilized into a robust invariant set under the proposed conditions. A simulation study is conducted to verify the theoretical results.

Periodic Event-Triggered Distributed Receding Horizon Control of Dynamically Decoupled Linear Systems

This paper is concerned with the distributed receding horizon control (DRHC) problem for large-scale linear systems with disturbances. A periodic event-triggered DRHC scheme is proposed to reduce communication and computation load. A detailed dual-mode periodic event-triggered DHRC algorithm is designed, and sufficient conditions for ensuring feasibility and stability are established, respectively. We show that the feasibility depends on the testing period, and that the stability is related with the testing period, and the cooperation matrices. The overall system is stable and the system state converges to a set under the designed algorithm.

Distributed Receding Horizon Control for Dynamically Coupled Large Scale Systems

This paper studies the distributed receding horizon control (DRHC) for the large scale system composed of a set of dynamically coupled subsystems, respecting the state and input constraints. In DRHC, in order to predict its evolution, each subsystem has to utilize the assumed predictive trajectories of its neighbors which are different from the corresponding actual ones. Considering the differences as uncertainties, this paper tightens the state and input constraints to tolerate the differences for the admissibility of the actual evolution, and designs a compatibility constraint for the recursive feasibility and closed-loop stability. Then, an individual optimization problem is constructed, and a DRHC algorithm presented, for each subsystem. An illustrative example is provided to verify the effectiveness and advantage of the result.