Event‐triggered asynchronous distributed MPC for multi‐quadrotor systems with communication delays

The complicated formation flight for multi-unmanned aerial vehicles is a challenge, especially when multi-mission requirements are taken into account. This paper studies the adaptive differential evolution-based distributed model predictive control approach to deal with the multi-unmanned aerial vehicle flight achieving obstacle/collision avoidance and formation keeping simultaneously in the complex environment. Specifically, the distributed model predictive controller is designed to achieve stable flight for each unmanned aerial vehicle as well as taking the state and input saturation into account, where the local optimization problem is solved by the adaptive differential evolution algorithm. Besides, the adaptive adjustment to the prediction horizon for the model predictive controller is introduced, while the asymptotic convergence of the rolling optimization is analyzed as well. Finally, simulation examples are provided to illustrate the validity of the proposed control structure.

An event-triggered distributed model predictive control (DMPC) approach for a type of dynamically decoupled, independently constrained systems with a coupled performance objective, is presented. The approach employs, for each agent, a compatibility constraint (in the spirit of Dunbar and Murray) in the optimization problem. An event-triggering condition, based-on the overall stability condition of the system, is developed. If the triggering condition for an agent is satisfied, then the agent solves its optimization problem; otherwise, then the agent retain feasibility and stability by simply adopting the tail of its previous solutions. A simulation example is provided to illustrate the effectiveness of the provided approach.

This is a position paper on the current state of the art in distributed Model Predictive Control (MPC) and our view on its future potential. We present results from a recent survey of 35 distributed MPC approaches. For this, we propose a way in which distributed MPC approaches can be categorized for comparison. We also link the potential that these approaches have to the domain of other fields such as integrated environmental optimal decision making and cyber-physical systems. Many challenges for realizing these links have to be faced. We present our views on how the advances in several highly active research domains could be used to overcome these challenges. As such, this paper is intended as a starting point for the exploration of various novel research cooperations.

Water networks are large-scale systems, consisting of many interacting components. They are currently typically operated by local decentralized controllers which receive setpoints from human operators. We discuss how communication among the local controllers can be included and in particular propose the use of distributed model predictive control for enabling the local controllers to determine setpoints autonomously using communication and coordination. We consider the control of a particular class of water networks, viz. irrigation canals. A simulation study on a 7-reach irrigation canal illustrates the potential of the proposed approach.

This paper investigates intersection control of multiple vehicles using a Model Predictive Control (MPC) framework. Vehicles follow pre-defined paths across the intersection and adjust their velocities to ensure collision-free passage while maximizing an objective. We choose a non-cooperative Distributed Model Predictive Control (DMPC) approach, where priorities need to be assigned to vehicles. The algorithm we present sets these priorities automatically by evaluating the vehicles’ time to react to stop before entering the intersection. We demonstrate our method in simulations of multiple vehicles and continuous traffic. It produces near-optimal velocity profiles and reduces the computation time in comparison to centralized MPC while avoiding vehicle collisions and deadlocks.

Designing a stabilized distributed model predictive control (DMPC) with constraints is an open and important problem for a class of large-scale distributed systems, which are composed by both weakly and strongly coupled subsystems. This paper proposes a design of DMPC network to stabilize this class of large-scale systems. A coupling degree-based clustering method is first designed to classify subsystems into some middle-scale subsystems (M-subsystem) off-line according to the adjacent matrix, so that these M-subsystems are weakly coupled with each other. Then, each M-subsystem is controlled by a virtual model predictive control (MPC), which is realized by several individual controllers with running iterative cooperative DMPC algorithm, since the solution of cooperative DMPC is able to converge to a fixed point without coupling constraints. Each MPC communicates with the corresponding interacted M-subsystems’ MPCs once in a control period for exchanging future state evolution estimation. All the subsystem-based MPCs are composed of the proposed peer-to-peer DMPC network. In addition, an additional consistency and stabilization constraints are added to guarantee the recursive feasibility and stability of the overall system. The convergence of the iterative DMPC algorithm for each M-subsystem and the stabilization analysis of the overall system are provided. The simulation results show the efficiency of the proposed method. Note to Practitioners —The proposed method is designed for the systems, which are composed of both strong and weak coupling subsystems and are controlled in a distributed structure. The aim of this method is to design a distributed model predictive control (MPC) network for the operational optimization of entire system. The designed control structure and the distributed MPC algorithm with the proposed method could guarantee the recursive feasibility and asymptotic stability of the entire system. To apply this method, the first step is to obtain the models of each subsystem. Then, design the distributed MPC network structure according to the proposed cluster algorithm, which determines the set of subsystems that each virtue MPC controls. Next step is to configure the network information exchanging among these subsystems and construct the optimization problem of each subsystem. Finally, use the existing quadratically constrained quadratic program solvers to calculate the optimal control laws and apply these optimal control laws to the corresponding subsystems. This method can be used in large-scale chemical processes, air conditioner systems for multizone buildings, distributed energy generation systems, and so on.

In this paper two model predictive control (MPC) approaches, an on-line and an off-line MPC approach, for constrained uncertain continuous-time systems with piecewise constant control input are presented. Both MPC approaches guarantee robust asymptotic stability by taking into account the hybrid dynamics of the closed-loop system, resulting from the continuous-time system dynamics and the discrete-time model predictive controller dynamics. Examples are presented to demonstrate the applicability of the proposed MPC approaches.

This work focuses on a class of nonlinear control problems that arise when new control systems which may use networked sensors and/or actuators are added to already operating control loops to improve closed‐loop performance. In this case, it is desirable to design the pre‐existing control system and the new control system in a way such that they coordinate their actions. To address this control problem, a distributed model predictive control method is introduced where both the pre‐existing control system and the new control system are designed via Lyapunov‐based model predictive control. Working with general nonlinear models of chemical processes and assuming that there exists a Lyapunov‐based controller that stabilizes the nominal closed‐loop system using only the pre‐existing control loops, two separate Lyapunov‐based model predictive controllers are designed that coordinate their actions in an efficient fashion. Specifically, the proposed distributed model predictive control design preserves the stability properties of the Lyapunov‐based controller, improves the closed‐loop performance, and allows handling input constraints. In addition, the proposed distributed control design requires reduced communication between the two distributed controllers since it requires that these controllers communicate only once at each sampling time and is computationally more efficient compared to the corresponding centralized model predictive control design. The theoretical results are illustrated using a chemical process example. © 2009 American Institute of Chemical Engineers AIChE J, 2009

In this chapter, a multi-time scale stochastic model predictive control (MPC) approach is applied to solve the cooperative distributed energy scheduling problem of smart homes. In this problem, a variety of energy resources are considered for each smart home, and every smart home has a capability of power transaction with the retailer through the electrical grid as well as with the other connected smart homes. The challenges of the problem include modeling the technical and economic constraints of the energy resources and addressing the variability and uncertainty issues of renewables’ power that change the optimization problem to a stochastic, dynamic (time-varying), and mixed-integer nonlinear programming (MINLP) problem. To deal with the variability and uncertainty issues, a multi-time scale stochastic MPC is applied. Applying the multi-time scale approach in the stochastic MPC is able to simultaneously consider the precise resolution for the problem variables and the vast vision for the optimization time horizon. In addition, linear programming (LP) and genetic algorithm (GA) are combined (GA-LP) and applied in the problem as an effective and fast optimization technique. The numerical studies about the small and large systems demonstrate the competences of the proposed approach.KeywordsCooperative distributed energy schedulingMulti-time scale model predictive control (MPC)Photovoltaic (PV) panelsSmart homesStochastic optimization

Frequency regulation balances the supply and demand of power within a power network to maintain the network's frequency about its nominal value. Using residential loads to supply frequency regulation while respecting user comfort can require costly communication infrastructure. Developing control algorithms that are resilient to communication network imperfections, e.g., delays, can allow the usage of less costly, lower reliability communication infrastructure. Previous work developed a model predictive control (MPC) approach that enables aggregations of loads to track a desired power signal despite communication delays. This work presents a novel model-reduction method to produce a minimal aggregate load model, and then uses state augmentation to include the effect of input delays. This allows the reformulation of the MPC controller into a linear controller yielding a closed-form control law that reduces online computation. We present simulations that compare the MPC and linear controllers' tracking ability given input delays. The linear controller neglects input constraints explicitly included within the MPC controller, and we characterize the impact of neglecting these constraints through simulations. The linear controller reduces the computation time by a factor of 100, but the RMS tracking error increases 11% in the cases studied.

Inland waterways are large, complex systems composed of interconnected navigation reaches dedicated mainly to navigation. These reaches are generally characterized by negligible bottom slopes and large time delays. The latter requires ensuring the coordination of the current control actions and their delayed effects in the network. Centralized control strategies are often impractical to implement due to the size of the system. To overcome this issue, a distributed Model Predictive Control (MPC) approach is proposed. The system partitioning is based on a reordering of the optimality conditions matrix, and the control actions are coordinated by means of the Optimality Condition Decomposition (OCD) methodology. The case study is inspired by a real inland waterways system and shows the performance of the approach.

This paper concerns a distributed model predictive control (DMPC) strategy in which each controller views the signals from other subsystems as disturbance inputs in its local model. The DMPC controllers exchange predictions on the bounds of their state trajectories and incorporate this information into their local DMPC problems. They also impose their own predicted state bounds as constraints in subsequent DMPC iterations to guarantee their subsystem satisfies the bounds broadcast to the other controllers. Each controller solves a local min-max problem on each iteration to optimize performance with respect to worst-case disturbances. Parameterized state feedback is introduced into the DMPC formulation to obtain less conservative solutions and predictions. The paper presents sufficient conditions for feasibility and stability. The approach is illustrated with an example.

By taking both control and state vectors as decision variables, the subproblems of model predictive control scheme can be considered as a class of separable convex optimisation problems with coupling linear constraints. A Lagrangian dual method is introduced to deal with the optimisation problem, in which, the primal problem is solved by a parallel coordinate descent method, and a fast dual ascend method is adopted to solve the dual problem iteratively. The proposed approach is applied to the well-known hierarchical and distributed model predictive control four-tank benchmark. Experimental results have testified the effectiveness of the proposed approach and shown that the benchmark problem can be well stabilised.

The hierarchical control strategy enables seamless integration of power electronics-based distributed generators (DGs) into microgrids (MGs). This work presents a distributed coordinated secondary voltage and frequency control strategy of islanded MGs, utilizing distributed model predictive control (DMPC) approach. The Proposed approach is entirely distributed in nature, with plug and play features and requires minimal communication network with information exchange between immediate neighbors. This technique facilitates efficient information exchange and obviates the need for centralized control. Droop control is the primary controller for all the DGs, which leads to the deviations in DG voltage and operating frequency from standard nominal values. Secondary control enables the restoration of DG voltage and frequency to their nominal values. Input–output feedback linearization (IOFL) is used to transform nonlinear dynamics of inverter-interfaced DGs into first-order linear dynamics between input and output. Compared to some published works, the single-integrator dynamics eliminates the need to compute the derivative of the output voltage. Furthermore, DMPC has been used for all DG units as secondary controller, to achieve voltage and frequency regulation. This approach takes advantage of distributed architecture with optimal control actions and enhances reliability and flexibility of MG operations. Moreover, the proposed approach ensures that voltage and frequency of overall system are restored to its reference value while maintaining accuracy in real power sharing. Effectiveness of proposed control scheme is validated with simulations conducted on islanded MG test system using MATLAB/Simulink toolbox.

Partitioned Based Cooperative Distributed Model Predictive Control for Large-Scale Nonlinear Systems