Nonlinear distributed model predictive control with dual decomposition and event-based communication approach

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

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

With an increasing number of vehicles on the road, multiple‐vehicle platoons have become a new solution under communication constraints. However, the existing studies seldom consider the effect of the tail vehicle on the information transfer and platoon control over long distances, and thus the control performance under time‐varying delays is unacceptable. In this study, a hierarchical multi‐platoon control architecture considering the backbone platoon and sub‐platoons is proposed under non‐ideal communication conditions, where the backbone platoon layer communication topology is designed to achieve backbone platoon control and appropriate coordination among sub‐platoons. Distributed model predictive controllers (DMPCs) for backbone‐ and sub‐platoons that integrate delay compensation have been proposed. Buffers and delay compensators in the proposed DMPC are designed to reduce the interference caused by non‐ideal communications. The asymptotic stability is analyzed at the sub‐ and multi‐platoon levels. The results show that compared with traditional DMPC without a compensator, the proposed DMPC can eliminate the velocity lag and steady‐state spacing errors and maintain the maximum velocity and spacing errors within 0.11 m/s and 0.17 m, respectively, under certain operating conditions. Thus, the proposed method guarantees the stability of multiple platoons under both the constant and time‐varying delay conditions.

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.

In distributed model predictive control (DMPC), where a centralized optimization problem is solved in distributed fashion using dual decomposition, it is important to keep the number of iterations in the solution algorithm small. In this technical note, we present a stopping condition to such distributed solution algorithms that is based on a novel adaptive constraint tightening approach. The stopping condition guarantees feasibility of the optimization problem and stability and a prespecified performance of the closed-loop system.

This work presents a learning-based approximation scheme to improve the computational burden of general distributed model predictive control (DMPC). Under the framework of dual decomposition, an independent neural network approximator with rectified linear unit is designed for each subsystem. The primal and Lagrangian dual analysis indicates that this error-containing approximation is a suboptimal solution of the global DMPC optimization problem. In addition, the distributed conditions designed to guarantee the feasibility and stability of global system, which inspired by an explicit-implicit procedure to approximate an MPC law, are derived from an decoupling process using dual decomposition. In cases with infeasible approximator output or the distributed conditions are violated, an backup controller will used to promote the implementation of approximation. The proposed learning-based DMPC approximator with feasibility and stability guarantees is finally employed to a reactor-separator process, and simulation results demonstrate the efficiency and superior performance of proposed strategy.

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.

The development of schemes for effectively examining unmeasured disturbances and plant-model mismatch in nonlinear model predictive control (NMPC) is an important area, which has attracted considerable attention over the past decade. In this work, we propose NMPC formulations for improving regulatory performance using nonlinear state space models identified from input-output data. The NARX-type MISO and MIMO nonlinear models identified in Srinivasarao et al.(17) are used to develop the state estimators and the predictors in the proposed NMPC formulations. We show that these models provide information about the covariances of the fast changing disturbances that are necessary for developing an extended Kalman filter (EKF) used in an NMPC scheme (EKF-NMPC). Rather than formulating an EKF to reject these disturbances, which we show has certain drawbacks, we proceed to propose an alternate prediction scheme based on the direct use of the identified noise model for future trajectory predictions. We show that the resulting NMPC formulation (DC-NMPC) is relatively easy to tune to achieve disturbance rejection as well as offset removal. The efficacy of the proposed control schemes is demonstrated using simulation studies on two benchmark control problems: (a) regulatory control of a continuously stirred tank reactor (CSTR) exhibiting input multiplicity at a singular point, and (b) servo control of a CSTR exhibiting output multiplicities. The analysis of simulation results reveals that the proposed EKF-NMPC and DC-NMPC schemes consistently generate significantly better regulatory performances, when compared to the performance of a conventional NDMC-type formulation, even in the presence of significant plant-model mismatch. In particular, the DC-NMPC performs significantly better than the EKF-NMPC formulation and can be tuned to achieve excellent regulatory performance without causing excessive input variability using parameters of a single disturbance filter. The conclusions reached through simulation studies are validated by conducting servo and regulatory control experiments on a laboratory-scale heater-mixer setup.

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.

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.

Combined environmental and economic dispatch of smart grids using distributed model predictive control

This paper presents a distributed model predictive control(DMPC) strategy to achieve cooperative tasks like consensus and synchronization of linear systems with coupled constraints. Based on the error of state between each subsystem and the center of its cooperative set, a novel DMPC algorithm is designed with its robust feasibility guaranteed by permitting only one subsystem to optimize at each time instant, while renew other subsystems' plans. Illustrative examples are finally conducted to verify the effectiveness of the DMPC strategy.

A novel distributed model predictive control scheme based on dynamic integrated system optimization and parameter estimation (DISOPE) was proposed for nonlinear cascade systems under network environment. Under the distributed control structure, online optimization of the cascade system was composed of several cascaded agents that can cooperate and exchange information via network communication. By iterating on modified distributed linear optimal control problems on the basis of estimating parameters at every iteration the correct optimal control action of the nonlinear model predictive control problem of the cascade system could be obtained, assuming that the algorithm was convergent. This approach avoids solving the complex nonlinear optimization problem and significantly reduces the computational burden. The simulation results of the fossil fuel power unit are illustrated to verify the effectiveness and practicability of the proposed algorithm.

In this paper, the parameterized dynamical model of the diesel engine intake and exhaust system using a data-based method, namely a Gain-Scheduled model is proposed and designed based on the data from a virtual engine test bench under normal load conditions. In the first step, the Multiple Input Multiple Output model structure is defined with five inputs and two outputs. Using the constructed model, it is possible to establish the relations between intake Manifold Pressure, Air Mass Flow, the control signals, and changes of the load. Then, the model is further used to design a Nonlinear Model Predictive Control controller, aimed at optimizing the efficiency of the combustion system in terms of the control reference value tracking with respect to emission reduction. This paper follows a model-based design approach to construct the Nonlinear Model Predictive Control objective function for the engine intake Manifold Pressure and Air Mass Flow nonlinear control problem. The proposed data-based dynamical modeling method is shown to increase the flexibility for the modeling of nonlinear plant at a low cost in computational requirements. The experimental results illustrate that the optimized nonlinear control approach significantly improve the control reference tracking performance and the exhaust emissions against the standard decentralized Single Input Single Output control in the standard production Engine Control Unit.

Distributed Model Predictive Control with Event-Based Optimization