Distributed model predictive control for continuous‐time nonlinear systems based on suboptimal ADMM

This paper presents a distributed model predictive control (DMPC) scheme for continuous‐time nonlinear systems based on the alternating direction method of multipliers (ADMM). A stopping criterion in the ADMM algorithm limits the iterations and therefore the required communication effort during the DMPC solution at the expense of a suboptimal solution. Stability results are presented for the suboptimal DMPC scheme under two different ADMM convergence assumptions. In particular, it is shown that the required iterations in each ADMM step are bounded, which is also confirmed in simulation studies.     

Distributed model predictive control for energy management in a network of microgrids using the dual decomposition method

This paper deals with the application of model predictive control (MPC) to optimize power flows in a network of interconnected microgrids (MGs). More specifically, a distributed MPC (DMPC) approach is used to compute for each MG how much active power should be exchanged with other MGs and with the outer power grid. Due to the presence of coupled variables, the DMPC approach must be used in a suitable way to guarantee the feasibility of the consensus procedure among the MGs. For this purpose, we adopt a tailored dual decomposition method that allows us to reach a feasible solution while guaranteeing the privacy of single MGs (ie, without having to share private information like the amount of generated energy or locally consumed energy). Simulation results demonstrate the features of the proposed cooperative control strategy and the obtained benefits with respect to other classical centralized control methods.     

Constrained discrete model predictive control of an arm‐manipulator using Laguerre function

This work presents a multivariable predictive controller applied on a redundant robotic manipulator with three degrees of freedom. The article focuses on the design of a discrete model‐based predictive controller (DMPC) using the Laguerre function as a control effort weighting method to enhance the solution of Hildreth's quadratic programming and to minimize the trade‐off problem in constrained case. The Laguerre functions are used to simplify and enhance the control horizon effect through parsimonious control trajectory, thus reducing the computational load required to find the optimal control solution. Furthermore, these results can be confirmed by simulations and experimental tests on the manipulator and comparing it to the traditional DMPC approach and the discrete linear quadratic regulator.     

Regularized economic model predictive control with barrier functions

In this article, we consider the use of barrier functions as a regularizing cost in economic model predictive control (EMPC). We focus on a specific variant, EMPC with generalized terminal constraints (G-EMPC), as it is suitable for tackling large-scale problems commonly arising in multiagent settings, which motivates our work. The benefits of using barrier functions are providing smoothing of the constrained problem, allowing the use of second-order methods and warm-starting, which reduces the iteration count significantly. Apart from these numerical benefits, recentered barrier functions can be used as a regularizing cost in the EMPC problem for enhancing closed-loop convergence properties. We show that in the case of G-EMPC, which allows the terminal state to be any equilibrium point, regularizing the problem provides (i) convergence of the predicted terminal state to a neighborhood of a globally optimal equilibrium point, (ii) asymptotic average performance guarantees for the closed-loop system, and (iii) empirical evidence of accelerated numerical solution of the optimal control problem. Specifically we use a proximal-like regularization, which penalizes the deviation from the previously predicted trajectories. We analyze system theoretic properties of the proposed scheme and provide simulation examples illustrating the numerical and system theoretical benefits of using barriers.     

Set‐valued observer‐based active fault‐tolerant model predictive control

This paper proposes an integrated actuator and sensor active fault‐tolerant model predictive control scheme. In this scheme, fault detection is implemented by using a set‐valued observer, fault isolation (FI) is performed by set manipulations, and fault‐tolerant control is carried out through the design of a robust model predictive control law. In this paper, a set‐valued observer is used to passively complete the fault detection task, while FI is actively performed by making use of the constraint‐handling capability of robust model predictive control. The set‐valued observer is chosen to implement fault detection and isolation (FDI) because of its simple mathematical structure that is not affected by the type of faults such as sensor, actuator, and system‐structural faults. This means that only one set‐valued observer is needed to monitor all considered actuator and sensor statuses (health and fault) and to carry out the fault detection and isolation task instead of using a bank of observers (each observer matching a health/fault status). Furthermore, in the proposed scheme, the advantage of robust model predictive control is that it can effectively deal with system constraints, disturbances, and noises and allow to implement an active FI strategy, which can improve FI sensitivity when compared with the passive FI methods. Finally, a case study based on the well‐known two‐tank system is used to illustrate the effectiveness of the proposed fault‐tolerant model predictive control scheme. Copyright © 2016 John Wiley & Sons, Ltd.     

LMI-based cooperative distributed model predictive control for Lipschitz nonlinear systems

In this paper, a distributed model predictive control is proposed to control Lipschitz nonlinear systems. The cooperative distributed scheme is considered where a global infinite horizon objective function is optimized for each subsystem, exploiting the state and input information of other subsystems. Thus, each control law is obtained separately as a state feedback of all system's states by solving a set of linear matrix inequalities. Due to convexity of the design, convergence properties at each iteration are established. Additionally, the proposed algorithm is modified to optimize only one control input at a time, which leads to a further reduction in the computation load. Finally, two application cases are studied to show the effectiveness of the proposed method.     

Finite‐time convergence results in robust model predictive control

Robust asymptotic stability (asymptotic attractivity and ?‐δ stability) of equilibrium regions under robust model predictive control (MPC) strategies was extensively studied in the last decades making use of Lyapunov theory in most cases. However, in spite of its potential application benefits, the problem of finite‐time convergence under fixed prediction horizon has not received, with some few exceptions, much attention in the literature. Considering the importance in several applications of having finite‐time convergence results in the context of fixed horizon MPC controllers and the lack of studies on this matter, this work presents a new set‐based robust MPC (RMPC) for which, in addition to traditional stability guarantees, finite‐time convergence to a target set is proved, and moreover, an upper bound on the time necessary to reach that set is provided. It is remarkable that the results apply to general nonlinear systems and only require some weak assumptions on the model, cost function, and target set.     

Multiobjective predictive cruise control for connected vehicle systems on urban conditions with InPA‐SQP

The connected vehicle (CV) system is one of the most effective core technologies in intelligent transportation systems. In order to solve the optimal velocity prediction problem for a CV system on urban roads, a multiobjective predictive cruise controller (MOPCC) for vehicles in the CV system is proposed to coordinate multiple performances including safety, tracking ability, ride comfort, and fuel economy. Firstly, with the ad hoc wireless communication technology, the signal phase and timing information is obtained to calculate the feasible velocity range for improving mobility. Then, the optimal target velocity of vehicles is computed by minimizing the fuel economic polynomial models of the vehicle system. Secondly, in order to systematically cope with those multiple performances, the Utopia point method is applied to change the multiobjective optimization problem into Utopia tracking problem. Furthermore, the MOPCC problem is formulated and solved by a fast numerical algorithm, ie, integrated perturbation analysis and sequential quadratic programming. Finally, simulations are presented to demonstrate the effectiveness of the proposed method in terms of improved the multiple performances.     

Stable impulsive zone model predictive control for type 1 diabetic patients based on a long-term model

In this work, the problem of regulating blood glucose (glycemia) in type I diabetic patients is studied by means of an impulsive zone model predictive control (iZMPC), which bases its predictions on a novel long-term glucose-insulin model. Taking advantage of the impulsive version of the model—which features real-life properties of diabetes patients that some other popular models do not—the given control guarantees the stability under moderate-to-severe plant-model mismatch and disturbances. Long-term scenarios—including meals and physiological parameter variations—are simulated and the results are satisfactory as every hyperglycemic and hypoglycemic episodes are suitably controlled.     

Analytical design of stable delta‐domain generalized predictive control

This paper addresses certain fundamental issues related to the discrete‐time design problem of the delta‐domain generalized predictive control (δ‐GPC) for both minimum phase and non‐minimum phase linear SISO plants including nominal stability and nominal performance of the closed‐loop system. The approach being presented is completely analytical, and the nominal performance of the control system is directly achieved by a prototype design of the closed‐loop system characteristics resulting in definite time‐domain specifications. Two design methods are offered in which a model‐based prediction paradigm is applied to achieve the future output and the future filtered output trajectory of the plant. Prediction of the first type is based on suitable emulations of the output δ‐derivatives and is used in the GPC controller design for minimum‐phase models of the plant. Prediction of the second type utilizes emulation of derivatives of the output filtered by the numerator polynomial of the transfer function of the controlled part of the plant. It can be employed both for minimum phase and non‐minimum phase plants. A numerical example is given that illustrates the δ‐GPC method for controller design. Copyright © 2002 John Wiley & Sons, Ltd.     

Optimal control of a delayed SIRC epidemic model with saturated incidence rate

In this paper, we present a susceptible‐infected‐recovered cross‐immune (SIRC) epidemic model, which describes Influenza A and analyzes the SIRC epidemic model through the optimal control theory and mathematical analysis. We show the existence of an optimal control pair for the optimal control problem by using Pontryagin's maximum principle with delay and derive the optimality condition. Finally, numerical simulation is carried out to verify our theoretical results.     

A primal‐dual active‐set method for distributed model predictive control

We present a novel distributed primal‐dual active‐set method for model predictive control. The primal‐dual active‐set method is used for solving model predictive control problems for large‐scale systems with quadratic cost, linear dynamics, additive disturbance, and box constraints. The proposed algorithm is compared with dual decomposition and an alternating direction method of multipliers. Theoretical and experimental results show the effectiveness of the proposed approach for large‐scale systems with communication delays. The application to building control systems is thoroughly investigated. Copyright © 2016 John Wiley & Sons, Ltd.     

A novel hybrid model predictive control design with application to a quadrotor helicopter

In this paper, a novel control design strategy based on a hybrid model predictive control in combination with fuzzy logic control is presented for a quadrotor helicopter system. In the proposed scheme, a 2‐part control structure is used. In the first part, a linear model predictive controller with receding horizon design strategy is combined with a nonlinear model predictive controller, which is applied as the main controller. In the second part, a 2‐level fuzzy logic controller is utilized to assist the first controller when the error exceeds a predefined value. The proposed nonlinear predictive control method utilizes a novel approach in which a prediction of the future outputs is used in the modeling stage. Using this simple technique, the problem can be solved using linear methods and, thereby, due to considerable reduction in the computational cost, it will be applicable for the systems with fast dynamics. Moreover, the fuzzy logic controller is used as a supervisor to adjust a proportional‐integral‐derivative controller to enhance the system performance by decreasing the tracking error. The proposed scheme is applied to a model of quadrotor system such that the difference between the predicted output of the system and the reference value is minimized while there are some constraints on inputs and outputs of the nonlinear quadrotor system. Simulation results demonstrate the efficiency of the proposed control scheme for the quadrotor system model.     

Gap metric–based model bank construction for wind turbine predictive control

This paper presents a novel model bank construction method for the multiple model predictive control of wind turbine system. The gap metric is used to measure the dynamic difference between the linearized models of the wind turbine system at different wind speed. Two algorithms are then proposed to divide the wind speed range in different operating regions. Meanwhile, a complete and nonredundant linear model bank is established to approximate the wind turbine system in the whole operating region. We take the robust model predictive control algorithm to design the local controller and utilize the wind speed as the switching criterion to combine the submodels. The simulation study on a 5‐MW wind turbine verifies the efficiency of the proposed method.     

A robust control system scheme based on model predictive controller (MPC) for continuous‐time systems

In this paper, an LMI framework based on model predictive strategy is addressed to design a robust dynamical control law in a typical control system. In the proposed method, instead of traditional static controller, a dynamic control law is used. With a suitable matrix transformation, the controller parameters selection are translated into an optimization problem with some LMI constraints. The plant input and output constraints are also handled with another LMIs. The controller is represented in state space form, and its parameters are computed in real‐time operation. For achieving this goal, by solving an optimization problem, a dynamic controller is designed, which meets the required plant performances. These results are used in 2 numerical examples to demonstrate the effectiveness of the proposed approach.     

ACADO toolkit—An open‐source framework for automatic control and dynamic optimization

In this paper the software environment and algorithm collection ACADO Toolkit is presented, which implements tools for automatic control and dynamic optimization. It provides a general framework for using a great variety of algorithms for direct optimal control, including model predictive control as well as state and parameter estimation. The ACADO Toolkit is implemented as a self‐contained C++ code, while the object‐oriented design allows for convenient coupling of existing optimization packages and for extending it with user‐written optimization routines. We discuss details of the software design of the ACADO Toolkit 1.0 and describe its main software modules. Along with that we highlight a couple of algorithmic features, in particular its functionality to handle symbolic expressions. The user‐friendly syntax of the ACADO Toolkit to set up optimization problems is illustrated with two tutorial examples: an optimal control and a parameter estimation problem. Copyright © 2010 John Wiley & Sons, Ltd.     

Constrained linear parameter‐varying control using approximate multiparametric programming

We develop an approximate multiparametric convex programming approach with its application to control constrained linear parameter‐varying systems. Recently, the application of the real‐time model predictive control (MPC) for various engineering systems has been significantly increased by using the multiparametric convex programming tool, known as explicit MPC approach. The main idea of explicit MPC is to move the major parts of the computations to offline phase and to provide an explicit piecewise affine solution of the constrained MPC problem, which is defined over a set of convex polyhedral partitions. In the proposed method, the idea of convex programming and partitioning is applied for linear parameter‐varying control systems. The feasible space of the time‐varying parameters is divided into simplices in which approximate solutions are calculated such that the approximation error is kept limited by solving sequences of linear programs. The approximate optimal solution within each simplex is obtained by linear interpolation of the optimal solutions in the simplex vertices, and then multiparametric programming tool is utilized to compute an explicit state feedback solution of linear quadratic optimal control problem for simplex vertices subject to state and input constraints. The proposed method is illustrated by a numerical example and the simulation results show the advantages of this approach.     

Minimizing control energy in a class of bounded‐control linear‐quadratic regulator problems

Minimal‐control‐energy strategies are substantiated and illustrated for linear‐quadratic problems with penalized endpoints and no state‐trajectory cost, when bounds in control values are imposed. The optimal solution for a given process with restricted controls, starting at a known initial state, is shown to coincide with the saturated solution to the unrestricted problem that has the same coefficients but starts at a generally different initial state. This result reduces the searching span for the solution: from the infinite‐dimensional set of admissible control trajectories to the finite‐dimensional Euclidean space of initial conditions. An efficient real‐time scheme is proposed here to approximate (eventually to find) the optimal control strategy, based on the detection of the appropriate initial state while avoiding as much as possible the generation and evaluation of state and control trajectories. Numerical (including model predictive control) simulations are provided, compared, and checked against the analytical solution to ‘the cheapest stop of a train’ problem in its pure‐upper‐bounded brake, flexible‐endpoint setting. Copyright © 2013 John Wiley & Sons, Ltd.     

Robust model predictive control of a micro machine tool for tracking a periodic force signal

The micro machine tool that can produce nanostructures by force modulation approach plays a significant role in nanotechnology. In this paper, to guarantee fast and high-precision cutting subject to external disturbances and input saturation, a robust model predictive control (MPC) using a tube-based method is exploited to develop a controller for the machining system consisting of a piezoelectric tube (PZT) actuator, a force sensor and a cutting tool, which updates the state of the art. In particular, the dynamic model of the machining system, with the voltage fed into PZT being input and the cutting force being output, is identified by incorporating the map between the cutting force and the displacement of PZT. Based on the voltage-force dynamic model, a tube-based MPC controller that consists of two optimizers is used to make PZT actuator track a desired periodic force signal. Finally, the effectiveness of the MPC method for force signal tracking under different frequencies is validated and advantages over the conventional proportional integral controller are also shown in the presence of the constraints of saturated input and external disturbances via numerical simulations.     

On fusion of PCA and a physical model‐based predictive control strategy for efficient load‐cycling operation of a thermal power plant

Controlling a thermal power plant optimally during load‐cycling operation is a very challenging control problem. The control complexity is enhanced further by the possibility of simultaneous occurrence of sensor malfunctions and a plethora of system disturbances. This paper proposes and evaluates the effectiveness of a sensor validation and reconstruction approach using principal component analysis (PCA) in conjunction with a physical plant model. For optimal control under severe operating conditions in the presence of possible sensor malfunctions, a predictive control strategy is devised by appropriate fusion of the PCA‐based sensor validation and reconstruction approach and a constrained model predictive control (MPC) technique. As a case study, the control strategy is applied for thermal power plant control in the presence of a single sensor malfunction. In particular, it is applied to investigate the effectiveness and relative advantage of applying rate constraints on main steam temperature and heat‐exchanger tube‐wall temperature, so that faster load cycling operation is achieved without causing excessive thermal stresses in heat‐exchanger tubes. In order to account for unstable and non‐minimum phase boiler–turbine dynamics, the MPC technique applied is an infinite horizon non‐linear physical model‐based state‐space MPC strategy, which guarantees asymptotic stability and feasibility in the presence of output and state constraints. Copyright © 2007 John Wiley & Sons, Ltd.