Stochastic model predictive control for tracking linear systems

This note presents a stochastic formulation of the model predictive control for tracking (MPCT), based on the results of the work of Lorenzen et al. The proposed controller ensures constraints satisfaction in probability, and maintains the main features of the MPCT, that are feasibility for any changing setpoints and enlarged domain of attraction, even larger than the one delivered by Lorenzen et al, thanks to the use of artificial references and relaxed terminal constraints. The asymptotic stability (in probability) of the minimal robust positively invariant set centered on the desired setpoint is guaranteed. Simulations on a DC-DC converter show the benefits and the properties of the proposal.     

Investment portfolio tracking using model predictive control

The composition of an investment portfolio aiming to increase the financial returns while reducing the exposure to risk is a topic of growing interest in the world. In this direction, we propose a model predictive control (MPC) strategy in order to optimize the investment portfolio selection taking into account the tracking of a reference portfolio with desired return. In addition, an analysis comparing different sizes of the prediction horizon according to VPH-MPC (Varying Predictive Horizon-MPC) and FPH-MPC (Fixed Predictive Horizon-MPC) algorithms is conducted. Finally, we propose an optimal control problem using the tracking error as a function of loss of CVaR (Conditional Value at Risk) measurement. Numerical experiments are run based on Brazilian Stock Exchange data. The experimental results are compared with the Markowitz portfolio optimization model, a conventional tracking strategy, and benchmarks from the Brazilian financial market. This comparison indicates a good tracking performance obtained by the proposed MPC in the two versions while satisfying the constraints.     

Economic model predictive control for time-varying system: Performance and stability results

We consider economic model predictive control (MPC) without terminal conditions for time-varying optimal control problems. Under appropriate conditions, we prove that MPC yields initial pieces of approximately infinite horizon optimal trajectories and that the optimal infinite horizon trajectory is practically asymptotically stable. The results are illustrated by numerical examples motivated by energy-efficient heating and cooling of a building.     

Solution of some model predictive control problems using slopes between unconstrained and constrained optimums

At times, the number of controlled variables equals the number of manipulated variables and the objective of the control system is to minimize the difference in the desired and predicted output trajectories subject only to constraints on the manipulated variables. If a simplified model predictive control algorithm is used for such applications, then solution to the optimization problem can be obtained by using the slopes between the unconstrained and constrained optimums. The solution procedure is described for a two‐input–two‐output case. A comparison with a linear programming (LP) formulation showed that the computational time for the proposed solution was about 35 times less than the time for the LP solution. Copyright © 1999 John Wiley & Sons, Ltd.     

Engine idle speed control using nonlinear multiparametric model predictive control

In this article, a real-time nonlinear model predictive idle speed controller based on multiparametric programming is designed for an SI engine. Idle speed is a crucial recurring condition in urban vehicles demanding proper control to avoid stall. As will be seen, the nonlinear model predictive control (NMPC) system designed, besides complying with the predefined constraints, demonstrates a far better performance than the prevalent industrial controllers and even conventional linear MPC controllers. More importantly, a new special structure combining offline nonlinear MPC and classical controller is employed to provide both robustness and fast response. Not only is the computational burden of the controller within that of the ordinary ECU controllers, it is also able to readily damp a disturbance of 20 N·m in less than 2.5 seconds and easily deal with parameter uncertainties. The control system also regulates engine gas pedal release, and converges to the set point with a settling time of less than 3 seconds and minimum fluctuations.     

Stochastic model predictive control approaches applied to drinking water networks

Control of drinking water networks is an arduous task, given their size and the presence of uncertainty in water demand. It is necessary to impose different constraints for ensuring a reliable water supply in the most economic and safe ways. To cope with uncertainty in system disturbances due to the stochastic water demand/consumption and optimize operational costs, this paper proposes three stochastic model predictive control (MPC) approaches, namely, chance‐constrained MPC, tree‐based MPC, and multiple‐scenario MPC. A comparative assessment of these approaches is performed when they are applied to real case studies, specifically, a sector and an aggregate version of the Barcelona drinking water network in Spain. Copyright © 2016 John Wiley & Sons, Ltd.     

Model predictive and linear quadratic Gaussian control of a wind turbine

Model Predictive and linear quadratic Gaussian controllers are designed for a 5MW variable‐speed pitch‐regulated wind turbine for three operating points – below rated wind speed, just above rated wind speed, and above rated wind speed. The controllers are designed based on two different linear dynamic models (at each operating point) of the same wind turbine to study the effect of utilising different control design models (i.e. the model used for designing a model‐based controller) on the control performance. The performance of the LQG controller is enhanced by improving the robustness, achieved by replacing the Kalman filter with a modified Luenberger observer, whose gain is obtained to minimise the effect of uncertainty and disturbance. Copyright © 2016 John Wiley & Sons, Ltd.     

Nonlinear model predictive control based on constraint transformation

The paper presents a constraint transformation approach for nonlinear model predictive control (MPC) subject to a class of state and control constraints. The approach uses a two‐stage transformation technique to incorporate the constraints into a new unconstrained MPC formulation with new variables. As part of the stability analysis, the relationship of the new unconstrained MPC scheme to an interior penalty formulation in the original variables is discussed. The approach is combined with an unconstrained gradient method that allows for computing the single MPC iterations in a real‐time manner. The applicability of the approach, for example, to fast mechatronic systems, is demonstrated by numerical as well as experimental results. Copyright © 2015 John Wiley & Sons, Ltd.     

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.     

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.     

Improving the grid frequency by optimal design of model predictive control with energy storage devices

This paper proposes the optimal design of model predictive control (MPC) with energy storage devices by the bat‐inspired algorithm (BIA) as a new artificial intelligence technique. Bat‐inspired algorithm‐based coordinated design of MPCs with superconducting magnetic energy storage (SMES) and capacitive energy storage (CES) is proposed for load frequency control. Three‐area hydrothermal interconnected power system installed with MPC and SMES is considered to carry out this study. The proposed design procedure can account for generation rate constraints and governor dead bands. Transport time delays imposed by governors, thermodynamic processes, and communication telemetry can be captured as well. In recent papers, the parameters of MPC with SMES and CES units are typically set by trial and error or by the designer's expertise. This problem is solved here by applying BIA to tune the parameters of MPC with SMES and CES units simultaneously to minimize the deviations of frequency and tie line powers against load perturbations. Simulation results are carried out to emphasize the superiority of the proposed coordinated design as compared with conventional proportional‐integral controller and with BIA‐based MPC without SMES and CES units.     

An alternating direction method of multipliers algorithm for symmetric model predictive control

This article presents an alternating direction method of multipliers (ADMM) algorithm for solving large‐scale model predictive control (MPC) problems that are invariant under the symmetric‐group. Symmetry was used to find transformations of the inputs, states, and constraints of the MPC problem that decompose the dynamics and cost. We prove an important property of the symmetric decomposition for the symmetric‐group that allows us to efficiently transform between the original and decomposed symmetric domains. This allows us to solve different subproblems of a baseline ADMM algorithm in different domains where the computations are less expensive. This reduces the computational cost of each iteration from quadratic to linear in the number of repetitions in the system. In addition, we show that the memory complexity for our ADMM algorithm is also linear in number of repetitions in the system, rather than the typical quadratic complexity. We demonstrate our algorithm for two case studies; battery balancing and heating, ventilation, and air conditioning. In both case studies, the symmetric algorithm reduced the computation‐time from minutes to seconds and memory usage from tens of megabytes to tens or hundreds of kilobytes, allowing the previously nonviable MPCs to be implemented in real time on embedded computers with limited computational and memory resources.     

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.     

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.     

PRESAS: Block-structured preconditioning of iterative solvers within a primal active-set method for fast model predictive control

Model predictive control (MPC) for linear dynamical systems requires solving an optimal control structured quadratic program (QP) at each sampling instant. This article proposes a primal active-set strategy, called PRESAS , for the efficient solution of such block-sparse QPs, based on a preconditioned iterative solver to compute the search direction in each iteration. Rank-one factorization updates of the preconditioner result in a per-iteration computational complexity of , where m denotes the number of state and control variables and N the number of control intervals. Three different block-structured preconditioning techniques are presented and their numerical properties are studied further. In addition, an augmented Lagrangian based implementation is proposed to avoid a costly initialization procedure to find a primal feasible starting point. Based on a standalone C code implementation, we illustrate the computational performance of PRESAS against current state of the art QP solvers for multiple linear and nonlinear MPC case studies. We also show that the solver is real-time feasible on a dSPACE MicroAutoBox-II rapid prototyping unit for vehicle control applications, and numerical reliability is illustrated based on experimental results from a testbench of small-scale autonomous vehicles.     

Characteristic model–based generalized predictive control and its application to the parafoil and payload system

Generalized predictive control (GPC) has been applied in systems to improve the control performance during the last decades. The designing of predictive model is the essential and vital problem in GPC application. Using characteristic model (CM) as predictive model in GPC can simplify the modeling procedure and improve computing efficiency of GPC. The CM is a kind of simple and easy‐to‐use dynamic model that is equivalent with precise model. Moreover, the creation of CM requires less system information than the practical models. The GPC with CM as predictive model named characteristic model–based generalized predictive control (CMGPC) is proposed in this paper, and it is used in the trajectory tracking control for parafoil and payload system. Simulations and analysis prove that CMGPC is equivalent to traditional GPC and CMGPC is a more efficient way for trajectory tracking of parafoil and payload system compared with conventional proportional integral derivative (PID) method.     

Multicriteria optimal operation of a microgrid considering risk analysis,renewable resources,and model predictive control

This paper proposes an optimal power dispatch by taking into account risk management and renewable resources. In particular, it examines how control engineering and risk management techniques can be applied in the field of power systems through their use in the design of risk-based model predictive controllers. To this end, this paper proposes a two-layer control scheme for microgrid management where both levels are based on model predictive control (MPC): the higher level is devoted to risk management while the lower layer is dedicated to power dispatching. In particular, the high-level controller is based on a risk-based approach where potential risks have been identified and evaluated. Mitigation actions are the decision variables to be optimized to reduce the consequences of risks and costs. The MPC-based algorithm decides the appropriate frequency of mitigation actions such as changes in references, constraints, and insurance contracting, by relying on a model that includes integer variables, identifiable risks, their costs, and the cost/benefit assessment of mitigating actions. On the other hand, the low-level controller drives the plant to suitable values to satisfy demands. A series of simulations on a nonlinear model of a real laboratory-scale power plant located in the facilities of the University of Seville are conducted under varying conditions to demonstrate the effectiveness of the algorithm when risks are explicitly considered.     

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.