Predictive Control Formulation Research Articles

On the Identification of Social Cognitive Theory Models and Closed-loop Intervention Simulations Using Hybrid Model Predictive Control

Abstract This paper presents closed-loop intervention simulations for an identified, data-validated model of Social Cognitive Theory (SCT). A reduced-complexity SCT model structure consisting of dynamic operant conditioning and self-efficacy loops is considered for the prediction of physical activity behavior. Consistent with real-world requirements, including the need for hybrid decision rules policies, the proposed closed-loop intervention design follows a Hybrid Model Predictive Control formulation. The prime goal of this paper is to reinforce the viability of the system identification and control engineering frameworks in the design of optimized and perpetually adaptive behavioral health interventions.

Adaptive multi-model predictive control applied to continuous stirred tank reactor

This paper investigates the design of a Model Predictive Control (MPC) formulation for the case of polytopic multi-model system representation. An adaptive MPC is developed taking into account the scheduling parameters in the multi-model and a terminal invariant set for all the systems that are within the system polytope. This proposed method uses a virtual model-process tuning variable, which is optimized to find the best Linear Time Invariant (LTI) prediction sequence for the horizon, based on the LTI vertices of the polytopic system. Finally, the proposed adaptive MPC is applied to a continuous stirred tank reactor (CSTR) system. Discussions are set upon the a-priori design procedure, the online computational effort and application difficulties.

Dynamic Process Operation Under Demand Response – A Review of Methods and Tools

AbstractParticipating in electricity markets through demand response causes new requirements for optimizing process control of chemical plants. The last ten years have brought great advances in the formulation and solution of economic nonlinear model predictive control and state estimation to support operation of processes under dynamic constraints. However, gaps remain regarding the availabilities of suitable plant models capable of describing processes active in demand response as well as of robust schemes for state estimation and economic nonlinear model predictive control in commercial tools.

Real-time walking step timing adaptation by restricting duration decision for the first footstep

ABSTRACT This paper presents two model predictive control formulations for automatically deciding walking step duration for humanoid robots. In the proposed schemes, constrained optimization problems are solved online to simultaneously decide center of mass jerks, foothold positions, and step timing while respecting actuation, geometry, and contact constraints. The main contribution of this work is showing that restricting the duration decision to the first footstep is an effective strategy to achieve real-time computational time. Simulated and real robot experiments were undertaken to present and discuss the capabilities of the proposed formulations.

Handbook of Model Predictive Control [Bookshelf

This handbook contains 27 chapters that are organized into three parts. Part 1 is on theory and comprises 12 chapters, ranging from basic MPC theory to advanced studies and model predictive control (MPC) formulations. Part 2, on computation, includes eight chapters and covers numerical implementation of MPC-related optimization algorithms. Part 3 discusses applications of MPC in numerous fields, such as automotive, power and energy systems, health care, and finance. The book is designed for a wide audience. It is an excellent reference for graduate students, researchers, and practitioners in the field of control systems and numerical optimization who want to understand the potential, challenges, and benefits of MPC and its applications. Alternately, it is an up-to-date reference for MPC research experts (both in academia and industry). For this audience, the book helps experts address new MPC-related problems and research directions. The book provides a thorough and comprehensive reference of the underlying theory, implementation, and applications of MPC. The content of the book, contributed by various experts in the field, is well written and suitably organized into three parts. Furthermore, this book does an excellent job meeting several competing goals: clarity of communication to a diversified audience, formal rigor, and a self-contained presentation of the topics in each chapter. This handbook enables the reader to gain a panoramic viewpoint of MPC theory and practice as well as provides a state-of-the art overview of new and exciting areas of application at the forefront of MPC research.

Implementation of MPC-Based Trajectory Tracking Considering Different Fidelity Vehicle Models

In order to investigate how model fidelity in the formulation of model predictive control(MPC) algorithm affects the path tracking performance, a bicycle model and an 8 degrees of freedom(DOF) vehicle model, as well as a 14-DOF vehicle model were employed to implement the MPC-based path tracking controller considering the constraints of input limit and output admissibility by using a lower fidelity vehicle model to control a higher fidelity vehicle model. In the MPC controller, the nonlinear vehicle model was linearized and discretized for state prediction and vehicle heading angle, lateral position and longitudinal position were chosen as objectives in the cost function. The wheel step steering and sine wave steering responses between the developed vehicle models and the Carsim model were compared for validation before implementing the model predictive path tracking control. The simulation results of trajectory tracking considering an 8-shaped curved reference path were presented and compared when the prediction model and the plant were changed. The results show that the trajectory tracking errors are small and the tracking performances of the proposed controller considering different complexity vehicle models are good in the curved road environment. Additionally, the MPC-based controller formulated with a high-fidelity model performs better than that with a low-fidelity model in the trajectory tracking.

Nonlinear temperature regulation of solar collectors with a fast adaptive polytopic LPV MPC formulation

Temperature control in solar collectors is a nonlinear problem: the dynamics of temperature rise vary according to the fluid flowing through the collector and to the temperature gradient along the collector area. In this way, this work investigates the formulation of a Model Predictive Control (MPC) application developed within a Linear Parameter Varying (LPV) formalism, which serves as a model of the solar collector process. The proposed system is an adaptive MPC, developed with terminal set constraints and considering the scheduling polytope of the model. At each instant, two Quadratic Programming (QPs) programs are solved: the first considers a backward horizon of N steps to find a virtual model-process tuning variable that defines the best LTI prediction model, considering the vertices of the polytopic system; then, the second QP uses this LTI model to optimize performances along a forward horizon of N steps. The paper ends with a realistic solar collector simulation results, comparing the proposed MPC to other techniques from the literature (linear MPC and robust tube-MPC). Discussions regarding the results, the design procedure and the computational effort for the three methods are presented. It is shown how the proposed MPC design is able to outrank these other standard methods in terms of reference tracking and disturbance rejection.

Novel Predictive Control for the IPMSM Fed by the 3L-SNPC Inverter for EVAs: Modified Lyapunov Function, Computational Efficiency, and Delay Compensation

This paper proposes a novel predictive strategy based on a model predictive control (MPC) for the interior permanent magnet synchronous motors (IPMSMs) driven by a three-level simplified neutral-point clamped inverter (3L-SNPC) for electric vehicle applications (EVAs). Based on the prediction of the future behavior of the controlled variables, a predefined multiobjective cost function incorporates the control objectives which are evaluated for every sampling period to generate the optimal switching state applied directly to the inverter without the modulation stage. The control objectives in this paper are tracking current capacity, neutral-point voltage balancing, common-mode voltage control, and switching frequency reduction. The principal concepts of the novel scheme are summarized as follows: first, the delay compensation based on the long horizon of prediction is adopted by a multilevel power converter structure. Second, based on the modified Lyapunov candidate function, both stability and recursive feasibility are ensured of the proposed predictive scheme. Third, the practicability of the real-time implementation is improved by the proposed “static voltage vector” (SVV) and “single state variation” (SSV) principles. Finally, the proposed concepts are implemented in the novel predictive control formulation as additional constraints without compromising the complexity and the good performances of the predictive controller. Therefore, only the switching states that guarantee the stability and the reduction of calculation burden criteria are considered in the evaluation of cost function. The proposed predictive scheme based on the “SVV” principle has demonstrated superior performance in simulation compared with the proposed scheme with the “SSV” principle. The computational burden and switching frequency rates are reduced by 35% and 56.22%, respectively.

A partial multiparametric optimization strategy to improve the computational performance of model predictive control

Determining the optimal manipulated action for large scale model predictive control formulations requires significant computational overhead. It has been demonstrated that the offline, explicit solution provided by multiparametric programming has the capacity to greatly improve the online computational performance of MPC strategies. For large scale problems, developing and deploying the full multiparametric solution remains an open challenge. In this work, a partial multiparametric solution is utilized to improve the initialization procedure for a hot start strategy. The hot start strategy provides an improved technique for determining the optimal solution of large scale MPC formulations, and the partial multiparametric solution ensures the initialization is suitable under varying conditions. The efficacy of the proposed strategy is verified on randomly generated large scale MPC problems.

Implicit predictive flux control for high-performance induction motor drives

The paper aims to present a new formulation of a model predictive control for induction motor (IM) drives. The proposed control approach is based on utilizing the stator flux components as control variables; consequently, the cost function can be formulated in terms of only flux terms avoiding the use of weighting factor usually present in the model predictive direct torque control (MP DTC) techniques. The motor is modelled considering stator iron losses. An effective stator flux estimator is used to enhance the flux predictive control. A loss minimization criterion (LMC) is proposed in order to minimize the machine losses, especially at light load operation. In order to simplify the overall control scheme, the PWM strategy is eliminated and new model predictive flux control (MP FC) is implemented by the finite control set principle which enables the direct selection of voltage vectors among those (eight) delivered by the inverter. To prove the validity of the proposed MP FC, a detailed comparative study has been carried out between the performances of the IM drive under the classic MP DTC and the proposed MP FC control approaches (with and without the LMC). Dynamic performance of the drive is firstly tested by MATLAB/Simulink; then, a dSpace 1104 fast control prototyping board is used for the experimental verifications. The obtained results approve the improved dynamic performance of the IM drive under the proposed MP FC technique in comparison with the MP DTC.

Collision Imminent Steering at High Speed Using Nonlinear Model Predictive Control

Collision imminent steering is an automotive active safety feature designed to perform an aggressive lane change to avoid a forward collision in the event that the system determines there is insufficient distance to avoid a collision by braking alone.In this paper, a collision imminent steering system is developed using nonlinear model predictive control to perform a lane change at high speed in a highway environment. Two formulations are presented: one formulation to show the theoretical minimum lane change distance within which a safe lane change can be performed, and a second formulation to find the minimum aggressive maneuver for a given lane change distance. The nonlinear model predictive control formulation is posed as a constrained optimization problem, where solutions obey hard safety constraints of the highway environment. Constraint aggregation techniques are analyzed and introduced to monitor the peak tire slip throughout the maneuver. Numerical simulations of a typical luxury sedan in a highway setting show that minimum distance required to change lanes is about half the limit braking distance. Hence, there is a window of feasibility where the vehicle cannot avoid collision by braking alone, but can change lanes safely and maintain a safe trajectory throughout the maneuver. Additional simulations show that an active four wheel steering architecture improves performance over front only steering.

Task allocation and trajectory planning for multiple agents in the presence of obstacle and connectivity constraints with mixed‐integer linear programming

SummaryThis article addresses the problem of maneuvering multiple agents that must visit a number of target sets, while enforcing connectivity constraints and avoiding obstacle as well as interagent collisions. The tool to cope with the problem is a formulation of model predictive control including binary decision variables. In this regard, two mixed‐integer linear programming formulations are presented, considering a trade‐off between optimality and scalability between them. Simulation results are also shown to illustrate the main features of the proposed approaches.

Efficient Representation and Approximation of Model Predictive Control Laws via Deep Learning.

We show that artificial neural networks with rectifier units as activation functions can exactly represent the piecewise affine function that results from the formulation of model predictive control (MPC) of linear time-invariant systems. The choice of deep neural networks is particularly interesting as they can represent exponentially many more affine regions compared to networks with only one hidden layer. We provide theoretical bounds on the minimum number of hidden layers and neurons per layer that a neural network should have to exactly represent a given MPC law. The proposed approach has a strong potential as an approximation method of predictive control laws, leading to a better approximation quality and significantly smaller memory requirements than previous approaches, as we illustrate via simulation examples. We also suggest different alternatives to correct or quantify the approximation error. Since the online evaluation of neural networks is extremely simple, the approximated controllers can be deployed on low-power embedded devices with small storage capacity, enabling the implementation of advanced decision-making strategies for complex cyber-physical systems with limited computing capabilities.

Harmonic Based Model Predictive Control for Set-Point Tracking

This paper presents a novel model predictive control (MPC) formulation for set-point tracking. Stabilizing predictive controllers based on terminal ingredients may exhibit stability and feasibility issues in the event of a reference change for small to moderate prediction horizons. In the MPC for tracking formulation, these issues are solved by the addition of an artificial equilibrium point as a new decision variable, providing a significantly enlarged domain of attraction and guaranteeing recursive feasibility for any reference change. However, it may suffer from performance issues if the prediction horizon is not large enough. This paper presents an extension of this formulation where a harmonic artificial reference is used in place of the equilibrium point. The proposed formulation achieves even greater domains of attraction and can significantly outperform other MPC formulations when the prediction horizon is small. We prove the asymptotic stability and recursive feasibility of the proposed controller, as well as provide guidelines for the design of its main ingredients. Finally, we highlight its advantages with a case study of a ball and plate system.

Formation of Generic UAVs-USVs System Under Distributed Model Predictive Control Scheme

This brief presents a distributed model predictive formation control algorithm of heterogeneous multi-agent systems with directed topology, which consists of unmanned surface vehicles (USVs) and generic unmanned aerial vehicles (UAVs). The dynamics of UAVs and USVs are modeled by the Newton-Euler equation and Euler-Lagrange equation, respectively. We design the distributed model predictive control scheme to coordinate the UAVs-USVs system, where both feasibility and stability analyses are presented to guarantee the satisfactory formation. Simulation results demonstrate the effectiveness of the proposed distributed predictive formation algorithm.

Microsecond nonlinear model predictive control for DC‐DC converters

SummaryIn this paper, we present a novel nonlinear model predictive control (NMPC) formulation for the transient control of a DC‐DC converter. We demonstrate that a real‐time implementation of the proposed NMPC scheme using the PANOC solver can be efficiently applied to control DC‐DC converters in the microsecond range. Moreover, an embedded, code‐generated version of PANOC can be implemented using microcontrollers or digital signal processors. The algorithm is incorporated in the transient simulator of PWM DC‐DC converters, and the operation of the simulator on the boost converter's example is presented, comparing the performance of our NMPC‐controller with that of a classical PID controller. The operation of the boost converter controlled using the proposed NMPC algorithm is validated experimentally.

Vertical hierarchical MPC for constrained linear systems

A hierarchical Model Predictive Control (MPC) formulation is presented for discrete-time linear systems with state and input constraints. A vertical hierarchical controller, with one controller per level, reduces the computational burden associated with the solution of centralized MPC having long prediction horizons and short time steps. To guarantee satisfaction of state and input constraints in the presence of both known and unknown disturbances, a robust MPC formulation is used at each level while waysets are used as a novel coordination mechanism between controllers at different levels. These waysets are implemented as terminal state constraints on lower-level controllers and are computed on-line based on the optimal state trajectory of upper-level controllers. To achieve the computational efficiency necessary for on-line calculation, waysets are represented as constrained zonotopes. State and input constraint satisfaction is proven for a hierarchical controller with an arbitrary number of levels and two numerical examples demonstrate the key features, performance, and scalability of the approach.

Infinite horizon model predictive control tracking application to helicopters

A novel formulation for infinite horizon model predictive control that is general and can accurately approximate and minimize the control cost is proposed. This method allows output tracking over a finite horizon when constraints are considered and equilibrium tracking in the linearized dynamics after that for the infinite horizon when constraints are not considered. The method allows prescribing weights simultaneously on the output tracking error, control rates, and control energy. Methods of weight selection are discussed to ensure strong cost convexity for reliable optimization. The control method is used to bring a helicopter that is far from a ship to a stable flight condition that is much closer to the ship. This is very important for helicopter ship landing automation.

Formulation of min-max model predictive control as a box-constrained robust least squares estimation problem

The purpose of this paper is to propose a new approach to the Min-Max Model Predictive Control (MMMPC) of Linear Time-Invariant Discrete-time Polytopic (LTIDP) systems. The purpose is to simplify the treatment of complex issues like stability and feasibility analysis of robust MPC as well as to reduce the complexity of the relative optimization procedure. The new approach is based on a two Degrees Of Freedom (2DOF) control scheme where the output r(k) of the feedforward Input Estimator (IE) is used as input forcing a stable closed-loop system Σf. Σf is the feedback connection of an LTIDP plant Σp with an LTI dynamic controller Σg. The task of Σg is to guarantee the quadratic stability of Σf, as well as the fulfillment of hard constraints on some physical variables of Σf for any input r(k) satisfying an ”a priori” determined admissibility condition. The input r(k) is computed by the feedforward IE through the on-line minimization of a worst case finite-horizon quadratic cost functional and is applied to Σf according to the usual receding horizon strategy. Rather than resorting to an ”ad hoc” software, the numerical complexity issue is here addressed reducing the number of both decision variables and constraints involved in the on-line constrained optimization procedure. This is obtained modeling r(k) as a B-spline function, which is known to be a universal approximator which also admits a parsimonious parametric representation. This allows us to reformulate the minimization of the worst case cost functional as a box-constrained Robust Least Squares (RLS) estimation problem which can be efficiently solved using Second Order Cone Programming (SOCP).

Successive Linearization based Stochastic Model Predictive Control for batch processes described by DAEs

This paper presents a formulation of Stochastic Model Predictive Control (SMPC) for control of batch processes modeled by nonlinear Differential algebraic Equations (DAEs). In presence of additive stochastic disturbances, states become stochastic variables and measurements are also corrupted with noise. Hence, to obtain refined state estimates we employ DAE-Extended Kalman Filter (EKF). Linear prediction model obtained by successive linearization is used in the SMPC formulation. Our proposed SMPC solves a chance constrained optimization problem in receding horizon window to calculate future control moves with pre-specified degree of constraint violation for trajectory tracking. Further, the probabilistic constraints are converted to hard constraints by accommodating necessary back-off. We present a simulation case study of batch transesterification reactor modeled by non-linear DAEs to validate the proposed SMPC framework.