Model Predictive Control Prediction Research Articles

Fault-tolerant control for satellite autonomous rendezvous with quality characteristics and actuator uncertainties

An autonomous fault detection and fault-tolerant control solution combining Model Predictive Control (MPC) and Label Distributed Learning (LDL) is developed for the position tracking and attitude synchronization problems in autonomous satellite rendezvous and docking. The proposed algorithm can deal with center of mass (CM) variations and time-varying mass characteristics due to satellite fuel consumption, actuator saturation and fault, and external disturbances. Firstly, a six-degree-of-freedom (6-DOF) satellite translation-rotation coupling model was established to express the relative motion between the satellite and the target, taking the above factors into account. Subsequently, an on-board autonomous closed-loop fault-tolerant control algorithm using MPC is proposed, in which an LDL-based fault detection mechanism is embedded. The scheme specifies that propulsion faults are estimated by calculating the difference between the MPC's prediction of the satellite's future state and the measured change in the actual state. And the mapping matrix between the commanded force/torque and the actual force of the propulsion system is updated in real time to achieve autonomous fault detection and compensation on board the satellite. Among them, the LDL-based fault detection scheme is trained offline. It requires only simple matrix operations for on-orbit use, which is low-cost and suitable for resource-limited space environments. The additional creation of a time-varying disturbance observer allows the estimation and compensation of unmodelled errors and external disturbances. The stability of the proposed fault-tolerant control algorithm is rigorously demonstrated using Lyapunov analysis. Finally, numerical simulations show that the proposed method can successfully achieve autonomous satellite docking under different combinations of thruster faults.

Linear parameter-varying model predictive control for nonlinear systems using general polytopic tubes

This paper deals with model predictive control (MPC) for nonlinear systems using linear-parameter varying (LPV) embedding of the nonlinear dynamics (LPVMPC). The proposed LPVMPC can incorporate information of the future evolution of the scheduling parameter over the MPC prediction horizon with uncertainty bounds, which are used to construct anticipated scheduling tubes for robustification. Therefore, this approach is less conservative than the methods that only consider knowledge of the bounds on the scheduling parameter’s rate of variation. The scheduling tubes are employed to synthesize online general polytopic invariant state tubes. The optimization problem of the proposed LPVMPC is a single quadratic program. Recursive feasibility is proven. A numerical example is presented for demonstrating the effectiveness of the proposed LPVMPC algorithm compared to nonlinear MPC and other standard approaches.

Robustness analysis of gain‐scheduled Model Predictive Control for Linear Parameter Varying systems: An Integral Quadratic Constraints approach

AbstractIn this paper, we evaluate the robustness qualities of Model Predictive Control (MPC) algorithms applied for Linear Parameter Varying (LPV) systems. Specifically, we analyze gain‐scheduled LPV MPC schemes, that is, those that use model predictions based on the LPV scheduling variables available at each sampling instant. Accordingly, we extend previous results on finite‐horizon robustness analysis of linear time‐variant (LTV) systems, employing Integral Quadratic Constraints (IQCs) to describe the input‐output behavior of prediction uncertainties. We provide two main novelties in our formulation: (i) we propose a parameter‐dependent Karush–Kuhn–Tucker (KKT) inequality to describe the existence and feasibility of the LPV MPC control inputs; and (ii) we model the uncertainties that arise due to the unavailability of the scheduling trajectory along the prediction horizon as a bounded interconnection in the form of a Linear Fractional Transformation (LFT). Accordingly, we use dissipativity arguments (‐hard IQCs) in order to compute robust induced gains of the closed‐loop system (specifically, the and ‐to‐Euclidean metrics), taking into account the MPC prediction uncertainties. We also generate the set of reachable states from a given initial condition. A benchmark example is used to illustrate the proposed analysis procedure.

Learning‐based model predictive control for improved mobile robot path following using Gaussian processes and feedback linearization

AbstractThis paper proposes a high‐performance path following algorithm that combines Gaussian processes (GP) based learning and feedback linearization (FBL) with model predictive control (MPC) for ground mobile robots operating in off‐road terrains, referred to as GP‐FBLMPC. The algorithm uses a nominal kinematic model and learns unmodeled dynamics as GP models by using observation data collected during field experiments. Extensive outdoor experiments using a Clearpath Husky A200 mobile robot show that the proposed GP‐FBLMPC algorithm's performance is comparable to existing GP learning‐based nonlinear MPC (GP‐NMPC) methods with respect to the path following errors. The advantage of GP‐FBLMPC is that it is generalizable in reducing path following errors for different paths that are not included in the GP models training process, while GP‐NMPC methods only work well on exactly the same path on which GP models are trained. GP‐FBLMPC is also computationally more efficient than the GP‐NMPC because it does not conduct iterative optimization and requires fewer GP models to make predictions over the MPC prediction horizon loop at every time step. Field tests show the effectiveness and generalization of reducing path following errors of the GP‐FBLMPC algorithm. It requires little training data to perform GP modeling before it can be used to reduce path‐following errors for new, more complex paths on the same terrain (see video at https://youtu.be/tC09jJQ0OXM).

Optimal control of TABS using a combined method of MPC and heat load prediction

AbstractThermally activated building systems (TABS), which use the building frame as a radiative and thermal storage site, have attracted attention as a means of achieving a thermal environment in office spaces that combines comfort and energy conservation. However, TABS have a large thermal capacity and a slow thermal response, making it desirable to introduce a control method based on model predictive control (MPC). There are problems with this method, such as its inability to predict periodic fluctuations in thermal load. Therefore, in this study, we propose a control method combining MPC and heat load prediction using a Neural Network, a type of supervised learning in machine learning, for an office space with TABS. The method was validated by co‐simulation using CFD and MATLAB/Simulink on a one‐span (7.20 × 7.20 × 3.87 m) TABS model. As a result, the proposed method reduced the integrated water flow rate and improved the energy performance while improving the control performance.

Model predictive trajectory tracking control of unmanned vehicles based on radial basis function neural network optimisation

To improve the accuracy of tracking unmanned vehicles on known trajectories, two optimised model predictive control (MPC) trajectory tracking control systems are designed based on the adaptive compensation and robust control of a radial basis function (RBF) neural network. Based on the traditional MPC trajectory tracking controller and the local approximation characteristics of the RBF neural network, the proposed RBF compensation–MPC control system is designed to compensate for the inaccuracy in the MPC prediction model arising from modelling errors. The results show that this method can achieve a root mean square error of less than 0.3703 m for the lateral position. Subsequently, to suppress the error generated by the RBF neural network and reduce the degree of vehicle sideslip, the error is considered to be external interference, and the anti-interference characteristic of the RBF robust control is incorporated into the RBF robust-MPC control system. Following the re-optimisation of the RBF robust control, the root mean square error of the lateral position is set within 0.2352 m. The results of a MATLAB/Carsim joint simulation show that using the RBF robust control can improve the tracking accuracy of the traditional MPC controller compared with RBF compensation control, while simultaneously improving the driving stability of the vehicle.

A low-cost pole-placement MPC algorithm for controlling complex dynamic systems

Due to the ability to handle constraints systematically and predict system evolution with models, model predictive control (MPC) methods have been widely studied and implemented in many industries. At the same time, low-cost MPC has received widespread attention due to its simple principle and easy implementation. This paper proposes a new low-cost MPC method and uses this method to put forward new insights on the performance improvement of complex dynamic system control. Firstly, using the concept of preprocessing, a novel MPC prediction structure is proposed under the independent model mode. Then through rigorous proofs, the properties of the proposed MPC algorithm are analyzed. Finally, through the study of three industrial cases, the proposal’s deployment procedure and efficacy are illustrated in detail. Compared with other low-cost predictive control algorithms, the effectiveness of the method has been presented.

Double-Layer Feedback Control Method for Synchronized Frequency Regulation of PMSG-Based Wind Farm

With the rapid growth of wind power penetration in power grid, the system operators need to implement the grid specification of wind farm participating in primary frequency regulation (PFR). In this paper, a double-layer control framework based on permanent magnet synchronous generator (PMSG) is proposed, which can simulate the inertia and droop characteristics similar to thermal units. The top-layer control adopts centralized model predictive control (MPC), while the bottom layer carries out distributed real-time correction control in case of inaccurate MPC prediction. In order to realize fast distributed correction among wind turbines (WTs), a distributed Newton method is proposed, which only requires WTs to exchange limited information with their neighbors on sparse communication network, and has a super-linear convergence rate. By introducing an index of state of energy, this method adequately exploits the kinetic energy of all WTs without loss of security. Compared with the centralized schemes, the dependence on prediction accuracy and data synchronization is greatly reduced. Compared with the distributed schemes, the overall characteristics and computing efficiency can be guaranteed. The simulation results show that the method has satisfactory dynamic performance and reliability, and the system frequency stability is significantly improved under the synchronized control method.

Enhanced Battery Power Constraint Handling in MPC-Based HEV Energy Management: A Two-Phase Dual-Model Approach

This article presents a novel two-phase dual-model approach to more appropriately handle battery power constraint in model predictive control (MPC)-based hybrid electric vehicle (HEV) energy management. The approach fuses two typical battery models with different fidelities in two consecutive phases of MPC's prediction horizon, where more accurate first-order resistor-capacitor (RC) model is adopted in the near phase, while a purely ohmic impedance model is used in the more distant phase. More importantly, it is mathematically rigorously proved that the first-order RC model can be reformulated as an equivalent single-state model while preserving accurate voltage calculation, provided that the length of phase one is properly determined. Finally, the formulated optimal energy management problem is solved using a forward dynamic programming (FDP) algorithm. Both numerical examination and model in the loop (MiL) test using an experimentally validated forward-facing simulator demonstrate that compared with traditional approach, the proposed approach can achieve better optimality in the condition of very sparse state discretization, which is imperative for real-time implementation.

LSTM and GRU Neural Networks as Models of Dynamical Processes Used in Predictive Control: A Comparison of Models Developed for Two Chemical Reactors.

This work thoroughly compares the efficiency of Long Short-Term Memory Networks (LSTMs) and Gated Recurrent Unit (GRU) neural networks as models of the dynamical processes used in Model Predictive Control (MPC). Two simulated industrial processes were considered: a polymerisation reactor and a neutralisation (pH) process. First, MPC prediction equations for both types of models were derived. Next, the efficiency of the LSTM and GRU models was compared for a number of model configurations. The influence of the order of dynamics and the number of neurons on the model accuracy was analysed. Finally, the efficiency of the considered models when used in MPC was assessed. The influence of the model structure on different control quality indicators and the calculation time was discussed. It was found that the GRU network, although it had a lower number of parameters than the LSTM one, may be successfully used in MPC without any significant deterioration of control quality.

Linearization of Recurrent-Neural-Network- Based Models for Predictive Control of Nano-Positioning Systems Using Data-Driven Koopman Operators

Recent studies have shown that the nonlinear dynamics of nano-positioning systems (e.g., piezo-electric actuators (PEAs)) can be accurately captured by recurrent neural networks (RNNs). One direct application of this technique is PEA system control for precision positioning: linearize the nonlinear RNN model and then apply model predictive control (MPC). However, due to the linearization approach commonly used (e.g., Taylor series), the control bandwidth and the control performance are quite limited as the obtained linear system is only guaranteed to be accurate within small neighborhood of the linearization point. To address this issue, we propose a Koopman operator-based approach for linearization and then use the obtained linear parameter-varying model for predictive control. This linearization scheme can significantly decrease the overall approximation error within the MPC prediction horizon, and thus, lead to improved tracking performance. The proposed approach was validated through two applications-trajectory tracking of PEA, and deformation control of polymers during atomic force microscope nano-indentation.

Multifactorial Prediction Errors Analysis and a Feedback Self-Correction on Model Predictive Control for the Three-Phase Inverter

To solve the problem of poor robustness due to the high dependence of model predictive control (MPC) on the three-phase inverter model, the influence mechanism of the mismatch of circuit parameters R and L , the model discretization error, and sampling errors on MPC prediction error are analyzed in this paper. A feedback self-correction is proposed, which the next current errors are predicted and used to modify the model, based on the previous prediction errors. This proposed method involves simple structure and a small amount of calculation. Steady-state effects of the proposed method are quantized to prove a good inhibitory ability on multifactorial prediction errors. Finally, experimental results in a three-phase inverter are presented to support the theoretical analysis and demonstrate the feasibility of the proposed method.

A novel MPC-based adaptive energy management strategy in plug-in hybrid electric vehicles

In this paper, an adaptive energy management strategy (AEMS) under model predictive control (MPC) framework is proposed. The main advantage of the AEMS is that it fully integrates the economy driving pro system (EDPS), which can provide the renewable energy consumption trajectory considering dynamic traffic information of target driving task, namely the state of charge (SOC) reference constraint for the MPC optimal calculation at each control step. Moreover, based on the dynamically updated traffic information, the SOC reference constraint will be re-planned with correction, which will further reflect the ideal energy consumption trend over the actual driving cycle. For the MPC prediction aspect, the deep neural network (DNN) is applied in this paper to predict the future short-term velocity with 5s, 10s and 15s horizon, respectively. Meanwhile, the dynamic programming (DP) is applied to calculate the optimal energy distribution at each MPC control step. Simulation results show that under the test driving cycle, the optimal MPC predictive horizon with the assistance of EDPS is 10s, and the fuel economy rate can improve up to 6.48% compared with energy management without the assistance of EDPS. Moreover, the HIL test indicates the AEMS has well real-time performance as well.

Design of a Path-Tracking Steering Controller for Autonomous Vehicles

This paper presents a linearization method for the vehicle and tire models under the model predictive control (MPC) scheme, and proposes a linear model-based MPC path-tracking steering controller for autonomous vehicles. The steering controller is designed to minimize lateral path-tracking deviation at high speeds. The vehicle model is linearized by a sequence of supposed steering angles, which are obtained by assuming the vehicle can reach the desired path at the end of the MPC prediction horizon and stay in a steady-state condition. The lateral force of the front tire is directly used as the control input of the model, and the rear tire’s lateral force is linearized by an equivalent cornering stiffness. The course-direction deviation, which is the angle between the velocity vector and the path heading, is chosen as a control reference state. The linearization model is validated through the simulation, and the results show high prediction accuracy even in regions of large steering angle. This steering controller is tested through simulations on the CarSim-Simulink platform (R2013b, MathWorks, Natick, MA, USA), showing the improved performance of the present controller at high speeds.

Optimal Placement and Sizing of Distributed Battery Storage in Low Voltage Grids Using Receding Horizon Control Strategies

In this paper we present a novel methodology for leveraging Receding Horizon Control (RHC), also known as Model Predictive Control (MPC) strategies for distributed battery storage in a planning problem using a Benders decomposition technique. Longer prediction horizons lead to better storage placement strategies but also higher computational complexity that can quickly become computationally prohibitive. The here proposed MPC strategy in conjunction with a Benders decomposition technique effectively reduces the computational complexity to a manageable level. We use the CIGRE low voltage (LV) benchmark grid as a case study for solving an optimal placement and sizing problem for different control strategies with different MPC prediction horizons. The objective of the MPC strategy is to maximize the photovoltaic (PV) utilization and minimize battery degradation in a local residential area, while satisfying all grid constraints. For this case study we show that the economic value of battery storage is higher when using MPC based storage control strategies than when using heuristic storage control strategies, because MPC strategies explicitly exploit the value of forecast information. The economic merit of this approach can be further increased by explicitly incorporating a battery degradation model in the MPC strategy.

Stochastic model predictive control based on Gaussian processes applied to drinking water networks

This study focuses on developing a stochastic model predictive control (MPC) strategy based on Gaussian processes (GPs) for propagating system disturbances in a receding horizon way. Using a probabilistic system representation, the state trajectories considering the influence of disturbances can be obtained through the uncertainty propagation by using GPs. This fact allows obtaining the confidence intervals for state evolutions over the MPC prediction horizon that are included into the MPC objective function and constraints. The feasibility of the proposed MPC strategy considering the incorporated results of disturbance forecasting is also discussed. Simulation results obtained from the application of the proposed approach to the Barcelona drinking water network taking real demand data into account are presented. The comparison with the well-known certainty-equivalent MPC shows the effectiveness of the proposed stochastic MPC approach.

Efficient MPC optimization using Pontryagin's minimum principle

AbstractA method of solving the online optimization in model predictive control (MPC) of input‐constrained linear systems is described. Using Pontryagin's minimum principle, the matrix factorizations performed by general purpose quadratic programming (QP) solvers are replaced by recursions of state and co‐state variables over the MPC prediction horizon. This allows for the derivation of solvers with computational complexity per iteration that depends only linearly on the length of the prediction horizon. Parameterizing predicted input and state variables in terms of the terminal predicted state results in low computational complexity but can lead to numerical sensitivity in predictions. To avoid ill‐conditioning an alternative parameterization is derived using Riccati recursions. Comparisons are drawn with the multiparametric QP solution, and the computational savings are demonstrated over generic QP solvers. Copyright © 2007 John Wiley & Sons, Ltd.