Using Particle Filters as an Optimizer for Model Predictive Control

This work investigates the event‐driven model predictive control problem for perturbed nonlinear systems with input and state constraints. Firstly, a new event‐driven triggering condition, considering the gradient and accumulation of the error between the optimal and actual states at adjacent moments with a state‐dependent relative threshold is designed with a guaranteed positive inter‐event time to avoid Zeno behaviour. Secondly, an error gradient and accumulation type event‐driven model predictive control framework is designed based on the new triggering condition and the dual‐mode strategy, for effectively reducing the calculation and communication burden of the model predictive control controller while ensuring desired control performance. Furthermore, the feasibility and the input‐to‐state practical stability (ISpS) of gradient and accumulation‐type event‐driven model predictive control are rigorously guaranteed theoretically. At last, the simulation results are provided to validate the this algorithm.

The efficiency of a SAGD operation depends on developing a uniform steam chamber and maintaining an optimal subcool along the length of the well pair. Heterogeneity in reservoir properties may lead to suboptimal subcool levels. Recently, Model Predictive Control (MPC) based on the real-time production, temperature, and pressure data along with other well and surface constraint information has been proposed for a real-time feedback control of SAGD well pairs. Reservoir dynamics in MPC is represented using either linear step response model or one-dimensional ordinary differential equation. However, such simplified models are insufficient in MPC since SAGD is more complex and highly nonlinear process. Therefore, MPC framework that represents nonlinear behaviour of SAGD over an extended control period is required to achieve optimized subcool and steam conformance. In this research, two novel workflows are proposed to handle nonlinear reservoir dynamics in MPC. First approach known as Adaptive MPC includes recursive estimations at each control interval based on system identification theory. This allows evolution of the coefficients of a fixed model structure such that the updated system identification model in MPC controller reflects current reservoir dynamics adequately. Another approach, Gain-Scheduled MPC, decomposes the subcool control problem in a parallel manner and uses a bank of multiple controllers rather than only one controller. This ensures effective control of the nonlinear reservoir system even in adverse control situations by employing aggressive variations in input parameters. Suggested workflows are implemented using history-matched numerical model of a reservoir located in northern Alberta. Steam injection rates and liquid production rate are considered as input variables in MPC, constrained to available surface facilities. Well-pair is divided into multiple sections and subcool of each section is considered as an output variable. Optimum set-point for subcool is considered as 20°C. Results are compared with actual field data (in which no control algorithm is used) and analyzed based on two criteria: 1) Do all subcools track optimum set-point while maintaining stability in input variables and 2) Does net present value (NPV) of oil improve in case of Adaptive and Gain-Scheduled MPC? In general, we conclude that both Adaptive and Gain-Scheduled MPC provide superior tracking of subcool set-point and hence better steam conformance due to adequate representation of reservoir dynamics by recursive estimation of coefficients and multiple controllers. In addition, results indicate stability in input parameters and improvement in economic performance. NPV is improved by 23.69% and 10.36% in case of Adaptive and Gain-Scheduled MPC, respectively. Under current economic scenario, proposed workflows can improve the NPV of a SAGD reservoir by optimizing the well operational parameters while considering constraints of surface facilities and minimizing environmental footprints.

In this paper, a model predictive control (MPC) framework for building energy system setpoint optimization is developed and tested. The performance of the MPC framework is presented in comparison to a baseline case, where a fixed setpoint schedule is used. To simulate the MPC procedure, an EnergyPlus building model is used to represent the actual building that the optimal setpoints are applied to, and a Gaussian process (GP) regression meta-model is used in the MPC procedure that generates the optimal setpoints. The performance outputs that are used for evaluation are total heating, ventilation and air conditioning (HVAC) energy usage and the Fanger predicted mean vote (PMV) thermal comfort measure. The inputs for the GP regression meta-models are selected to be representative of data points that could be obtained by modern supervisory control and data acquisition (SCADA) systems to support data-driven building models. The supervisory MPC framework is capable of reducing the total energy usage with minor adjustments in thermal comfort.

Recently, the increase of burden to operators and lack of skilled operators are the issue in the work of the hydraulic excavator. These problems are expected to be improved by autonomous control. In this paper, we present experimental results of hydraulic excavators using model predictive control (MPC) which incorporates servo mechanism. MPC optimizes digging operations by the optimal control input which is calculated by predicting the future states and satisfying the constraints. However, it is difficult for MPC to cope with the reaction force from soil when a hydraulic excavator performs excavation. Servo mechanism suppresses the influence of the constant disturbance using the error integration. However, the bucket tip deviates from a specified shape by the sudden change of the disturbance. We can expect that the tracking performance is improved by combining MPC and servo mechanism. Path-tracking controls of the bucket tip are performed using the optimal control input. We apply the proposed method to the Komatsu- made micro hydraulic excavator PC01 by experiments. We show the effectiveness of the proposed method through the experiment of digging soil by comparing servo mechanism and pure MPC with the proposed method.

International audience

A novel topology-aware model predictive control (MPC) framework is presented for navigating off-road wheeled vehicles with extreme mobility on 3-D terrains. Prior studies have oversimplified the problem by either treating it solely as a path-planning problem or disregarding the terrain topology. To bridge this gap, this article presents a one-layer model predictive planning and control framework that considers terrain topology for off-road vehicles at operationally relevant speeds. The algorithm is tested in various simulated scenarios with comparisons to benchmarks. The proposed algorithm demonstrates superior performance by capturing the dynamic constraints, while the benchmarks either fail to complete tasks or exhibit inferior performance due to inaccurate representation of the dynamic limitations of the vehicle. Furthermore, the algorithm is tested for robustness to demonstrate its ability to handle uncertainties in terrain topology.

The active SLAM problem considered in this paper aims to plan a robot trajectory for simultaneous localization and mapping (SLAM) as well as for an area coverage task with robot pose uncertainty. Based on a model predictive control (MPC) framework, these two problems are solved respectively by different methods. For the uncertainty minimization MPC problem, based on the graphical structure of the 2D feature-based SLAM, a non-convex constrained least-squares problem is presented to approximate the original problem. Then, using variable substitutions, it is further transformed into a convex problem, and then solved by a convex optimization method. For the coverage task considering robot pose uncertainty, it is formulated and solved by the MPC framework and the sequential quadratic programming (SQP) method. In the whole process, considering the computation complexity, we use linear SLAM, which is a submap joining approach, to reduce the time for planning and estimation. Finally, various simulations are presented to validate the effectiveness of the proposed approach.

This article concerns nonlinear model predictive control (MPC) with guaranteed feasibility of inequality path constraints (PCs). For MPC with PCs, the existing methods, such as direct multiple shooting, cannot guarantee feasibility of PCs because the PCs are enforced at finitely many time points only. Therefore, this article presents a novel MPC framework that is capable of not only achieving stability control but also guaranteeing feasibility of PCs during the rolling optimization stages of MPC. Under the above MPC framework, an algorithm is first proposed by applying the semi-infinite programming technique to the rolling optimization of MPC. However, it takes heavy computational time to achieve guaranteed feasibility of PCs. Therefore, to guarantee feasibility of PCs meanwhile effectively reducing the computation burden of the closed-loop system, an event-triggered sampling mechanism is constructed in the above path-constrained MPC algorithm. Moreover, sufficient conditions are given for asymptotic convergence of the closed-loop systems. Finally, the effectiveness of the proposed results is illustrated via a cart-damper-spring system.

Renewable energy in cities: by the Center for Renewable Resources. Van Nostrand Reinhold Co., New York, 1984

Model-based network-wide optimizations in real-time emergency control of power systems are largely bottlenecked by the fast computational requirements. Furthermore, the operational aspects of modern power and energy systems are going through transformative changes to tackle global renewable energy expansion-related issues. Decentralized operations in power systems are becoming essential with the influx of distributed energy resources (DERs), dynamic loads, and electric vehicles (EVs). This research considers a well-known model-based strategy, Model Predictive Control (MPC), for real-time operation and controls of power systems and proposes novel methods utilizing machine learning, data-driven methods, and operator theory to solve computational challenges by making those real-time for the first time. Additionally, we develop a distributed MPC framework to address the recent needs of power systems' operation and control. In Part I, we first present a machine learning (ML)-accelerated MPC implementation in emergency voltage control problems. This method computes an optimal control strategy for the nominal system model offline and performs successive online control corrections at each control instant to adapt the offline computed controls for real-time scenarios. In the online phase, the required voltage trajectory prediction and its sensitivity computation to control inputs are achieved by machine learning-based approaches, thereby accelerating the overall control computation multiple times. Next, we present an alternative data-learned linear Koopman embedding approach for model predictive emergency voltage control in a power grid. This approach involves a "basis-dictionary free" method to lift the nonlinear power system dynamics to a higher dimensional linear space where MPC is exercised in a real-time fashion. We propose a novel data-driven encoder-decoder architecture, Koopman-inspired deep neural network (KDNN), which supports end-to-end learning from trajectory data. The MPC optimization in linear space makes the problem scalable and rapid for real-time implementations. Part II of this research focuses on distributed MPC design for quasi-static power flow-based voltage control problems under short-term (15-minute) variations of load and generation profiles. To realize the proposed distributed control, first, a centralized voltage control problem assuming grid observability is formulated and next transferred to the distributed versions based on both bus-wise and area-wise decomposition of the network. Distributed versions are solved via the alternating direction method of multipliers (ADMM), utilizing only neighbor-to-neighbor communications to attain optimal solutions. The implementation, efficacy, performance, and robustness of proposed research approaches are validated with IEEE test system benchmarks.

This paper investigates intersection control of multiple vehicles using a Model Predictive Control (MPC) framework. Vehicles follow pre-defined paths across the intersection and adjust their velocities to ensure collision-free passage while maximizing an objective. We choose a non-cooperative Distributed Model Predictive Control (DMPC) approach, where priorities need to be assigned to vehicles. The algorithm we present sets these priorities automatically by evaluating the vehicles’ time to react to stop before entering the intersection. We demonstrate our method in simulations of multiple vehicles and continuous traffic. It produces near-optimal velocity profiles and reduces the computation time in comparison to centralized MPC while avoiding vehicle collisions and deadlocks.

This thesis addresses the design of optimization-based control laws for the case where convergence to a desired set-point, minimization of an arbitrary performance index, or a combination of the two, is the desired objective. The results are developed within the sample-data Model Predictive Control (MPC) framework considering constrained nonlinear continuous-time time-varying dynamical systems. For a given time sampling, a sample-data MPC control strategy consists of i) choosing among all future finite horizon predictions of state and input trajectories of the system the one that minimizes the given performance index, ii) applying the optimal input trajectory to the system until a new time sample is reached, and iii) iterating this process. The performance index is chosen to describe the specific control problem under consideration. In a classic Tracking-MPC framework, where the main goal is to steer the state of the system to a desired steady-state, the performance index is properly chosen to penalize the distance from the current state to a desired one. In order to capture more complex control objectives, in recent years a growing attention has been dedicated to a new class of controllers that goes under the name of Economic-MPC. Here, the term economic is used to stress the fact that the performance index is a general index of interest that we wish to minimize, e.g., economic, which does not denote the distance to a desired set point. This setting makes full use of the potentialities of optimization-based control strategies. Although, it comes with disadvantages. In fact, by choosing an arbitrary performance index, it is difficult to predict, and therefore certify, the evolution of the closed-loop system, which could potentially manifest undersirable behaviors. This thesis provides analysis and certification of a variety of closed-loop behaviors stemming from the use Economic-MPC controllers. A set of tools for design of provably correct MPC controllers is provided for the case where the performance index is of the Tracking-MPC type, purely economic, or a combination of the two. The results focus the certification of both closed-loop economic performance and closed-loop state evolution. The proposed strategies are applied to a range of motion control problems for underactuated vehicles. An MPC controller for Trajectory-Tracking and Path-Following with convergence guarantees is first proposed and then extended, using the results presented on Economic-MPC, to address the control problems of distributed formation keeping, energy efficient trajectory-tracking, and target-following through highly observable trajectories.

Gust load alleviation of a flexible flying wing with linear parameter-varying modeling and model predictive control

2D MODEL PREDICTIVE ITERATIVE LEARNING CONTROL SCHEMES FOR BATCH PROCESSES

Model predictive control of a building renewable energy system based on a long short-term hybrid model