Fast Explicit Nonlinear Model Predictive Control Via Multiresolution Function Approximation with Guaranteed Stability Nonlinear Control Systems

In this paper an algorithm for nonlinear explicit model predictive control is introduced based on multiresolution function approximation that returns a low complexity approximate receding horizon control law built on a hierarchy of second order interpolets. Feasibility and stability guarantees for the approximate control law are given using reachability analysis, where interval methods are used to construct a capture basin (feasible region). A constructive algorithm is provided that combines adaptive function approximation with interval methods to build a receding horizon control law that is suboptimal, yet with a region of guaranteed feasibility and stability. The resulting control law is built on a grid hierarchy that is fast to evaluate in real-time systems

Optimization based energy-efficient control inmobile communication networks

In this work we consider how best to control mobility and transmission for the purpose of datatransfer and aggregation in a network of mobile autonomous agents. In particular we considernetworks containing unmanned aerial vehicles (UAVs). We first consider a single link betweena mobile transmitter-receiver pair, and show that the total amount of transmittable data isbounded. For certain special, but not overly restrictive cases, we can determine closed-formexpressions for this bound, as a function of relevant mobility and communication parameters.We then use nonlinear model predictive control (NMPC) to jointly optimize mobility and trans-mission schemes of all networked nodes for the purpose of minimizing the energy expenditureof the network. This yields a novel nonlinear optimal control problem for arbitrary networksof autonomous agents, which we solve with state-of-the-art nonlinear solvers. Numerical re-sults demonstrate increased network capacity and significant communication energy savingscompared to more na ̈ıve policies. All energy expenditure of an autonomous agent is due tocommunication, computation, or mobility and the actual computation of the NMPC solutionmay be a significant cost in both time and computational resources. Furthermore, frequentbroadcasting of control policies throughout the network can require significant transmit andreceive energies. Motivated by this, we develop an event-triggering scheme which accounts forthe accuracy of the optimal control solution, and provides guarantees of the minimum timebetween successive control updates. Solution accuracy should be accounted for in any triggeredNMPC scheme where the system may be run in open loop for extended times based on pos-sibly inaccurate state predictions. We use this analysis to trade-off the cost of updating ourtransmission and locomotion policies, with the frequency by which they must be updated. Thisgives a method to trade-off the computation, communication and mobility related energies ofthe mobile autonomous network.Open Acces

Design and Certification of Industrial Predictive Controllers

Three decades have passed since milestone publications by several industrial and academic researchers spawned a flurry of research and commercial, industrial activities on model predictive control (MPC). The improvement in efficiency of the on-line optimization part of MPC led to its adoption in mechanical and mechatronic systems from process control and petrochemical applications. However, the massive strides made by the academic community in guaranteeing stability through state-space MPC have not always been directly applicable in an industrial setting. This thesis is concerned with design and a posteriori certification of feasibility/stability of input-output MPC controllers for industrial applications without terminal conditions (i.e. terminal penalty, terminal constraint, terminal control). MPC controllers which differ in their modelling and prediction method are categorized into three major groups, and a general equivalence between these forms is established. Then an overview on robust set invariance is given as it plays a fundamental role in our analysis of the constrained control systems. These tools are used to give new tuning guidelines as well as a posteriori tests for guaranteeing feasibility of the suboptimal or optimal predictive control law without terminal conditions, which is fundamental towards stability of the closed loop. Next, penalty adaptation is used as a systematic procedure to derive asymptotic stability without any terminal conditions and without using set invariance or Lyapunov arguments. This analysis however is restricted to repetitive systems with input constraints. Then, predictive control without terminal conditions is considered for nonlinear and distributed systems. The invariance tools are extended to switching nonlinear systems, a proof of convergence is given for the iterative nonlinear MPC (NMPC), and a guarantee on overall cost decrease is developed for distributed NMPC, all without terminal conditions. Reference generation and parameter adaptation are shown to be effective mechanisms for NMPC and distributed NMPC (DNMPC) under changing environmental conditions. This is demonstrated on two benchmark test-cases i.e. the wet-clutch and hydrostatic drivetrain, respectively. Terminal conditions in essence are difficult to compute, may compromise performance and are not used in the industry. The main contribution of the thesis is a systematic development and analysis of MPC without terminal conditions for linear, nonlinear and distributed systems.This work was supported within the framework of the LeCoPro project (grant nr. 80032) of the Institute for the Promotion of Innovation through Science and Technology in Flanders (IWT-Vlaanderen)

Robust nonlinear receding horizon control with constraint tightening: off line approximation and application to networked control system

2007/2008Nonlinear Receding Horizon (RH) control, also known as moving horizon control or nonlinear Model Predictive Control (MPC), refers to a class of algorithms that make explicit use of a nonlinear process model to optimize the plant behavior, by computing a sequence of future ma- nipulated variable adjustments. Usually the optimal control sequence is obtained by minimizing a multi-stage cost functional on the basis of open-loop predictions. The presence of uncertainty in the model used for the optimization raises the question of robustness, i.e., the maintenance of certain properties such as stability and performance in the presence of uncertainty. The need for guaranteeing the closed-loop stability in presence of uncertainties motivates the conception of robust nonlinear MPC, in which the perturbations are explicitly taken in account in the design of the controller. When the nature of the uncertainty is know, and it is assumed to be bounded in some compact set, the robust RH control can be determined, in a natural way, by solving a min–max optimal control problem, that is, the performance objective is optimized for the worst-case scenario. However, the use of min-max techniques is limited by the high computational burden required to solve the optimization problem. In the case of constrained system, a possibility to ensure the robust constraint satisfaction and the closed-loop stability without resorting to min-max optimization consists in imposing restricted (tightened) constraints on the the predicted trajectories during the optimization. In this framework, an MPC scheme with constraint tightening for discrete-time nonlinear systems affected by state-dependent and norm bounded uncertainties is proposed and discussed. A novel method to tighten the constraints relying on the nominal state prediction is described, leading to less conservative set contractions than in the existing approaches. Moreover, by imposing a stabilizing state constraint at the end of the control horizon (in place of the usual terminal one placed at the end of the prediction horizon), less stringent assumptions can be posed on the terminal region, while improving the robust stability properties of the MPC closed-loop system. The robust nonlinear MPC formulation with tightened constraints is then used to design off- line approximate feedback laws able to guarantee the practical stability of the closed-loop system. By using off-line approximations, the computational burden due to the on-line optimization is removed, thus allowing for the application of the MPC to systems with fast dynamics. In this framework, we will also address the problem of approximating possibly discontinuous feedback functions, thus overcoming the limitation of existent approximation scheme which assume the continuity of the RH control law (whereas this condition is not always verified in practice, due to both nonlinearities and constraints). Finally, the problem of stabilizing constrained systems with networked unreliable (and de- layed) feedback and command channels is also considered. In order to satisfy the control ob- jectives for this class of systems, also referenced to as Networked Control Systems (NCS’s), a control scheme based on the combined use of constraint tightening MPC with a delay compen- sation strategy will be proposed and analyzed. The stability properties of all the aforementioned MPC schemes are characterized by using the regional Input-to-State Stability (ISS) tool. The ISS approach allows to analyze the depen- dence of state trajectories of nonlinear systems on the magnitude of inputs, which can represent control variables or disturbances. Typically, in MPC the ISS property is characterized in terms of Lyapunov functions, both for historical and practical reasons, since the optimal finite horizon cost of the optimization problem can be easily used for this task. Note that, in order to study the ISS property of MPC closed-loop systems, global results are in general not useful because, due to the presence of state and input constraints, it is impossible to establish global bounds for the multi-stage cost used as Lyapunov function. On the other hand local results do not allow to analyze the properties of the predictive control law in terms of its region of attraction. There- fore, regional ISS results have to employed for MPC controlled systems. Moreover, in the case of NCS, the resulting control strategy yields to a time-varying closed-loop system, whose stability properties can be analyzed using a novel regional ISS characterization in terms of time-varying Lyapunov functions.XXI Ciclo198

Numerical Solution of Optimal Control Problems with Explicit and Implicit Switches

This dissertation deals with the efficient numerical solution of switched optimal control problems whose dynamics may coincidentally be affected by both explicit and implicit switches. A framework is being developed for this purpose, in which both problem classes are uniformly converted into a mixed–integer optimal control problem with combinatorial constraints. Recent research results relate this problem class to a continuous optimal control problem with vanishing constraints, which in turn represents a considerable subclass of an optimal control problem with equilibrium constraints. In this thesis, this connection forms the foundation for a numerical treatment. We employ numerical algorithms that are based on a direct collocation approach and require, in particular, a highly accurate determination of the switching structure of the original problem. Due to the fact that the switching structure is a priori unknown in general, our approach aims to identify it successively. During this process, a sequence of nonlinear programs, which are derived by applying discretization schemes to optimal control problems, is solved approximatively. After each iteration, the discretization grid is updated according to the currently estimated switching structure. Besides a precise determination of the switching structure, it is of central importance to estimate the global error that occurs when optimal control problems are solved numerically. Again, we focus on certain direct collocation discretization schemes and analyze error contributions of individual discretization intervals. For this purpose, we exploit a relationship between discrete adjoints and the Lagrange multipliers associated with those nonlinear programs that arise from the collocation transcription process. This relationship can be derived with the help of a functional analytic framework and by interrelating collocation methods and Petrov–Galerkin finite element methods. In analogy to the dual-weighted residual methodology for Galerkin methods, which is well–known in the partial differential equation community, we then derive goal–oriented global error estimators. Based on those error estimators, we present mesh refinement strategies that allow for an equilibration and an efficient reduction of the global error. In doing so we note that the grid adaption processes with respect to both switching structure detection and global error reduction get along with each other. This allows us to distill an iterative solution framework. Usually, individual state and control components have the same polynomial degree if they originate from a collocation discretization scheme. Due to the special role which some control components have in the proposed solution framework it is desirable to allow varying polynomial degrees. This results in implementation problems, which can be solved by means of clever structure exploitation techniques and a suitable permutation of variables and equations. The resulting algorithm was developed in parallel to this work and implemented in a software package. The presented methods are implemented and evaluated on the basis of several benchmark problems. Furthermore, their applicability and efficiency is demonstrated. With regard to a future embedding of the described methods in an online optimal control context and the associated real-time requirements, an extension of the well–known multi–level iteration schemes is proposed. This approach is based on the trapezoidal rule and, compared to a full evaluation of the involved Jacobians, it significantly reduces the computational costs in case of sparse data matrices

Real-time Optimal Energy Management System for Plug-in Hybrid Electric Vehicles

Air pollution and rising fuel costs are becoming increasingly important concerns for the transportation industry. Hybrid electric vehicles (HEVs) are seen as a solution to these problems as they off er lower emissions and better fuel economy compared to conventional internal combustion engine vehicles. A typical HEV powertrain consists of an internal combustion engine, an electric motor/generator, and a power storage device (usually a battery). Another type of HEV is the plug-in hybrid electric vehicle (PHEV), which is conceptually similar to the fully electric vehicle. The battery in a PHEV is designed to be fully charged using a conventional home electric plug or a charging station. As such, the vehicle can travel further in full-electric mode, which greatly improves the fuel economy of PHEVs compared to HEVs. In this study, an optimal energy management system (EMS) for a PHEV is designed to minimize fuel consumption by considering engine emissions reduction. This is achieved by using the model predictive control (MPC) approach. MPC is an optimal model-based approach that can accommodate the many constraints involved in the design of EMSs, and is suitable for real-time implementations. The design and real-time implementation of such a control approach involves control-oriented modeling, controller design (including high-level and low-level controllers), and control scheme performance evaluation. All of these issues will be addressed in this thesis. A control-relevant parameter estimation (CRPE) approach is used to make the control-oriented model more accurate. This improves the EMS performance, while maintaining its real-time implementation capability. To reduce the computational complexity, the standard MPC controller is replaced by its explicit form. The explicit model predictive controller (eMPC) achieves the same performance as the implicit MPC, but requires less computational effort, which leads to a fast and reliable implementation. The performance of the control scheme is evaluated through different stages of model-in-the-loop (MIL) simulations with an equation-based and validated high-fidelity simulation model of a PHEV powertrain. Finally, the CRPE-eMPC EMS is validated through a hardware-in-the-loop (HIL) test. HIL simulation shows that the proposed EMS can be implemented to a commercial control hardware in real time and results in promising fuel economy figures and emissions performance, while maintaining vehicle drivability

Automation and Control Architecture for Hybrid Pipeline Robots

The aim of this research project, towards the automation of the Hybrid Pipeline Robot (HPR), is the development of a control architecture and strategy, based on reconfiguration of the control strategy for speed-controlled pipeline operations and self-recovering action, while performing energy and time management. The HPR is a turbine powered pipeline device where the flow energy is converted to mechanical energy for traction of the crawler vehicle. Thus, the device is flow dependent, compromising the autonomy, and the range of tasks it can perform. The control strategy proposes pipeline operations supervised by a speed control, while optimizing the energy, solved as a multi-objective optimization problem. The states of robot cruising and self recovering, are controlled by solving a neuro-dynamic programming algorithm for energy and time optimization, The robust operation of the robot includes a self-recovering state either after completion of the mission, or as a result of failures leading to the loss of the robot inside the pipeline, and to guaranteeing the HPR autonomy and operations even under adverse pipeline conditions Two of the proposed models, system identification and tracking system, based on Artificial Neural Networks, have been simulated with trial data. Despite the satisfactory results, it is necessary to measure a full set of robot’s parameters for simulating the complete control strategy. To solve the problem, an instrumentation system, consisting on a set of probes and a signal conditioning board, was designed and developed, customized for the HPR’s mechanical and environmental constraints. As a result, the contribution of this research project to the Hybrid Pipeline Robot is to add the capabilities of energy management, for improving the vehicle autonomy, increasing the distances the device can travel inside the pipelines; the speed control for broadening the range of operations; and the self-recovery capability for improving the reliability of the device in pipeline operations, lowering the risk of potential loss of the robot inside the pipeline, causing the degradation of pipeline performance. All that means the pipeline robot can target new market sectors that before were prohibitive

Model predictive control of water quality in drinking water distribution systems considering disinfection by-products

The shortage in water resources have been observed all over the world. However, the safety of drinking water has been given much attention by scientists because the disinfection will react with organic matters in drinking water to generate disinfection by-products (DBPs) which are considered as the cancerigenic matters. Although much research has been carried out on the water quality control problem in DWDS, the water quality model considered is linear with only chlorine dynamics. Compared to the linear water quality model, the nonlinear water quality model considers the interaction between chlorine and DBPs dynamics. The thesis proposes a nonlinear model predictive controller which utilises the newly derived nonlinear water quality model as a control alternative for controlling water quality. EPANET and EPANET-MSN are simulators utilised for modelling in the developed nonlinear MPC controller. Uncertainty is not considered in these simulators. This thesis proposes the bounded PPM in a form of multi-input multi-output to robustly bound parameters of chlorine and DBPs jointly and to robustly predict water quality control outputs for quality control purpose. The methodologies and algorithms developed in this thesis are verified by applying extended case studies to the example DWDS. The simulation results are presented and critically analysed

A unified metaheuristic and system-theoretic framework for petroleum reservoir management

With phenomenal rise in world population as well as robust economic growth in China, India and other emerging economies; the global demand for energy continues to grow in monumental proportions. Owing to its wide end-use capabilities, petroleum is without doubt, the world’s number one energy resource. The present demand for oil and credible future forecasts – which point to the fact that the demand is expected to increase in the coming decades – make it imperative that the E&P industry must device means to improve the present low recovery factor of hydrocarbon reservoirs. Efficiently tailored model-based optimization, estimation and control techniques within the ambit of a closed-loop reservoir management framework can play a significant role in achieving this objective. In this thesis, some fundamental reservoir engineering problems such as field development planning, production scheduling and control are formulated into different optimization problems. In this regard, field development optimization identifies the well placements that best maximizes hydrocarbon recovery, while production optimization identifies reservoir well-settings that maximizes total oil recovery or asset value, and finally, the implementation of a predictive controller algorithm which computes corrected well controls that minimizes the difference between actual outputs and simulated (or optimal) reference trajectory. We employ either deterministic or metaheuristic optimization algorithms, such that the choice of algorithm is purely based on the peculiarity of the underlying optimization problem. Altogether, we present a unified metaheuristic and system-theoretic framework for petroleum reservoir management. The proposed framework is essentially a closed-loop reservoir management approach with four key elements, namely: a new metaheuristic technique for field development optimization, a gradient-based adjoint formulation for well rates control, an effective predictive control strategy for tracking the gradient-based optimal production trajectory and an efficient model-updating (or history matching) – where well production data are used to systematically recalibrate reservoir model parameters in order to minimize the mismatch between actual and simulated measurements. Central to all of these problems is the use of white-box reservoir models which are employed in the well placement optimization and production settings optimization. However, a simple data-driven black-box model which results from the linearization of an identified nonlinear model is employed in the predictive controller algorithm. The benefits and efficiency of the approach in our work is demonstrated through the maximization of the NPV of waterflooded reservoir models that are subject to production and geological uncertainty. Our procedure provides an improvement in the NPV, and importantly, the predictive control algorithm ensures that this improved NPV are attainable as nearly as possible in practice

Advances in Intelligent Vehicle Control

This book is a printed edition of the Special Issue Advances in Intelligent Vehicle Control that was published in the journal Sensors. It presents a collection of eleven papers that covers a range of topics, such as the development of intelligent control algorithms for active safety systems, smart sensors, and intelligent and efficient driving. The contributions presented in these papers can serve as useful tools for researchers who are interested in new vehicle technology and in the improvement of vehicle control systems