The impact of the input parameterisation on the feasibility of MPC and its parametric solution

Feasibility is an important issue in predictive control, but the influence of many important parameters such as the desired steady-state, or target, the current value of the input are rarely discussed in the literature. This paper makes two contributions. First it gives visibility to the issue that including core parameters such as the target and the current input vastly increases the dimension of the parametric space, with possible consequences on the complexity of any parametric solutions. Secondly, it is shown that a simple re-parameterisation of the d.o.f. to take advantage of reference governor concepts can lead to large increases in feasible volumes, with no increases in the dimension of the required optimisation variables

Predictive safety filter using system level synthesis

Safety filters provide modular techniques to augment potentially unsafe control inputs (e.g. from learning-based controllers or humans) with safety guarantees in the form of constraint satisfaction. In this paper, we present an improved model predictive safety filter (MPSF) formulation, which incorporates system level synthesis techniques in the design. The resulting SL-MPSF scheme ensures safety for linear systems subject to bounded disturbances in an enlarged safe set. It requires less severe and frequent modifications of potentially unsafe control inputs compared to existing MPSF formulations to certify safety. In addition, we propose an explicit variant of the SL-MPSF formulation, which maintains scalability, and reduces the required online computational effort - the main drawback of the MPSF. The benefits of the proposed system level safety filter formulations compared to state-of-the-art MPSF formulations are demonstrated using a numerical example.Comment: https://gitlab.ethz.ch/ics/SLS_safety_filter

Robust Tube Model Predictive Control with Uncertainty Quantification for Discrete-Time Linear Systems

This paper is concerned with model predictive control (MPC) of discrete-time linear systems subject to bounded additive disturbance and hard constraints on the state and input, whereas the true disturbance set is unknown. Unlike most existing work on robust MPC, we propose an MPC algorithm incorporating online uncertainty quantification that builds on prior knowledge of the disturbance, i.e., a known but conservative disturbance set. We approximate the true disturbance set at each time step with a parameterised set, which is referred to as a quantified disturbance set, using the scenario approach with additional disturbance realisations collected online. A key novelty of this paper is that the parameterisation of these quantified disturbance sets enjoy desirable properties such that the quantified disturbance set and its corresponding rigid tube bounding disturbance propagation can be efficiently updated online. We provide statistical gaps between the true and quantified disturbance sets, based on which, probabilistic recursive feasibility of MPC optimisation problems are discussed. Numerical simulations are provided to demonstrate the efficacy of our proposed algorithm and compare with conventional robust MPC algorithms.Comment: 8 page

The feasibility of parametric approaches to predictive control when using far future feed forward information

This paper considers the tractability of parametric solvers for predictive control based optimisations, when future target information is incorporated. it is shown that the inclusion of future target information can significantly increase the implied parametric dimension to an extent that is undesirable and likely to lead to intractable problems. The paper then proposes some alternative methods for incorporating the desired target information, while minimising he implied growth in the parametric dimensions, at some possibly small cost to optimality

Stochastic output feedback MPC with intermittent observations

This paper considers constrained linear systems with stochastic additive disturbances and noisy measurements transmitted over a lossy communication channel. We propose a model predictive control (MPC) law that minimises a discounted cost subject to a discounted expectation constraint. Sensor data is assumed to be lost with known probability, and data losses are accounted for by expressing the predicted control policy as an affine function of future observations, which results in a convex optimal control problem. An online constraint-tightening technique ensures recursive feasibility of the online optimisation problem and satisfaction of the expectation constraint without imposing bounds on the distributions of the noise and disturbance inputs. The discounted cost evaluated along trajectories of the closed loop system is shown to be bounded by the initial optimal predicted cost. We also provide conditions under which the averaged undiscounted closed loop cost accumulated over an infinite horizon is bounded. Numerical simulations are described to illustrate these results.Comment: 12 pages. arXiv admin note: substantial text overlap with arXiv:2004.0259

Long horizon input parameterisations to enlarge the region of attraction of MPC

In this paper, the efficacy of structured and unstructured parameterisations of the degree of freedom within a predictive control algorithm is investigated. While several earlier papers investigated the enlargement of the region of attraction using structured prediction dynamics, little consideration has been given to the potential of unstructured parameterisations to handle the trade-off between the region of attraction, performance and computational burden. This paper demonstrates how unstructured dynamics can be both selected and used effectively and furthermore gives a comparison with structured methods

Alternative parameterisations for predictive control: how and why?

This paper looks at the efficiency of the parameterisation of the degrees of freedom within an optimal predictive control algorithm. It is shown that the conventional approach of directly determining each individual future control move is not efficient in general, and can give poor feasibility when the number of degrees of freedom are limited. Two systematic alternatives are explored and both shown to be far more efficient in general

Blockchain, parameterisation and automated arbitrage applied to the chemical industry

This thesis considers three scenarios related to chemical industry where the concepts of eco-industrial parks (EIPs), Industry 4.0, parameterisation, blockchain and arbitrage are brought together to explore the issues of simulation speed and accuracy, machine-to-machine (M2M) communication and automated participation in financial markets. In the first scenario, a biodiesel plant flow sheet model is analysed and parameterised. The relations between 11 inputs typical to a biodiesel plant and its energy requirements are approximated using surrogate models, of which accuracy is assessed. Additionally, the effects of dimensionality, domain size and surrogate type on the accuracy are investigated and global sensitivities of the outputs are computed using High Dimensional Model Representation (HDMR). Most surrogate models achieved at least a reasonable fit regardless of the domain size and number of dimensions. It was observed that in all cases only 4 or fewer inputs have significant influence on any of the outputs and that the interaction terms have only minor effect on any one output. In the second scenario, applications of blockchain technology related to Industry 4.0 are explored and an example where blockchain is employed to facilitate M2M interactions and establish a M2M electricity market in the context of the chemical industry is presented. Successful implementation of two electricity producers and one electricity consumer trading with each other over a blockchain-based network is presented. In the third scenario, an automated arbitrage spotter is developed and applied to two cases: conversion of natural gas to methanol and crude palm oil to biodiesel. The spotter is designed to search for opportunities to make additional profit by analysing the futures market prices for both the reagent and the product. It considers cost of storage and conversion (other feedstock, steam, electricity and other utilities) derived from physical simulations of the chemical process. In a profitable scenario up to 345.17 USD per tonne of biodiesel can be earned by buying contracts for delivery of crude palm oil in September 2018 and selling contracts for delivery of biodiesel in December 2018 in a ratio of 4 to 1.Department of Chemical Engineering and Biotechnology in the University of Cambridge and Cambridge CARES Ltd

Efficient Real-Time Solutions for Nonlinear Model Predictive Control with Applications

Nonlinear Model Predictive Control is an advanced optimisation methodology widely used for developing optimal Feedback Control Systems that use mathematical models of dynamical systems to predict and optimise their future performance. Its popularity comes from its general ability to handle a wide range of challenges present when developing control systems such as input/output constraints, complex nonlinear dynamics multi-variable systems, dynamic systems with significant delays as well as handling of uncertainty, disturbances and fault-tolerance. One of the main and most important challenges is the computational burden associated with the optimisation, particularly when attempting to implement the underlying methods in fast/real-time systems. To tackle this, recent research has been focused on developing efficient real-time solutions or strategies that could be used to overcome this problem. In this case, efficiency may come in various different ways from mathematical simplifications, to fast optimisation solvers, special algorithms and hardware, as well as tailored auto-generated coding tool-kits which help to make an efficient overall implementation of these type of approaches. This thesis addresses this fundamental problem by proposing a wide variety of methods that could serve as alternatives from which the final user can choose from depending on the requirements specific to the application. The proposed approaches focus specifically of developing efficient real-time NMPC methods which have a significantly reduced computational burden whilst preserving desirable properties of standard NMPC such as nominal stability, recursive feasibility guarantees, good performance, as well as adequate numeric conditioning for their use in platforms with reduced numeric precision such as ``floats'' subject to certain conditions being met. One of the specific aims of this work is to obtain faster solutions than the popular ACADO toolkit, in particular when using condensing-based NMPC solutions under the Real-Time Iteration Scheme, considered for all practical purposes the state-of-the-art standard real-time solution to which all the approaches will be bench-marked against. Moreover, part of the work of this thesis uses the concept of ``auto-generation'' for developing similar tool-kits that apply the proposed approaches. To achieve this, the developed tool-kits were supported by the Eigen 3 library which were observed to result in even better computation times than the ACADO toolkit. Finally, although the work undertaking by this thesis does not look into robust control approaches, the developed methods could be used for improving the performance of the underlying ``online'' optimisation, eg. by being able to perform additional iterations of the underlying SQP optimisation, as well as be used in common robust frameworks where multi-model systems must be simultaneously optimised in real-time. Thus, future work will look into merging the proposed methods with other existing strategies to give an even wider range of alternatives to the final user