Fast Non-Parametric Learning to Accelerate Mixed-Integer Programming for Online Hybrid Model Predictive Control

Today's fast linear algebra and numerical optimization tools have pushed the frontier of model predictive control (MPC) forward, to the efficient control of highly nonlinear and hybrid systems. The field of hybrid MPC has demonstrated that exact optimal control law can be computed, e.g., by mixed-integer programming (MIP) under piecewise-affine (PWA) system models. Despite the elegant theory, online solving hybrid MPC is still out of reach for many applications. We aim to speed up MIP by combining geometric insights from hybrid MPC, a simple-yet-effective learning algorithm, and MIP warm start techniques. Following a line of work in approximate explicit MPC, the proposed learning-control algorithm, LNMS, gains computational advantage over MIP at little cost and is straightforward for practitioners to implement

Advanced multiparametric optimization and control studies for anaesthesia

Anaesthesia is a reversible pharmacological state of the patient where hypnosis, analgesia and muscle relaxation are guaranteed and maintained throughout the surgery. Analgesics block the sensation of pain; hypnotics produce unconsciousness, while muscle relaxants prevent unwanted movement of muscle tone. Controlling the depth of anaesthesia is a very challenging task, as one has to deal with nonlinearity, inter- and intra-patient variability, multivariable characteristics, variable time delays, dynamics dependent on the hypnotic agent, model analysis variability, agent and stability issues. The modelling and automatic control of anaesthesia is believed to (i) benefit the safety of the patient undergoing surgery as side-effects may be reduced by optimizing the drug infusion rates, and (ii) support anaesthetists during critical situations by automating the drug delivery systems. In this work we have developed several advanced explicit/multi-parametric model predictive (mp-MPC) control strategies for the control of depth of anaesthesia. State estimation techniques are developed and used simultaneously with mp-MPC strategies to estimate the state of each individual patient, in an attempt to overcome the challenges of inter- and intra- patient variability, and deal with possible unmeasurable noisy outputs. Strategies to deal with the nonlinearity have been also developed including local linearization, exact linearization as well as a piece-wise linearization of the Hill curve leading to a hybrid formulation of the patient model and thereby the development of multiparametric hybrid model predictive control methodology. To deal with the inter- and intra- patient variability, as well as the noise on the process output, several robust techniques and a multiparametric moving horizon estimation technique have been design and implemented. All the studies described in the thesis are performed on clinical data for a set of 12 patients who underwent general anaesthesia.Open Acces

Approximation methodologies for explicit model predictive control of complex systems

This thesis concerns the development of complexity reduction methodologies for the application of multi-parametric/explicit model predictive (mp-MPC) control to complex high fidelity models. The main advantage of mp-MPC is the offline relocation of the optimization task and the associated computational expense through the use of multi-parametric programming. This allows for the application of MPC to fast sampling systems or systems for which it is not possible to perform online optimization due to cycle time requirements. The application of mp-MPC to complex nonlinear systems is of critical importance and is the subject of the thesis. The first part is concerned with the adaptation and development of model order reduction (MOR) techniques for application in combination to mp-MPC algorithms. This first part includes the mp-MPC oriented use of existing MOR techniques as well as the development of new ones. The use of MOR for multi-parametric moving horizon estimation is also investigated. The second part of the thesis introduces a framework for the ‘equation free’ surrogate-model based design of explicit controllers as a possible alternative to multi-parametric based methods. The methodology relies upon the use of advanced data-classification approaches and surrogate modelling techniques, and is illustrated with different numerical examples.Open Acces

Multi-parametric Analysis for Mixed Integer Linear Programming: An Application to Transmission Planning and Congestion Control

Enhancing existing transmission lines is a useful tool to combat transmission congestion and guarantee transmission security with increasing demand and boosting the renewable energy source. This study concerns the selection of lines whose capacity should be expanded and by how much from the perspective of independent system operator (ISO) to minimize the system cost with the consideration of transmission line constraints and electricity generation and demand balance conditions, and incorporating ramp-up and startup ramp rates, shutdown ramp rates, ramp-down rate limits and minimum up and minimum down times. For that purpose, we develop the ISO unit commitment and economic dispatch model and show it as a right-hand side uncertainty multiple parametric analysis for the mixed integer linear programming (MILP) problem. We first relax the binary variable to continuous variables and employ the Lagrange method and Karush-Kuhn-Tucker conditions to obtain optimal solutions (optimal decision variables and objective function) and critical regions associated with active and inactive constraints. Further, we extend the traditional branch and bound method for the large-scale MILP problem by determining the upper bound of the problem at each node, then comparing the difference between the upper and lower bounds and reaching the approximate optimal solution within the decision makers' tolerated error range. In additional, the objective function's first derivative on the parameters of each line is used to inform the selection of lines to ease congestion and maximize social welfare. Finally, the amount of capacity upgrade will be chosen by balancing the cost-reduction rate of the objective function on parameters and the cost of the line upgrade. Our findings are supported by numerical simulation and provide transmission line planners with decision-making guidance

Integration of process design and control: A review

There is a large variety of methods in literature for process design and control, which can be classified into two main categories. The methods in the first category have a sequential approach in which, the control system is designed, only after the details of process design are decided. However, when process design is fixed, there is little room left for improving the control performance. Recognizing the interactions between process design and control, the methods in the second category integrate some control aspects into process design. With the aim of providing an exploration map and identifying the potential areas of further contributions, this paper presents a thematic review of the methods for integration of process design and control. The evolution paths of these methods are described and the advantages and disadvantages of each method are explained. The paper concludes with suggestions for future research activities

Multi-parametric programming : novel theory and algorithmic developments

Imperial Users onl

Design of multi-parametric NCO-tracking controllers for linear continuous-time systems

Process optimization for industrial applications aims to achieve performance enhancements while satisfying system constraints. A major challenge for any such method lies in the problem of uncertainty stemming from model mismatch and process disturbances. Classical approaches such as model predictive control usually handle the uncertainty by repeatedly solving the optimization problem on-line, which may prove a rather computationally demanding task nonetheless and cause serious delays for fast dynamic systems. Existing approaches for mitigating the on-line computational burden via off-line optimization include multi-parametric programming and NCO-tracking. Multi-parametric programming aims to generate a mapping of control strategies as a function of given parameters; whereas NCO-tracking involves tracking the necessary conditions of optimality (NCOs) based on a precomputed control switching structure, which enables a dynamic real-time optimization problem to be transferred into an on-line tracking problem using a feedback controller. A methodology, called multi-parametric (mp-)NCO-tracking is developed in this thesis, whereby multi-parametric dynamic optimization and NCO-tracking methods are combined into a unified framework. An algorithm for the design of mp-NCO-tracking controllers for continuous-time, linear-quadratic optimal control problems is presented in Chapter 2. The off-line step defines the multi-parametric control structure mapped to given uncertain (measurable) parameters in terms of so-called critical regions and feedback laws. Specifically, each critical region corresponds to a unique control switching structure in terms of the sequence of active constraints. The on-line step involves determining the current critical region once the parameter value has been revealed, and then applying the corresponding feedback control laws in a receding horizon manner. The mp-NCO-tracking approach provides a means for relaxing the invariant switching structure assumption in NCO-tracking by constructing critical regions for various switching structures. Moreover, addressing the problem directly in continuous-time can potentially reduce the number of critical regions compared with standard multi-parametric programming based on a time discretization and a control vector parameterization. The methodology and its benefits are illustrated for a number of simple case studies. To obtain the mathematical representation of the generally nonlinear critical regions, Chapter 3 investigates a machine learning model as a classifier, based on deep neural network. This feed-forward network is selected for its representational power as a universal approximator for arbitrary continuous functions. Here, the classifier takes the unknown parameter as input and maps the corresponding critical regions in terms of their switching structures. An algorithm for training the classifier is presented, which involves generating the training data set, setting up a neural network architecture, and applying optimization based training. By using a Softmax classifier in the output layer of the network, a normalized probability distribution is obtained, which consist of a vector with as many elements as the total number of critical regions, and each element representing the likelihood for a region to be the correct one. The classifier is conveniently embedded into the multi-parametric NCO-tracking controller for choosing the real-time switching structure in on-line control. Lastly, a robustification of the mp-NCO-tracking methodology is developed in Chapter 4, where constraints are guaranteed to be satisfied under all possible uncertainty scenarios, which leads to a min-max formulation. A robust counterpart formulation of the multi-parametric dynamic optimization problem is presented, which considers both additive or multiplicative time-varying disturbances. The approach involves backing-off the path and terminal constraints of the linear-quadratic optimal control problem based on a worst-case uncertainty propagation computed using either interval or ellipsoidal reachability tubes. The uncertain system state is decomposed into a nominal reference and a perturbed component, and a convex enclosure of the reachable set for the perturbed component is precomputed via some auxiliary differential equations. Conservative constraint back-offs are obtained from the precomputed reachability tubes, which enables the controller design procedure in the nominal case to be directly applied for the robust control problem, and to retain the same computational effort as in the nominal case. These developments are demonstrated by numerical case studies, and ways of extending this approach to more general, nonlinear optimal control problems are discussed in Chapter 5.Open Acces