Explicit Model Predictive Control of Hybrid Systems using Multi-parametric Mixed Integer Polynomial Programming

Hybrid systems are dynamical systems characterized by the simultaneous presence of discrete and continuous variables. Model-based control of such systems is computationally demanding. To this effect, explicit controllers which provide control inputs as a set of functions of the state variables have been derived, using multiparametric programming mainly for the linear systems. Hybrid polynomial systems are considered resulting in a Mixed Integer Polynomial Programming problem. Treating the initial state of the system as a set of bounded parameters, the problem is reformulated as a multiparametric Mixed Integer Polynomial optimization (mp-MIPOPT) problem. A novel algorithm for mp-MIPOPT problems is proposed and the exact explicit control law for polynomial hybrid systems is computed. The key idea is the computation of the analytical solution of the optimality conditions while the binary variables are treated as relaxed parameters. Finally, using symbolic calculations exact nonconvex critical regions are compute

A unified framework for model-based multi-objective linear process and energy optimisation under uncertainty

Process and energy models provide an invaluable tool for design, analysis and optimisation. These models are usually based upon a number of assumptions, simplifications and approximations, thereby introducing uncertainty in the model predictions. Making model based optimal decisions under uncertainty is therefore a challenging task. This issue is further exacerbated when more than one objective is to be optimised simultaneously, resulting in a Multi-Objective Optimisation (MO2MO2) problem. Even though, some methods have been proposed for MO2MO2 problems under uncertainty, two separate optimisation techniques are employed; one to address the multi-objective aspect and another to take into account uncertainty. In the present work, we propose a unified optimisation framework for linear MO2MO2 problems, in which the uncertainty and the multiple objectives are modelled as varying parameters. The MO2MO2 under uncertainty problem (MO2U2)(MO2U2) is thus reformulated and solved as a multi-parametric programming problem. The solution of the multi-parametric programming problem provides the optimal solution as a set of parametric profiles

Parameter estimation of partial differential equations using artificial neural network

The work presented in this paper aims at developing a novel meshless parameter estimation framework for a system of partial differential equations (PDEs) using artificial neural network (ANN) approximations. The PDE models to be treated consist of linear and nonlinear PDEs, with Dirichlet and Neumann boundary conditions, considering both regular and irregular boundaries. This paper focuses on testing the applicability of neural networks for estimating the process model parameters while simultaneously computing the model predictions of the state variables in the system of PDEs representing the process. The capability of the proposed methodology is demonstrated with five numerical problems, showing that the ANN-based approach is very efficient by providing accurate solutions in reasonable computing times

Multi-parametric linear programming under global uncertainty

Multi-parametric programming has proven to be an invaluable tool for optimisation under uncertainty. Despite the theoretical developments in this area, the ability to handle uncertain parameters on the left-hand side remains limited and as a result, hybrid, or approximate solution strategies have been proposed in the literature. In this work, a new algorithm is introduced for the exact solution of multi-parametric linear programming problems with simultaneous variations in the objective function's coefficients, the right-hand side and the left-hand side of the constraints. The proposed methodology is based on the analytical solution of the system of equations derived from the first order Karush–Kuhn–Tucker conditions for general linear programming problems using symbolic manipulation. Emphasis is given on the ability of the proposed methodology to handle efficiently the LHS uncertainty by computing exactly the corresponding nonconvex critical regions while numerical studies underline further the advantages of the proposed methodology, when compared to existing algorithms

Multi-parametric mixed integer linear programming under global uncertainty

Major application areas of the process systems engineering, such as hybrid control, scheduling and synthesis can be formulated as mixed integer linear programming (MILP) problems and are naturally susceptible to uncertainty. Multi-parametric programming theory forms an active field of research and has proven to provide invaluable tools for decision making under uncertainty. While uncertainty in the right-hand side (RHS) and in the objective function's coefficients (OFC) have been thoroughly studied in the literature, the case of left-hand side (LHS) uncertainty has attracted significantly less attention mainly because of the computational implications that arise in such a problem. In the present work, we propose a novel algorithm for the analytical solution of multi-parametric MILP (mp-MILP) problems under global uncertainty, i.e. RHS, OFC and LHS. The exact explicit solutions and the corresponding regions of the parametric space are computed while a number of case studies illustrates the merits of the proposed algorithm

Multi set-point explicit model predictive control for nonlinear process systems

In this article, we introduce a novel framework for the design of multi set-point nonlinear explicit controllers for process systems engineering problems where the set-points are treated as uncertain parameters simultaneously with the initial state of the dynamical system at each sampling instance. To this end, an algorithm for a special class of multi-parametric nonlinear programming problems with uncertain parameters on the right-hand side of the constraints and the cost coefficients of the objective function is presented. The algorithm is based on computed algebra methods for symbolic manipulation that enable an analytical solution of the optimality conditions of the underlying multi-parametric nonlinear program. A notable property of the presented algorithm is the computation of exact, in general nonconvex, critical regions that results in potentially great computational savings through a reduction in the number of convex approximate critical regions

TLC Separation of Closely Related Amino Acids

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Discrete Formulation for Multi-objective Optimal Design of Produced Water Treatment

Produced Water is naturally occurring water that is brought to the surface during the extraction of the oil and gas and it constitutes the largest waste stream in the oil and gas industry. In offshore platforms, the majority of the produced water is discharged into the ocean, threatening marine life. The treatment of produced water is attractive, not only to meet regulations but to secure a potential source of fresh water. The design of water treatment should consider economic, environmental, and social aspects. This paper presents a discrete model for the evolution of oil droplet distribution due to breakage and coalescence phenomena. The discrete model combined with a superstructure representation for process design results in a mixed integer non-linear program which is solved using a nature-inspired meta-heuristic optimization method