## Research Topics

### at the Process Control & Informatics Unit

**Control**

**Optimal control of hybrid systems:**

We have developed multiparametric optimization algorithms and solved optimal control problems for a variety of discrete-time dynamical systems such as markov jump linear systems and switched linear systems subject to control and state constraints. The approach relies on the formulation of the optimal control problems in a dynamic programming framework and the solution of the dynamic programming subproblems via in-house developed multiparametric programming algorithms. The methods led to the solution of some optimal control problems that have never been tackled in the literature or thought to be intractable. Furthermore, the solution to these optimal control problems is computed off-line thus making the techniques applicable to systems with fast dynamics.

**Optimal control of nonlinear distributed parameter systems:**

The radial basis function neural network architecture has been used to model the dynamics of Distributed Parameter Systems (DPSs). Two pure data driving schemes which do not require knowledge of the governing equations have been developed. In the first method, the neural network methodology generates the full model of the system that is able to predict the process outputs at any spatial point. Past values of the process inputs and the coordinates of the specific location provide the input information to the model. The second method uses empirical basis functions produced by the Singular Value Decomposition (SVD) on the snapshot matrix to describe the spatial behavior of the system, while the neural network model is used to estimate only the temporal coefficients. The models produced by both methods are then implemented in Model Predictive Control (MPC) configurations, suitable for constrained DPSs. An alternative control strategy has been developed by transforming the nonlinear model into a nonlinear state space formulation, which in turn is used for deriving a robust H∞ control law.

**Fuzzy model predictive control:**

A popular methodology has been developed based on a dynamic fuzzy model of the process to be controlled, which is used for predicting the future behavior of the output variables. A nonlinear optimization problem is then formulated, which minimizes the difference between the model predictions and the desired trajectory over the prediction horizon and the control energy over a shorter control horizon. The problem is solved on line using a specially designed genetic algorithm, which has a number of advantages over conventional nonlinear optimization techniques. The method can be used with any type of fuzzy model and is particularly useful when a direct fuzzy controller cannot be designed due to the complexity of the process and the difficulty in developing fuzzy control rules.

**Production planning and inventory control:**

New methodologies based on control theory have been developed. An adaptation method for the online identification of lead time is incorporated in production-inventory control systems. Based on the lead time estimate, the tuning parameters are updated in real time to improve the efficiency of the system. Combination of the adaptive scheme with a proportional control law is able to eliminate the inventory drift that appears when the actual lead time is not known in advance or when it varies with time. An adaptive MPC configuration has also been developed for the identification and control of production-inventory systems. The time varying dynamic behavior of the production process is approximated by an adaptive Finite Impulse Response (FIR) model. The well known Recursive Least Squares (RLS) method is used for the on line identification of the model coefficients. The adapted model along with a smoothed estimation of the future customer demand, are used to predict inventory levels over the optimization horizon. The proposed scheme is able to eliminate the inventory drift and suppress the bullwhip effect. We have developed software tools for obtaining optimal production plans for the food, petrochemical and pulp and paper industries.

**Informatics**

**Chemoinformatics and bioinformatics:**

Development of mathematical relationships linking chemical structure and pharmacological activity in a quantitative manner for a series of compounds. Standard statistical tools as well as advanced machine learning methodologies (neural networks, kernel methods, evolutionary algorithms) have been employed. Emphasis is given in the development of Quantitative Structure Activity Relationships for drug design. We have also introduced a metaheuristic method for the reconstruction of the DNA string from its *l*-mer content in the presence of large amounts of positive and negative errors, based on the formulation of an Asymmetric Traveling Salesman problem.

**Algorithm Development**

**Development of training algorithms for artificial neural networks and fuzzy logic systems:**

Three training algorithms for radial basis function neural networks have been developed. The fuzzy means algorithm uses a fuzzy partition of the input space and combines self-organized and supervised learning. For a given fuzzy partition of the input space, the proposed method is able to determine the proper network structure, without using a trial and error procedure. The second method is based on the subtractive clustering technique. Both methods are characterized by low computational complexities. The third training method is based on a specially designed Genetic Algorithm (GA), which is used to auto-configure the structure of the networks and obtain the model parameters. This technique formulates a complete optimization problem, which includes the network structure into the set of free variables that are used to minimize the prediction error. An additional algorithm has been developed for training fuzzy systems from numerical data. The main advantage of the method is the lack of complicated iterative mechanisms and therefore, its implementation is carried out easily. The suggested algorithm employs a fuzzy model with simplified rules, assuming a fuzzy partition of the input space into fuzzy subspaces. The output is inferred by expanding the model into fuzzy basis functions (FBFs), where each FBF corresponds to a certain fuzzy subspace. The number of rules and the respective premise parts (fuzzy subspaces) are determined using the nearest neighbor approach.

**Development of evolutionary algorithms:**

A complete framework has been presented for solving nonlinear constrained optimization problems, based on the line-up differential evolution (LUDE) algorithm which solves unconstrained problems. Linear and/or non-linear constraints are handled by embodying them in an augmented Lagrangian function, where the penalty parameters and multipliers are adapted as the execution of the algorithm proceeds. The LUDE algorithm maintains a population of solutions, which is continuously improved as it thrives from generation to generation. In each generation the solutions are lined up according to the corresponding objective function values. The position of each solution in the line-up is very important, since it determines to what extent the crossover and mutation operators are applied to each solution. A stochastic algorithm has been developed for solving hierarchical multiobjective optimization problems. The algorithm is based on the simulated annealing concept and returns a single solution that corresponds to the lexicographic ordering approach. The algorithm optimizes simultaneously the multiple objectives by assigning a different initial temperature to each one, according to its position in the hierarchy. A major advantage of the proposed method is its low computational cost. This is very critical, especially for on line applications, where the time available for decision making is limited. A new heuristic method for solving instances of the travelling salesman problem. The proposed algorithm uses a variant of the Threshold Accepting method, enhanced with intense Local Search, while the candidate solutions are produced through an Insertion Heuristic scheme.

**Systems Modelling & Optimization**

**Dynamic portfolio allocation:**

A framework has been developed based on coherent risk measures and multiparametric programming for the formulation and solution of multi-stage stochastic optimization problems that arise in the context of dynamic portfolio allocation. To address mean-risk trade-off we have used a mean-risk function based on CV@R. We show that this risk measure inherits coherence of CV@R. We have developed dynamic programming equations for the problem and have obtained the explicit feedback control law via solving a sequence of multiparametric linear programs.

**Optimal management and control of energy systems:**

Methodologies have been developed for managing large-scale energy systems and hybrid renewable energy systems, which are expected to become competitive in the near future and, thus, optimization of their operation is of particular interest. The methodologies are based on the rolling horizon philosophy. An important innovation for renewable energy systems is that the weather forecast is taken into account. We have also developed an MPC strategy for the real time control of fuel cell systems, which satisfies standard control targets (set-point tracking, disturbance rejection), but at the same time minimizes the hydrogen consumption.

**Development of a forest fire simulation tool:**

Our laboratory has contributed in the development of a forest fire simulation tools based on two fold reasoning; a discrete contour propagation model for estimating fire consequences and a fuzzy / neural system for the estimation of fire spread as a function of influencing factors such as terrain characteristics, vegetation type and density and meteorological conditions.