## 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.