Optimal Control Implementation for Linear Systems via Riccati Equation.

Document Type : Research Studies

Author

Automatic Control & Computers Engineering Department, Faculty of Engineering, Mansoura University, Mansoura, Egypt.

Abstract

The paper deals with the implementation of optimal controller design for linear dynamic systems. The implementation is carried out with the use of quadratic cost function for both cases of continuous and discrete systems. The mathematical optimal control theory is applied to dynamical systems with considering the form of either vector differential equations in continuous time case, or difference equations in discrete time- or sampled data-case. 
The bulk of the work provides design techniques for synthesizing the optimal control structure by applying the Pontryagin's Maxi mum principle to linear systems with using Matrix Riccati Equation. The work is focused upon regulator problems; that is problems where the goal is to maintain the system states at zero level. 
The implemented techniques are tested by the application on fourth order practical example represents the linearized control model of two-reach river pollution System. Also comparative study between the continuous and discrete optimal regulator problems will be presented and discussed from a numerical point-of-view. 

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