Showing papers by "Antonios Armaou published in 2017"

A Moving Horizon Estimation Algorithm Based on Carleman Approximation: Design and Stability Analysis

Abstract: The moving horizon estimation (MHE) method is an optimization-based technique to estimate the unmeasurable state variables of a nonlinear dynamic system with noise in transition and measurement. One of the advantages of MHE over extended Kalman filter, the alternative approach in this area, is that it considers the physical constraints in its formulation. However, to offer this feature, MHE needs to solve a constrained nonlinear dynamic optimization problem which slows down the estimation process. In this paper, we introduce and employ the Carleman approximation method in the MHE design to accelerate the solution of the optimization problem. The Carleman method approximates the nonlinear system with a polynomial system at a desired accuracy level and recasts it in a bilinear form. By making this approximation, the Karush–Kuhn–Tucker (KKT) matrix required to solve the optimization problem becomes analytically available. Additionally, we perform a stability analysis for the proposed MHE design. As a result ...

Stochastic MPC design for a two-component granulation process

Abstract: We address the issue of control of a stochastic two-component granulation process in pharmaceutical applications through using Stochastic Model Predictive Control (SMPC) and model reduction to obtain the desired particle distribution. We first use the method of moments to reduce the governing integro-differential equation down to a nonlinear ordinary differential equation (ODE). This reduced-order model is employed in the SMPC formulation. The probabilistic constraints in this formulation keep the variance of particles' drug concentration in an admissible range. To solve the resulting stochastic optimization problem, we first employ polynomial chaos expansion to obtain the Probability Distribution Function (PDF) of the future state variables using the uncertain variables' distributions. As a result, the original stochastic optimization problem for a particulate system is converted to a deterministic dynamic optimization. This approximation lessens the computation burden of the controller and makes its real time application possible.

Stochastic MPC Design for a Two-Component Granulation Process

Abstract: We address the issue of control of a stochastic two-component granulation process in pharmaceutical applications through using Stochastic Model Predictive Control (SMPC) and model reduction to obtain the desired particle distribution. We first use the method of moments to reduce the governing integro-differential equation down to a nonlinear ordinary differential equation (ODE). This reduced-order model is employed in the SMPC formulation. The probabilistic constraints in this formulation keep the variance of particles' drug concentration in an admissible range. To solve the resulting stochastic optimization problem, we first employ polynomial chaos expansion to obtain the Probability Distribution Function (PDF) of the future state variables using the uncertain variables' distributions. As a result, the original stochastic optimization problem for a particulate system is converted to a deterministic dynamic optimization. This approximation lessens the computation burden of the controller and makes its real time application possible.

Synthesis of Equation-Free Control Structures for Dissipative Distributed Parameter Systems Using Proper Orthogonal Decomposition and Discrete Empirical Interpolation Methods

Abstract: We describe an equation-free control framework for the regulation of dissipative distributed parameter systems, with emphasis on improving the accuracy of the estimation by using a correction term. This control method is capable of regulating systems that have unknown dynamics but known effect of the control action. The system state and the dynamics are estimated by using the offline observations (snapshots ensemble) and the online continuous measurement of a restricted number of point sensors. First, we construct a reduced order model (ROM) with unknown terms using Galerkin/proper orthogonal decomposition (POD). Then the state of the ROM is estimated by a static observer with the information from the state sensors, and the mapping between the dynamics of the system and velocity sensors are generated using a similar approach. A discrete empirical interpolation method (DEIM) is employed to determine the sensor locations. To improve the accuracy of the estimation, a correction term is updated consistently. ...

On the design of equation-free controllers for dissipative PDEs via DEIM

Abstract: We propose an equation free control method to control dissipative distributed parameter systems, in which the dynamics of the system are unknown while the effect of the control action is. A static observer is used to estimate the state using proper orthogonal decomposition (POD) so that a complete profile of the system can be estimated when a limited number of point sensors are available. Sensor locations are determined by interpolation indices in discrete empirical interpolation method (DEIM). By using both velocity and state sensors an explicit form of the complete equation become superfluous, needing to only have a description of the actuator effect. The proposed method is successfully employed in a diffusion-reaction process with Dirichlet and Neumann boundary conditions. Feedback linearization is combined with the proposed method to regulate the system. Computational results demonstrate that this method can regulate a dissipative distributed parameter system without explicitly requiring a model of it and is robust to disturbances.