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Krzysztof Pawula Supervisor: Prof. Krzysztof Gałkowski

Master of Science Thesis. Iterative control algorithms of learning (ILC) for support of people after recovering from a stroke. Krzysztof Pawula Supervisor: Prof. Krzysztof Gałkowski. Contents. Introduction Rehabilitation Robot Aim of the study Software Implementation methods

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Krzysztof Pawula Supervisor: Prof. Krzysztof Gałkowski

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  1. Master of Science Thesis Iterative control algorithms of learning (ILC) for support of people after recovering from a stroke. Krzysztof Pawula Supervisor: Prof. Krzysztof Gałkowski

  2. Contents • Introduction • Rehabilitation Robot • Aim of the study • Software • Implementation methods • Hammerstein and Wiener model • Simulations

  3. Introduction • One immediate life-threatening illness is the stroke, formerly called apoplexy. • Ischemic stroke - caused by sudden stopping of blood flow to the brain. May be due to obstruction of the supplying artery or insufficient blood flow through the area of the brain. • Haemorrhagic stroke of the Brain, a brain haemorrhage - a stroke caused by the incursion of the blood vessel outside the brain. As a consequence, leads to the destruction of tissue by blood vascularization. Most occur as a result of the rupture of small cerebral arteries in the course of hypertension.

  4. Introduction • Blood clot, which flows with the blood toward the brain, following the blocking blood vessels. The effect of fiber die and the person is partially paralyzed on one side of the body. • The brain is constantly and rapidly changing, learning new skills, so they can generate new nerve connections to replace lost.

  5. Rehabilitation Robot • The device is designed to track the trajectories to deal with individual use of the equipment and the introduction of any adjustments, if rehabilitation divergence is too far from the intended trajectory. The program will follow the trajectory and the introduction of corrections in the next step of the algorithm.

  6. Aim of the study • The aim of my work is to write an algorithm which will working like a rehabilitation robot for people after a stroke. • It is necessary to apply the method of iterative learning control (called Iterative Learning Control - ILC), and computational algorithms of linear matrix inequalities (called Linear Matrix Inequality - LMI) systems with nonlinear Hamerstein model. • To create a program I use Matlab and additional toolboxes.

  7. Software • Solvers LMISolver - a feature of scientific calculators or computer software that allows after the introduction of the equation, setting the value of any variable that are being looked for, when the data is set to the values of other variables, or the designation of the variable at which the entire expression is equal to zero. • Matlab environment MATLAB is a computer program which is an interactive environment to perform scientific and engineering calculations, and to create computer simulations.

  8. Software • Yalmip YALMIP is a modelling language for advanced modeling and solution of convex and nonconvex optimization problems. It is implemented as a free toolbox for MATLAB. • Sedumi SeDuMi is a software package to solve optimization problems over symmetric cones. Thisincludes linear, quadratic, second order conic and semidefinite optimization, and any combination of these.

  9. Iterative Learning Control (ILC) • Iterative Learning Control (ILC) is a method of tracking control for systems that work in a repetitive mode. • Examples of systems that operate in a repetitive manner include robot arm manipulators, chemical batch processes and reliability testing rigs. • In each of these tasks the system is required to perform the same action over and over again with high precision.

  10. Algorithms of linear matrix inequalities - LMI In convex optimization, a linear matrix inequality (LMI) is an expression of the form LMI(y) := A0 + y1A1 + y2A2 + … + ymAm ≥ 0 where y = [yi, i = 1, …, m] is a vector, A0, A1, A2, …, Am are nxn symetric matrices Sn, B ≥ 0 is generalized inequality meaning B is a positive semidefinite matrix belonging to the positivesemidefinite cone S+ in the subspace of symmetric matrixes S.

  11. Hammerstein model • The model consists of a zero-memory nonlinear element N(∙) in cascade with a LTI system with transfer function G(q) є H2mxn(T). It is assumed that the measured output yk contains an unknown additive noise component vk . The input-output relationship is given by yk=G(q)N(uk)+vk where yk, vkє Rm, uk є Rn.

  12. Wiener model • The model consists of the cascade of a LTI system with transfer function G(z) є H2mxn(T), followed by a zero-memory nonlinear element with input-output characteristic given by N(∙): Rm→Rm, where yk, vkє Rm, uk є Rn.

  13. Compute the signal input and the tracking error • The ILC system • The tracking error • The control law • Matrices define the system • Boundary conditions • LMI calculations

  14. Simulation Hammerstein model

  15. Compute the signal input and the tracking error • The ILC system • The tracking error • The control law • Matrices define the system • Boundary conditions • LMI calculations

  16. Simulation Wiener model

  17. What I must to do now? • Create a model using Matlab – Simulink. • Create a program which allows the implementation of spline interpolation. THE END

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