Course Details

Course details of EE6431
Course NoEE6431
Course TitleNonsmooth analysis in control and optimization
Course Content1. Applications: Nonsmooth harmonic oscillator, stick-slip system and systems involving discontinuous stabilizing control law2. Semicontinuity, proper and improper convex functions, Lipschitz property of convex function, projection of a point onto a set, distance function, gradient of the distance function and the projection inequality, normal and tangent cones, properties of normal cones3. Subdifferential of a convex function and its properties, connection to convex geometry, basic inequality, subgradient calculus and optimality conditions.4. Directional derivatives, relation between subgradients and directional derivatives, existence of subgradient, subdifferential and gradient direction of steepest descent, examples involving the subgradient of a norm, distance function, indicator function, max function and maximum eigen value of a symmetric matrix.5. Solution notions for discontinuous systems, Caratheodory, Fillipov, sample-and-hold solutions.6. Lyapunov-like stability theorems for nonsmooth systems and optimality conditions for nonsmooth optimization.
Course Offered this semesterNo
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