We study a semi-blind robust identification motivated from the fact that sometimes only partial input data is exactly known. Derived from a time-domain algorithm for robust identification, this semi-blind robust identification is stated as a non convex problem. We develop a convex relaxation, by combining two variables into a new variable, to reduce it to an LMI optimization problem. Applying this convex relaxation, a macro-economy modeling problem can be solved. The problem of identification of Wiener Systems, a special type of nonlinear systems, is analyzed from a set-membership standpoint. We propose an algorithm for time-domain based identification by pursuing a risk-adjusted approach to reduce it to a convex optimization problem. An arising non-trivial problem in computer vision, tracking a human in a sequence of frames, can be solved by modeling the plant as Wiener system using the proposed identification method. The book can serve as a reference for financial engineers and finance-oriented professionals in macro-economics and a textbook for graduate courses on robust control theory and macro-economics.

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