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Synthesis of optimal controllers for model predictive control

This paper studies the synthesis analysis for robust quadratic programming, whose data are not known, but in the uncertainty set, such as ellipsoids. Synthesis analysis means both the combination with the theory and practice. Given one quadratic programming problem, whose data are not always known exactly, but in typically known in a domain, i,e, one uncertainty set, this robust quadratic programming problem becomes one conic quadratic programming through our own derivations. After applying semidefinite relaxation and linear matrix inequality on this robust quadratic programming, one necessary and sufficient condition of the existence of the optimal robust feasible is formulated as one linear matrix inequality. And one special affinely adjustable robust counterpart of quadratic programming is shown to solve other two decision variables. To complete the synthesis analysis for robust quadratic programming from the points of theory and practice, all our derived theoretical results are applied in state estimation with uncertainty set through using the idea of direct data driven.