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Constrained finite time optimal control problems can be expressed as mathematical programs parameterized by the current state of the system: the so-called multi-parametric programs. These problems have received a great deal of attention in the control community during the last few years because solving the parametric program is equivalent to synthesizing the optimal state-feedback controller. For many cases of interest, the resulting synthesized controllers are simple piecewise-affine functions, which enables receding horizon control to be used not only in slowly sampled systems requiring powerful computers but now also in high-speed embedded applications. The primary limitation of these optimal dasiaexplicit solutionspsila is that the complexity can grow quickly with problem size. In this talk I will introduce new methods to compute approximate explicit and online control laws that can trade-off time and space complexity against sub-optimality while providing guarantees of stability and feasibility.