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Robust explicit nonlinear model predictive control with integral sliding mode

A robust control strategy for stabilizing nonlinear systems in the presence of additive bounded disturbances is proposed. The proposed control architecture is a novel combination of explicit nonlinear model predictive control (EMPC) and integral sliding mode control (ISMC). Feasibility analysis of a finite-horizon optimal control problem involved in deriving the EMPC control action is performed over a polytope of interest in the state space. A sparse sampling-based boundary detection algorithm is employed to compute an approximating polynomial bounding the feasible region. A sparse-grid based interpolation scheme with Chebyshev-Gauss-Lobatto nodes and Legendre-basis polynomials are used to design the stabilizing EMPC surface. The proposed method is appealing because of the simplicity of the controller construction in conjunction with its applicability to higher-dimensional problems, which stems from the scale-ability property of sparse-grids. Robustness to the designed EMPC is provided by the ISMC. A simulated example is provided to illustrate the efficacy and performance of the proposed control strategy for the stabilization of an uncertain nonlinear dynamical system.