Complexity minimisation of suboptimal MPC without terminal constraints

This paper generalises stability analysis of Nonlinear Model Predictive Control without terminal constraints to incorporate possible suboptimality of MPC solutions and develops a framework for minimisation of computational efforts associated with obtaining such a solution. The framework is applied to primal-dual interior-point solvers by choosing the length of the prediction horizon together with a degree of suboptimality of the solution in a way that reduces algorithmic complexity while satisfying certain stability and performance guarantees. The framework ensures an optimal choice for the prediction horizon in order to minimise computational complexity if applied to linear or convex quadratic MPC problems, and acts as a good indicator to this end in the more general case of nonlinear systems. This is illustrated in a numerical case study, where we apply the proposed framework to a nonholonomic robot.