An SVD based strategy for receding horizon control of input constrained linear systems

A sub‐optimal receding horizon control strategy for input constrained linear systems is presented. The strategy is based on a singular value decomposition (SVD) of the Hessian of the quadratic performance index generally considered in model predictive control (MPC). The singular vectors are employed to generate a basis function expansion of the unconstrained solution to the finite horizon optimal control problem. At each sampling time, a feasible control sequence is determined by selecting a variable subset of the basis representation. No solution to the associated quadratic program is needed. For cases in which the Hessian is poorly conditioned, the proposed strategy can provide a sub‐optimal solution with minimal performance degradation. Properties of the singular values of the Hessian are also studied: it is shown that, for sufficiently long prediction horizons, the singular values are arbitrarily close to the magnitude of the energy density spectrum of the system seen by the performance index.