Quadratic MPC with ℓ₀-input constraint

In this paper we propose a novel quadratic model predictive control technique that constrains the number of active inputs at each control horizon instant. This problem is known as sparse control. We use an iterative convex optimization procedure to solve the corresponding optimization problem subject to sparsity constraints defined by means of the ℓ₀-norm. We also derive a sufficient condition on the minimum number of active of inputs that guarantees the exponential stability of the closed-loop system. A simulation example illustrates the benefits of the control design method proposed in the paper