Sparse Linear-Quadratic Feedback Design Using Affine Approximation

2015/07/30 by Bahavarnia, MirSaleh · 1 citation
#FOS: Electrical engineering #FOS: Mathematics #Optimization and Control (math.OC) #Systems and Control (eess.SY) #electronic engineering #information engineering

paper · doi:10.48550/arxiv.1507.08592

Abstract

We consider a class of ℓ₀-regularized linear-quadratic (LQ) optimal control problems. This class of problems is obtained by augmenting a penalizing sparsity measure to the cost objective of the standard linear-quadratic regulator (LQR) problem in order to promote sparsity pattern of the state feedback controller. This class of problems is generally NP hard and computationally intractable. First, we apply a ℓ₁-relaxation and consider the ℓ₁-regularized LQ version of this class of problems, which is still nonconvex. Then, we convexify the resulting ℓ₁-regularized LQ problem by applying affine approximation techniques. An iterative algorithm is proposed to solve the ℓ₁-regularized LQ problem using a series of convexified ℓ₁-regularized LQ problems. By means of several numerical experiments, we show that our proposed algorithm is comparable to the existing algorithms in the literature, and in some cases it even returns solutions with superior performance and sparsity pattern.

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