Two-Timescale Optimization Framework for Sparse-Feedback Linear-Quadratic Optimal Control
This work addresses distributed control systems where reducing communication links is crucial, but it appears incremental as it builds on existing optimization frameworks for sparse feedback.
The paper tackles the problem of designing sparse-feedback controllers for linear-quadratic optimal control with stability guarantees, using methods like two-timescale algorithms and BSUM to minimize a modified cost function with penalties on communication links, achieving accelerated convergence rates in some cases.
A $\mathcal{H}_2$-guaranteed sparse-feedback linear-quadratic (LQ) optimal control with convex parameterization and convex-bounded uncertainty is studied in this paper, where $\ell_0$-penalty is added into the $\mathcal{H}_2$ cost to penalize the number of communication links among distributed controllers. Then, the sparse-feedback gain is investigated to minimize the modified $\mathcal{H}_2$ cost together with the stability guarantee, and the corresponding main results are of three parts. First, the $\ell_1$ relaxation sparse-feedback LQ problem is of concern, and a two-timescale algorithm is developed based on proximal coordinate descent and primal-dual splitting approach. Second, piecewise quadratic relaxation sparse-feedback LQ control is investigated, which exhibits an accelerated convergence rate. Third, sparse-feedback LQ problem with $\ell_0$-penalty is directly studied through BSUM (Block Successive Upper-bound Minimization) framework, and precise approximation method and variational properties are introduced.