Parallel algorithms for LQ optimal control of discrete-time periodic linear systems
Consider the periodic linear quadratic optimization problem \(\sum^\infty_{i=0} y^\top_iQ_iy_i+u_i^\top R_iu_i \to\min\) under the constraints \(x_{k+1}= A_kx_k+B_ku_k\), \(y_k=C_kx_k\), where \(x_k\in\mathbb{R}^n\), \(u_k\in \mathbb{R}^m\) and the involved matrices are \(p\)-periodic in the sense that \(A_k=A_{k+p}\), etc. Under standard assumptions the optimal control \(u^*_k\) is a periodic feedback defined by a discrete-time periodic Riccati equation (DPRE). The paper deals with the parallelizations of two DPRE solvers proposed earlier by the first two authors. The performance of the two parallel algorithms is analyzed. Experimental results are presented which show high performance and scalability of the proposed parallelizations.
scientific article; zbMATH DE number 1763510