2014/02/14 by Ather Gattami, Gattami, Ather
Computer Science · Engineering · Mathematics · #Advanced Control Systems Optimization #Control Systems and Identification #FOS: Mathematics #Optimization and Control (math.OC) #Stability and Control of Uncertain Systems #Target Tracking and Data Fusion in Sensor Networks #math.OC
paper · pdf · doi:10.48550/arxiv.1402.3402
arxiv created 2014/02/14 · openalex publication_date 2014/02/14 · arxiv updated 2014/02/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we consider the problem of multi-objective optimal control of a dynamical system with additive and multiplicative noises with given second moments and arbitrary probability distributions. The objectives are given by quadratic constraints in the state and controller, where the quadratic forms maybe indefinite and thus not necessarily convex. We show that the problem can be transformed to a semidefinite program and hence convex. The optimization problem is to be optimized with respect to a certain variable serving as the covariance matrix of the state and the controller. We show that affine controllers are optimal and depend on the optimal covariance matrix. Furthermore, we show that optimal controllers are linear if all the quadratic forms are convex in the control variable. The solutions are presented for both the finite and infinite horizon cases. We give a necessary and sufficient condition for mean square stabilizability of the dynamical system with additive and multiplicative noises. The condition is a Lyapunov-like condition whose solution is again given by the covariance matrix of the state and the control variable. The results are illustrated with an example.