A control problem for a linear stochastic system with an arbitrary fractional Brownian motion and a cost functional that is quadratic in the system state and the control is solved. An optimal control is given explicitly as the sum of a prediction of the future fractional Brownian motion and the well known linear feedback control for the associated deterministic linear-quadratic control problem....

Self-triggered control is a recently proposed paradigm that abandons the more traditional periodic timetriggered execution of control tasks with the objective of reducing the utilization of communication resources, while still guaranteeing desirable closed-loop behavior. In this paper, we introduce a selftriggered strategy based on performance levels described by a quadratic discounted cost. Th...

The use of piecewise quadratic cost functions is extended from stability analysis of piecewise linear systems to performance analysis and optimal control. Lower bounds on the optimal control cost are obtained by semi-definite programming based on the Bellman inequality. This also gives an approximation to the optimal control law. An upper bound to the optimal cost is obtained by another convex ...

in this article, we characterize the involutiveness of the linear combination of the forma1a1 +a2a2 when a1, a2 are nonzero complex numbers, a1 is a quadratic or tripotent matrix,and a2 is arbitrary, under certain properties imposed on a1 and a2.

Controlling network systems has become a problem of paramount importance. In this paper, we consider distributed linear-quadratic and propose the use graph neural networks (GNNs) to parametrize design controller for systems. GNNs exhibit many desirable properties, such as being naturally scalable. We cast self-supervised learning problem, which is then used train GNN-based controllers. also obt...