A set of N independent Gaussian linear time-in variant systems is observed by M sensors whose task is to provide a steady-state causal estimate minimizing the mean-square error on the system states, subject to additional measurement costs. The sensors can switch between systems instantaneously, and there are additional resource constraints, for example on the number of sensors that can observe a given system simultaneously. We first derive a tractable relaxation of the problem, which provides a bound on the achievable performance. This bound can be computed by solving a convex program involving linear matrix inequalities, and moreover this program can be decomposed into coupled smaller dimensional problems. In the scalar case with identical sensors, we give an analytical expression of an index policy proposed in a more general context by Whittle. In the general case, we develop open-loop periodic switching policies whose performance matches the bound arbitrarily closely.

A stable gain scheduled controller for a gas turbine engine that drives a variable pitch propeller is developed and described. A stability proof is developed for gain scheduled closed-loop system using global linearization and linear matrix inequality (LMI) techniques. Using convex optimization tools, a single quadratic Lyapunov function is computed for multiple linearizations near equilibrium and nonequilibrium points of the nonlinear closed-loop system. This approach guarantees stability of the closed-loop gas turbine engine system. To verify the stability of the closed-loop system on-line, an optimization problem is proposed, which is solvable using convex optimization tools. Simulation results show that the developed gain scheduled controller is capable to regulate a turboshaft engine for large thrust commands in a stable fashion with proper tracking performance.

This paper addresses the generation of aircraft emergency trajectories with obstacle avoidance. After presenting in detail the fast marching tree algorithm, in this paper we propose an improvement of its performance. First, the free space checking function is sped up. Then, the algorithm is used twice, firstly with the sampling of a few points to generate an approximate trajectory, and secondly with a sampling of points close to the first computed trajectory to refine it. The proposed method significantly reduces the computing time of the emergency geometric trajectory generation.