This paper proposes, for the first time, a unified optimal approach applicable for both fuel-powered and allelectric aircraft to solve a direct operating cost (DOC) minimization problem where the cost index (CI) is modeled as a timevarying parameter, which is either commanded by Air Traffic Control (ATC) or assigned by the airline. Furthermore, this paper demonstrates how a variable CI affects the solution of the optimization problem as it presents the equations that allow the computation of optimal constant cruise airspeed and flight time in response to step changes in the CI value. The proposed methodology is validated using a simulated flight scenario, where inputs from ATC are received during flight, requiring the aircraft to adjust its optimal airspeed, flight time, and total energy consumption accordingly. The optimal values of airspeed, flight time, and energy consumption are calculated for both a fuelpowered and an all-electric aircraft, thus allowing applications of the proposed approach to future air mobility all-electric vehicles.

This paper proposes a nonlinear estimator for the position of a quadrotor in waypoint navigation using squared range measurements perturbed by white noise. The convergence of the state estimate is studied along with an investigation of the stationary distribution of the estimation error. The stationary distribution is proved to converge to a zero-mean Gaussian with adjustable variance. Moreover, the proposed method is applied to pipeline inspection carried out by an autonomous quadrotor Uninhabited Air Vehicle (UAV). The simulation results demonstrate a stable estimation error that consistently converged to a neighborhood of zero and the quadrotor maintained its flight path directly above the pipeline geometry. The proposed nonlinear estimator is compared favorably with other methods in the literature in terms of convergence time and error (accuracy).

This paper shows that the training of a two-layer quadratic neural network using a 2-norm loss function and without a regularization term can be cast as a constrained least squares problem for which there is an analytical solution. The main advantages of having an analytical solution are that one can prove that the global optimum is achieved and it is easier to be implemented in real-time applications for which one must train a neural network based on incoming data. It also allows an analysis of the sensitivity of the solution to measurement noise using an analytical formula for noise propagation. Additionally, recursive least squares are suggested for adapting the neural network in real-time as more data become available. The proposed least squares solutions are applied to a nonlinear system identification example. The results confirm that the least squares analytical solutions match the numerical solutions of a convex training proposed previously in the literature for quadratic neural networks. To the best of the author’s knowledge this is the first time that an analytical solution is proposed for the training of a neural network.

This paper proposes a novel nonlinear estimator for the position of a quadrotor in waypoint navigation using range measurements. It is assumed that the flying vehicle follows a straight line at a constant altitude between two waypoints. The positions of the waypoints are known and the measurements are assumed to be the squared distance to the point source located at the departure waypoint. The measurement is corrupted by additive noise. Under these conditions it is shown that the dynamics of the estimation error are described by a nonlinear Verhulst logistc equation. This observation unveils a link between navigation of a vehicle using range measurements and population dynamics, which to the best of the authors' knowledge is new. The stability of the error dynamics and the stationary distribution of the error are investigated for both constant and ramp velocity inputs. The performance of the proposed estimator is evaluated and compared with a Kalman filter for an augmented system. A numerical example illustrates the proposed method.

This paper addresses backstepping controller synthesis for piecewise affine (PWA) systems. The main contribution of the paper is to formulate controller design for a large class of PWA systems as a convex problem. Integrator backstepping is proposed as the principal design step in constructing Lyapunov functions for PWA systems in strict feedback form. The controller synthesis problem is divided into two cases. The first case consists of the construction of a sum of squares (SOS) Lyapunov function for PWA systems with discontinuous vector fields. The second case addresses the construction of a piecewise polynomial Lyapunov function for PWA systems with continuous vector fields. After constructing a (piecewise) polynomial Lyapunov function, controller synthesis for a PWA system can be formulated as an SOS program, which is a convex optimization problem and can be efficiently solved. The new synthesis method is applied to a numerical example.