The article proposes a nonlinear optimal (H-infinity) control approach for a type of underactuated power-line inspection robots. To implement this control scheme, the state-space model of the power-line inspection robots undergoes first approximate linearization around a temporary operating point, through first-order Taylor series expansion and through the computation of the associated Jacobian matrices. To select the feedback gains of the controller an algebraic Riccati equation is solved at each time step of the control method. The global stability properties of the control loop are proven through Lyapunov analysis. The significance of the article’s results is outlined in the following: (i) the proposed control method is suitable for treating underactuated robotic systems and in general nonlinear dynamical systems with control inputs gain matrices which are in a nonquadratic form, (ii) by achieving stabilization of the power-line inspection robots in underactuation conditions the proposed control method ensures the reliable functioning of these robotic systems in the case of actuators’ failures or enables the complete removal of certain actuators and the reduction of the weight of these robotic systems, (iii) the proposed control method offers a solution to the nonlinear optimal control problem which is of proven global stability while also remaining computationally tractable, (iv) the proposed nonlinear optimal control method retains the advantages of linear optimal control that is fast and accurate tracking of reference setpoints under moderate variations of the control inputs, and (v) by minimizing the amount of energy that is dispersed by the actuators of the power-line inspection robots the proposed control method improves the autonomy and operational capacity of such robotic systems.

Aided Inertial Navigation Systems (INS) systems are commonly implemented in land vehicles for a variety of applications. Several methods have been reported in the literature for evaluating aided INS performance. Yet, the INS error-state-model dependency on time and trajectory implies that no closed-form solutions exist for such evaluation. In this paper, we derive analytical solutions to evaluate the fusion performance. We show that the derived analytical solutions manage to predict the error covariance behavior of the full aided INS error model. These solutions bring insight into the effect of the various parameters involved in the fusion of the INS and an aiding sensor.

In this paper, we study the stabilization of a two-dimensional Burgers equation around a stationary solution by a nonlinear feedback boundary control. We are interested in Dirichlet and Neumann boundary controls. In the literature, it has already been shown that a linear control law, determined by stabilizing the linearized equation, locally stabilizes the two-dimensional Burgers equation. In this paper, we define a nonlinear control law which also provides a local exponential stabilization of the two-dimensional Burgers equation. We end this paper with a few numerical simulations, comparing the performance of the nonlinear law with the linear one.

The maximization of the long-term growth rate of expected utility is considered under drawdown constraints. In a general situation, the value and the optimal strategy of the problem are related to those of another ‘standard’ risk-sensitive-type portfolio optimization problem. Furthermore, an upside-chance maximization problem of a large deviation probability is stated as a ‘dual’ optimization problem. As an example, a ‘linear-quadratic’ model is studied in detail: the conditions to ensure the solvabilities of the problems are discussed and explicit expressions for the solutions are presented.