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The use of robotic limb exoskeletons is growing fast either for rehabilitation purposes or in an aim to enhance human ability for lifting heavy objects or for walking for long distances without fatigue. The paper proposes a nonlinear optimal control approach for a lower-limb robotic exoskeleton. The method has been successfully tested so far on the control problem of several types of robotic manipulators and this paper shows that it can also provide an optimal solution to the control problem of limb robotic exoskeletons. To implement this control scheme, the state-space model of the lower-limb robotic exoskeleton 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 H-infinity 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. Finally, to implement state estimation-based feedback control, the H-infinity Kalman Filter is used as a robust state estimator.

To define a vaccination policy and antiviral treatment against the spreading of viral infections a nonlinear optimal (H-infinity) control approach is proposed. Actually, because of the scarcity of the resources for treating infectious diseases in terms of vaccines, antiviral drugs and other medical facilities, there is need to implement optimal control against the epidemics deployment. In this approach, the state-space model of the epidemics dynamics undergoes first approximate linearization around a temporary operating point which is recomputed at each time-step of the control method. The linearization is based on Taylor series expansion and on the computation of the associated Jacobian matrices. Next, an optimal (H-infinity) feedback controller is developed for the approximately linearized model of the epidemics. To compute the controller’s feedback gains an algebraic Riccati equation is solved at each iteration of the control algorithm. Furthermore, the global asymptotic stability properties of the control scheme are proven through Lyapunov stability analysis. This paper’s results confirm that optimal control of the infectious disease dynamics allows for eliminating its spreading while also keeping moderate the consumption of the related medication, that is vaccines and antiviral drugs.

Attitude control and stabilization of micro-satellites is a nontrivial problem due to the highly nonlinear and multivariable structure of the satellites’ state-space model. In this paper, a novel nonlinear optimal (H-infinity) control approach is developed for this control problem. The dynamic model of the satellite’s attitude dynamics undergoes first approximate linearization around a temporary operating point which is updated at each iteration of the control algorithm. The linearization process relies on first-order Taylor series expansion and on the computation of the Jacobian matrices of the state-space model of the satellite’s attitude dynamics. For the approximately linearized description of the satellite’s attitude a stabilizing H-infinity feedback controller is designed. To compute the controller’s feedback gains, an algebraic Riccati equation is solved at each time-step of the control method. The stability properties of the control scheme are proven through Lyapunov analysis. It is also demonstrated that the control method retains the advantages of linear optimal control that is fast and accurate tracking of the reference setpoints under moderate variations of the control inputs.