On the reachability in any fixed time for positive continuous-time linear systems.
This paper deals with the reachability of continuous-time linear positive systems. The reachability of such systems, which we will call here the strong reachability, amounts to the possibility of steering the state in any fixed time to any point of the positive orthant by using nonnegative control functions. The main result of this paper essentially says that the only strongly reachable positive systems are those made of decoupled scalar subsystems. Moreover, the strongly reachable set is also characterized.
Ch. Commault and M. Alamir. On the reachability in arbitrary time of positive continuous time linear systems. Systems & Control Letters. Vol 56, Issue 4, pages 272-276 (2007). [download]
Robust Stabilization of Nonlinear Systems by Discontinuous Dynamic State Feedback
In this paper, a discontinuous dynamic state feedback that robustly stabilizes affine in control uncertain nonlinear systems is proposed. The formulation is based on Hamilton-Jacobi-Isaacs partial differential equations with two boundary conditions. The resulting dynamic state feedback is then expressed in terms of the solution of the related PDE’s. An interesting feature is that the internal state of the resulting dynamic state feedback may have discontinuous behavior as a function of time. The proposed scheme is illustrated through the example of the stabilization of the angular velocities of a rigid body under two actuators.
Alamir, M.; Balloul, I.; Marchand, N. Robust stabilization of nonlinear systems by discontinuous dynamic state feedback. Int. J. Control 75, No.6, 421-433 (2002). [download]
Nonlinear receding horizon sub-optimal guidance law for the minimum interception time problem
In this paper, a state feedback law that yields a sub-optimal solution of the minimum interception time problem is proposed. Sub-optimality is de"ned over the potential interception times that correspond to the system-compatible parabolic trajectories. Such trajectories are computed at each sampling instant and the whole procedure is reiterated in a receding horizon manner yielding a piece-wise continuous dynamic state feedback law. Simulations were proposed and the robustness was tested against the modeling errors.
Alamir, M. Nonlinear Receding Horizon sub-optimal Guidance Law for minimum interception time problem. Control Engineering Practice 9, No.1, 107-116 (2001). [download]