Mazen Alamir

Remote Stabilization Via Communication Networks With a Distributed Control Law

In this note, we investigate the problem of remote stabilization via communication networks involving some time-varying delays of known average dynamics. This problem arises when the control law is remotely implemented and leads to the problem of stabilizing an open-loop unstable system with time-varying delay. We use a time-varying horizon predictor to design a stabilizing control law that sets the poles of the closed-loop system. The computation of the horizon of the predictor is investigated and the proposed control law explicitly takes into account an estimation of the average delay dynamics. The resulting closed loop system robustness with respect to some uncertainties on the delay estimation is also considered. Simulation results are finally presented.

Brief Discontinuous exponential stabilization of chained form systems

In this paper a novel approach to exponential stabilization of chained form system is proposed. Provided that the control law fulfills mild assumptions, it is shown that a Brunovsky-like change of coordinates depending on the control transforms any chained form system into a system having a linearly bounded nonlinear part. Using linear tools, it is possible to exponentially stabilize a chained form system for any initial condition outside a submanifold containing the origin. This result is then generalized to global exponential stabilization. The so obtained static discontinuous feedback is bounded for bounded states and exponentially converges to zero along the closed-loop trajectories of the system.

Stability of a truncated infinite constrained receding horizon scheme: the general discrete nonlinear case

Some results concerning the constrained receding horizon formulation with infinite and truncated prediction horizon are presented. In this formulation a distinction is made between prediction and control horizons. The main result is a generalization of a known fact for linear systems, namely that, under certain technical requirements, the asymptotic stability of the above formulation holds for a sufficiently large finite prediction horizon. Existence results are also provided under stabilizability assumptions.

Optimization based non-linear observers revisited

Optimization based non-linear observers are those where the integrated output prediction error is used to define the dynamic of the observers state. Their main advantage is genericity and the natural assumptions that are needed for the related convergence results to hold. Here, we present some new theoretical results concerning these observers. Despite the title we use, our observer is not based on the search for a global minimum of a cost function. It is based on a descent-like approach without the use of the Hessian matrix. A nice feature is that the resulting observer takes a classical form of in the sense that it is defined by a set of ordinary differential equations. Besides the theoretical results, some implementation issues are discussed. In particular, we propose to use the post stabilization approach, well known when dealing with differential systems with invariant submanifolds. This enables to increase the sampling period while keeping very good precision. Two illustrative examples are presente...

On the stability of receding horizon control of nonlinear discrete-time systems

Abstract In this paper, we give sufficient conditions that guarantee the existence of the receding horizon control and the stability of the feedback system. The controlled system is a general nonlinear discrete-time system. Local and global stability are studied separately, giving rise to two sets of sufficient conditions. The context is that of regulation and tracking with internal model control scheme.

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.

Nonlinear receding-horizon state estimation for dispersive adsorption columns with nonlinear isotherm

Abstract In this paper, a nonlinear receding-horizon estimation scheme is proposed for general nonlinear diffusive binary chromatographic processes. This is done by approximating the concentration profiles over a suitable truncated functional basis. The resulting vector of unknowns is first reduced using available measurements. Then the remaining part is computed by nonlinear optimization. Numerical simulations are proposed to illustrate the efficiency of the proposed scheme.

Constrained minimum-time-oriented feedback control for the stabilization of nonholonomic systems in chained form

In this paper, a discontinuous state-feedback law is proposed for the stabilization of nonholonomic systems in power form. The feedback law is based on a receding-horizon strategy in which the open-loop optimization problem is a minimum-time steering process. Suboptimal formulations are used explicitly to meet the real-time implementability requirements. Stability is established in a sampled-data context and illustrative simulations are given to show the effectiveness and the real-time implementability of the proposed scheme.

On the use of State Predictors in Networked Control Systems

Without pretending to be exhaustive, the aim of this chapter is to give an overview on the use of the state predictor in the context of time-delay systems, and more particularly for the stabilisation of networked control systems. We show that the stabilisation of a system through a deterministic network can be considered as the stabilisation of a time-delayed system with a delay of known dynamics. The predictor approach is proposed, along with some historical background on its application to time-delayed systems, to solve this problem. Some simulation results are also presented.

Robust constrained control algorithm for general batch processes

In this paper, an implementable algorithm that enables to robustly control batch processes is proposed. The resulting state feedback algorithm is based on repeated on-line solution of constrained open loop min-max problems associated to the worst-case perturbations and/or uncertainties. These solutions are then used in a receding horizon scheme in order to yield a robust state feedback controller. A novel algorithm is proposed for the solution of the open loop constrained minmax problems that is based on chattering control combined with the variable stabilizing penalty approach. Simulations are provided in order to illustrate the effectiveness of the proposed control algorithm.