On reachable sets for a class of nonlinear systems with constraints

The determination of the reachable set for a class of nonlinear systems with control and state trajectory constraints is investigated. The main result links this problem with the determination of the set of admissible controls, for which procedures already exist. The paper also gives a procedure to generate an admissible control which steers the system to a reachable state. (C) 1999 Academic Press

Admissible Controls and Attainable States for a Class of Nonlinear-systems With General Constraints

We consider nonlinear control systems where the control and the state variables are submitted to explicit constraints. This paper has two objectives. First, for a class of nonlinear systems with constraints, an existence result of nontrivial admissible controls and some of their interesting properties are proved. Then, we investigate the problem of local controllability in a neighbourhood of an equilibrium point, while observing state and control constraints along the whole trajectory. An iterative procedure is also given, which allows one to compute the steering admissible control function. This procedure is illustrated with a classical example

Predictive Control for a Class of Distributed Parameter Systems

Focus the extension of the predictive control theory to a class of distributed parameter systems. Predictive control is one of the control strategies, which optimize control action within some horizon, in order to make the predicted processus behavior as close as possible in the desired trajectory. An example is proposed in order to specify the effect of each parameter of design on the convergence towards the desired trajectory

Trajectory analysis of nonisothermal tubular reactor nonlinear models

The existence and uniqueness of the state trajectories (temperature and reactant concentration) are analyzed for nonisothermal plug flow and axial dispersion tubular reactor models. It is mainly shown that these trajectories exist on the whole (nonnegative real) time axis and the set of all physically feasible state values is invariant under the dynamics equations. The main nonlinearity in the model originates from the Arrhenius-type kinetics term in the model equations. The analysis essentially uses Lipschitz and dissipativity properties of the nonlinear operator involved in the dynamics and the concept of state trajectory positivity. (C) 2001 Elsevier Science B.V. All rights reserved

Multiple equilbrium profiles for nonisothermal tubular reactor nonlinear models

The multiplicity of the equilibrium profiles is shown for axial dispersion non-isothermal tubular reactors described by Arrhenius type nonlinear models. It is proved that there is at least one steady state among the physically feasible states for such models. Moreover physically meaningful conditions which ensure the multiplicity of equilibrium profiles are given

Control of a class of nonlinear systems with general constraints

The problem of steering the state of a nonlinear system from the origin to a desired final state, while observing state and control constraints along the whole trajectory, is examined. An iterative procedure that allows computation of the steering admissible control function is given.Anglai

Positivity and invariance properties of nonisothermal tubular reactor nonlinear models

The existence and uniqueness of the state trajectories (temperature and reactant concentration) and the existence and multiplicity of equilibrium profiles are analyzed for a nonistohermal axial dispersion tubular reactor model. It is reported that the trajectories exist on the whole (nonnegative real) time axis and the set of all physically feasible state values is invariant under the dynamics equations. The main nonlinearity in the model originates from the Arrhenius-type kinetics term in the model equations. The analysis uses Lipschitz and dissipativity properties of the nonlinear operator involved in the dynamics and the concept of state trajectory positivity. In addition, the multiplicity of the equilibrium profiles is reported: there is at least one steady state among the physically feasible states for such models, and conditions which ensure the multiplicity of equilibrium profiles are given