Many systems can be represented using polynomial differential equations, particularly in process control, biotechnology, and systems biology [1], [2]. For example, models of chemical and biochemical reaction networks derived using the law of mass action have the form ẋ = Sv(k,x), (1) where x is a vector of concentrations, S is the stoichiometric matrix, and v is a vector of rate expressions formed by multivariate polynomials with real coefficients k . Furthermore, a model containing nonpolynomial nonlinearities can be approximated by such polynomial models as explained in \"Model Approximation\". The primary aims of differential algebra (DALG) are to study, compute, and structurally describe the solution of a system of polynomial differential equations,f (x,ẋ, ...,x^{(k)}) =0, (2) where f is a polynomial [3]-[6]. Although, in many instances, it may be impossible to symbolically compute the solutions, or these solutions may be difficult to handle due to their size, it is still useful to be able to study and structurally describe the solutions. Often, understanding properties of the solution space and consequently of the equations is all that is required for analysis and control design.

A novel methodology is proposed for coordination of dynamical systems. The scheme is based on the sliding mode reference conditioning technique in a sort of supervisory level. The approach addresses the problem of coordinating dynamical systems with possible different dynamics (eg linear and nonlinear, different orders, constraints, etc). To achieve this, the dynamics of each subsystem are emph{hidden} from the coordination mechanism. The main idea is to shape the systems local references in order to keep them coordinated. This implies considering the global goals, the systems constraints and the achievable performances as well. Sliding Mode Reference Conditioning (SMRC) is used for this purpose by means of a hierarchical supervisory structure. To show the applicability of the approach, the problem of coordinating a number of different dynamical systems with control saturations is addressed as a particular case. Coordination will be understood as actuating on the systems references to achieve some emph{collective behavior} considering the individual restrictions of each system.

}, keywords = {Control of constrained systems, Control of switched systems, Coordination, Switching stability and control}, isbn = {978-3-902661-93-7}, doi = {10.3182/20110828-6-IT-1002.02727}, url = {http://www.ifac-papersonline.net/Detailed/51115.html}, author = {A Vignoni and J Pic{\'o} and F Garelli and Hern{\'a}n De Battista}, editor = {Sergio, Bittanti,} }