Antonio A Alonso | PubMed Health

PubMed2006

Stabilization of inhomogeneous patterns in a diffusion-reaction system under structural and parametric uncertainties.

Many phenomena such as neuron firing in the brain, the travelling waves which produce the heartbeat, arrythmia and fibrillation in the heart, catalytic reactions or cellular organization activities, among others, can be described by a unifying paradigm based on a class of nonlinear reaction-diffusion mechanisms. The FitzHugh-Nagumo (FHN) model is a simplified version of such class which is known to capture most of the qualitative dynamic features found in the spatiotemporal signals. In this paper, we take advantage of the dissipative nature of diffusion-reaction systems and results in finite dimensional nonlinear control theory to develop a class of nonlinear feedback controllers which is able to ensure stabilization of moving fronts for the FHN system, despite structural or parametric uncertainty. In the context of heart or neuron activity, this class of control laws is expected to prevent cardiac or neurological disorders connected with spatiotemporal wave disruptions. In the same way, biochemical or cellular organization related with certain functional aspects of life could also be influenced or controlled by the same feedback logic. The stability and robustness properties of the controller will be proved theoretically and illustrated on simulation experiments.

Diffusion↗

PubMed2005

Dynamic optimization of bioprocesses: efficient and robust numerical strategies.

The dynamic optimization (open loop optimal control) of non-linear bioprocesses is considered in this contribution. These processes can be described by sets of non-linear differential and algebraic equations (DAEs), usually subject to constraints in the state and control variables. A review of the available solution techniques for this class of problems is presented, highlighting the numerical difficulties arising from the non-linear, constrained and often discontinuous nature of these systems. In order to surmount these difficulties, we present several alternative stochastic and hybrid techniques based on the control vector parameterization (CVP) approach. The CVP approach is a direct method which transforms the original problem into a non-linear programming (NLP) problem, which must be solved by a suitable (efficient and robust) solver. In particular, a hybrid technique uses a first global optimization phase followed by a fast second phase based on a local deterministic method, so it can handle the nonconvexity of many of these NLPs. The efficiency and robustness of these techniques is illustrated by solving several challenging case studies regarding the optimal control of fed-batch bioreactors and other bioprocesses. In order to fairly evaluate their advantages, a careful and critical comparison with several other direct approaches is provided. The results indicate that the two-phase hybrid approach presents the best compromise between robustness and efficiency.

Algorithms↗