Dynamic Optimisation

This research concerns determination of the optimal open-loop and/or closed-loop control trajectories or parameter estimation. The systems under study are described by a system of nonlinear differential and algebraic equations. The optimal control and estimation methods developed are from the family of the called Control Vector Parametrisation and Orthogonal Collocation methods. The original continuous control vector is parametrised as a linear function of some basis functions. States remain continuous for CVP and are also parametrised in OC. Thus, the original dynamic optimisation problem is transformed into a static optimisation problem. Gradient and nongradient methods have been developed.

Analytic and numeric methods are investigated for optimal operation of batch membrane filtration processes. We have derived analytical solutions for minimum time and minimum diluant consumption problems containing optimal state curves as special cases of singular control trajectories. The analytical solutions have been confirmed numerically. The obtained results show that existing methods of membrane operation are close to optimal but there are cases when the proposed approach yields improved operation and profit.

Deterministic global methods in dynamic optimisation are investigated using rigorous approach of convex underestimators. The original nonconvex NLP problem is then solved usign a spatial branch-and-bound method to global optimality. Problems solved include global NMPC and global parameter estimation.

People in Group

Former colleagues: T. Hirmajer (PhD 2007), M. Podmajerský (PhD 2011), M. Jelemenský (PhD 2016), A. Sharma (PhD 2020), M. Čižniar, D. Pakšiová.

Software Packages

A FORTRAN F77 package for dynamic optimisation that can deal with ODE systems subject to a general set of constraints using CVP.
A MATLAB package for dynamic optimisation. It is based on total discretisation with orthogonal collocations on finite elements.
A MATLAB package for dynamic optimisation. It is based on control vector parametrisation and gradients are calculated using sensitivity equations.