Branislav Rehák

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A method for parameter estimation of two timescale model of photosynthesis and photoinhibition is presented. The model structure coincides with the earlier mechanistic concept of photosynthetic factory by Eilers and Peeters, however, our formulation respects the decomposition of the phase-space into the fast phase x A , and the slow one, x B. The(More)
This paper presents iterative methods for computing center and center-stable manifolds. The methods are based on the contraction mapping theorem and compute flows on the invariant manifolds. An important application includes the design of optimal output regulators. It will be shown that the center manifold algorithm solves the regulator equation and the(More)
A numerical method to solve the so-called regulator equation is presented here. This equation consists of partial differential equations combined with algebraic ones and arises when solving the output-regulation problem. Solving the regulator equation is becoming difficult especially for the nonminimum phase systems where reducing variables against(More)
The topic of the paper is a procedure for observer design for polynomial systems. The design is based on sum-of-squares through construction of suitable Lyapunov-Krasovskii functionals. As the resulting problem is not convex, an iterative formula is proposed to obtain the solution. Estimates of observation error are derived, the usage of the method is(More)
An unconditionally stable finite difference scheme for systems whose dynamics are described by a fourth-order partial differential equation is developed with the use of a regular hexagonal grid. The scheme is motivated by the well-known Crank-Nicolson discretization that was originally developed for second-order systems and it is used to develop a discrete(More)