Branislav Rehák

Model for Photosynthesis and Photoinhibition: Parameter Identification Based on the Harmonic Irradiation

A method for parameter identification of a model describing the growth of the algae is presented. The method is based on the description in the form of the so-called photosynthetic factory. The experimental data are gained by measuring the steady-state photosynthetic production when the input of the photosynthetic factory (light intensity) is a harmonic signal. Estimation of parameters is based on a sufficient number of experiments compared with simulated data via the least-squares technique. As the input signal is harmonic and the dynamics of the unforced system is exponentially stable, the resulting asymptotical steady-state trajectory of the photosynthetic factory is also periodic and can be computed via determining an appropriate center manifold graph by solving the corresponding first-order partial differential equation. The latter is performed by the finite-element method. The application of the proposed method is demonstrated on an example using real experimental data.

O_{2}

The article presents a new method for the design of decentralized networked switched controllers to mitigate the response of building structures under earthquakes. It consists of two phases. The first phase generates low-order gain matrices based on the linear quadratic Gaussian LQG control design. It includes a substructural approach when the equations of motion of substructures are extracted from the equation of motion of the overall structures described by a finite element in-plane 2-D model. Appropriate model reduction procedures, determination of damping as well as the selection of sensor and actuators locations and models are applied to each substructure. The sensors and actuators are implemented into the design model. Both resulting reduced-order state space models of substructures are used for the proper LQG control design. The obtained local controllers are implemented into the overall structure to evaluate the performance of the closed-loop system. Displacement, drift, acceleration, maximal actuator forces as well as dynamic responses on selected locations are checked. The computational originality is the method derived under the subsequent second phase, where the gain matrices computed in the first phase serve as a tool for the design of decentralized networked switched controller. The switching is realized periodically between two switched modes. Each mode corresponds with only one active local feedback loop for a certain period of time. The network parameter is the time interval of activity of each mode determined by a given protocol. Robustness of performance against packet dropouts and sensor faults is tested. A numerical example of the decentralized networked switched controller design applied on the 20-story high-fidelity building benchmark model is supplied. The simulation tests show the proposed method exhibits acceptable performance.

Response Measurement

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 center-stable manifold algorithm computes controllers for optimal output regulation.

Decentralized Networked Control of Building Structures

The paper studies the problem of decentralized H ∞ fault tolerant state feedback control design for a class of continuous-time complex systems composed of identical subsystems and symmetric interconnections. We consider a time-varying interval-bounded delay in the feedback of each channel. Single delay as well as multiple delay cases is considered. By exploiting a particular structure of the systems, sufficient conditions are derived for the gain matrix selection. The controller design is performed using a reduced-order system under linear matrix inequality approach constraints. The asymptotic stability with disturbance attenuation γ of the overall multiple delay closed-loop system is guaranteed when synthesizing the gain matrix into the decentralized controller. Moreover, sufficient conditions for the H ∞ bound tolerance under local control channel failures of the overall closed-loop system are derived. The tolerance can be easily tested on several low-order systems. A numerical example illustrates the effectiveness of the proposed method.

Iterative methods to compute center and center-stable manifolds with application to the optimal output regulation problem

Abstract A necessary and sufficient condition for reducibility of multi-input multi-output nonlinear delta differential system is given in terms of the greatest common left divisor of two delta differential polynomial matrices, associated with the set of the input-output (i/o) equations of the system, defined on a homogenous time scale. This condition provides a basis for system reduction, i.e. for finding the transfer equivalent minimal irreducible representation of the set of the i/o equations.

Decentralized H -infinity control of complex systems with delayed feedback

A real time implementation of an error feedback output regulation problem for the gyroscopical platform is presented here. It is based on a numerical method for the solution of the so-called regulator equation. The regulator equation consists of partial differential equations combined with algebraic ones and arises when solving the output-regulation problem. Error-feedback output regulation problem aims to find a dynamic feedback compensator using only tracking error measurements to ensure tracking given reference and/or rejecting unknown disturbance. Solving the regulator equation is becoming difficult especially for the non-minimum phase systems where reducing variables against algebraic part leads to possible unsolvable differential part. The proposed numerical method is based on the successive approximation of the differential part of the regulator equation by the finite-element method while trying to minimize functional expressing the error of its algebraical part. This solution is then used to design real-time controller which is successfully experimentally tested.

Reduction of MIMO nonlinear systems on homogeneous time scales

Abstract The paper studies the problem of decentralized state feedback control design for a class of continuous-time complex systems. These systems are composed of identical nominal subsystems, symmetric nominal interconnections, and nonlinear perturbations. We consider local time-varying delayed feedback at each channel. Single delay as well as multiple delay cases are considered. By exploiting the special structure of the systems, sufficient conditions are derived for the gain matrix selection performed on the design system of reduced dimension under linear matrix inequality approach constraints. It is shown that the robust delay-dependent stability of the global multiple delay closed-loop system is guaranteed when implementing the gain matrix into the global decentralized controller. Moreover, sufficient conditions are derived for the tolerance of local control channel failures in such a global closed-loop system. The fault tolerance can be effectively tested on systems of reduced dimensions.

Real-Time Error-Feedback Output Regulation of Nonhyperbolically Nonminimum Phase System

This paper examines decentralized observer-based stabilization for symmetric interconnected systems. The structure of these systems is composed of identical subsystems with symmetric interconnections. Linear time-invariant dynamic systems are considered within the continuous-time case. The observer inputs operate with a delayed system output. Single as well as multiple time-varying interval bounded delays in the loop are considered. The state space matrices of these systems are decomposable into block diagonal matrices. Their properties and a robust stabilization approach are used to construct the design model which is subsequently used for the gain matrices selection by using Linear Matrix Inequalities. The main result shows that when these gain matrices are implemented into the overall system as local controller-observers, then the entire closed-loop system guarantees asymptotic stability. An application example illustrates the effectiveness of this method.

Decentralized stabilization of complex systems with delayed feedback

Microalgae have the potential to be a major biofuel source in the future. Computational biology plays a key role in understanding biological processes within microalgae and optimizing biofuel production. Here, we present a multidisciplinary, multi-timescale modeling approach of microalgae growth in photobioreactors. Our modeling framework bridges biology (cell growth), physics (hydrodynamics and light distribution), and optimization together. This framework consists of (i) the state system (mass balance equations in form of advection-diffusion-reaction PDEs), (ii) the fluid flow equations (the Navier-Stokes equations), and (iii) the optimization problem formulation. The modeling and optimization of microalgae growth in a Couette-Taylor reactor is presented to demonstrate this method. We show how the flashing light effect can be an intrinsic part of the model. Finally, we discuss further methodological integration with the metabolomic-transcriptomic kinetic model, which explains cellular concentrations of key metabolites in connection with cell growth.

Decentralized stabilization of symmetric systems with delayed observer-based feedback

Abstract The objective of this investigation is to present a decentralized design of decentralized controllers for a 20-story steel structure benchmark. The benchmark problem was proposed within the structural control community to design and compare control schemes for seismically excited buildings. The control design problem is focused on an in-plane analysis of one-half of the structure. The height of the building naturally suggests the disjoint decomposition of a finite element overall dynamic model into two subsystems, each covering 10 stories. Inter-story elements appearing between the 10th and the 11th fool serve as the coupling elements of the overall interconnected system. The idea of decentralization of control has been numerically tested and compared to the benchmark sample centralized LQG design. The performance of the decentralized control design has been assessed by means of given benchmark evaluation criteria, eigenvalue analysis and time responses for both pre-earthquake and post-earthquake structures.