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The parameter identification problem of cell population balance models in a yeast batch process is addressed. The model is described by a partial integro-differential equation coupled with a set of ordinary differential equations. Based on the solution equivalence of the mass balance model and the first moment of the cell population balance model, the identification process is carried out in two steps. The growth related parameters are identified by only taking mass balance based measurements into account. The growth parameters are then utilized to identify the parameters related to cell division in the cell population balance model by means of optimization. The results are verified with an R2 analysis.

A dissipativity-based observer design for a class of cell population balance models is presented and evaluated using experimental data. The population balance model is described by a partial integro-differential equation coupled with an ordinary differential equation for a batch bioreactor with biomass measurement via an optical density sensor. The dissipative observer is proven to exponentially converge in the first moment of the cell size distribution and the substrate concentration in the absence of modeling and measurement errors. The theoretical results are evaluated using experimental data from a 2 liter lab-scale reactor for anaerobic yeast fermentation on glucose using nitrogen gas supply, showing a good performance of the dissipativity-based estimation scheme.

The observer design problem for the cell population estimation in a yeast batch process is addressed. The cell population balance model is described by a partial integro-differential equation coupled with a set of ordinary differential equations. Based on the observability property of the first moment of the cell distribution and the structural observability of the discretized cell population balance model, an extended Kalman Filter operating on online biomass measurements is designed for the model equations. The observer is validated using experimental data.

The problem of dissipative proportional-integral (PI) output-feedback control for a class of semilinear heat equations with actuator disturbance is addressed. Sufficient conditions for strict dissipativity in the state and thus exponential stability of the closed-loop system are derived which are stated in terms of the dissipavity properties of the nonlinearity, the controller gains and the actuator and sensor shape functions (i.e., their form and localization). Based on these conditions a dissipation maximization procedure is proposed to appropriately choose the degrees of freedom using optimization algorithms. Numerical simulation results illustrate the performance of the proposed controller.

The problem of safety verification for a subclass of hybrid systems, namely for impulsive systems with fixed moments of jumps is considered. Sufficient conditions are derived for the safety of impulsive systems whose continuous dynamics may steer the state outside the safe region. For this purpose auxiliary barrier certificates with nonlinear rates are introduced and equipped with appropriate dwell-time conditions which restrict the upper bound for the inter-jump interval in order to ensure the desired safety property. The proposed approach is demonstrated by performing safety verification of linear and nonlinear impulsive systems.

This paper describes how to design flatness-based distributed feedforward controllers for the solution of the trajectory planning problem of semilinear time-fractional reaction-diffusion systems (TFRDSs), where the first-order time derivative of conventional reaction-diffusion system is extended to a Caputo fractional derivative of order α ϵ (0,1]. To this end, an implicit system variable and control input parametrization is determined based on the spectral property of system operator with respect to a basic output and its fractional-order derivatives. The convergence of the parametrizations is guaranteed by restricting the basic output to some certain Gevrey classes. With these, we propose two approaches on solving the trajectory planning problem within a prescribed finite time interval. A simulation example is finally included to illustrate our results.

The purpose of this research is to design optimal boundary control to solve demand tracking problems for manufacturing systems represented at the factory level in terms of conservation laws coupled with ordinary differential equations. The factory level is modeled as a network with arcs describing specific production policies, e.g., velocity, processing rate, number of machines, and each vertex represents the buffer zone. Different interconnection topologies that correspond to dispersing and merging networks are considered. Numerical solutions are performed using direct and indirect methods.

A flatness-based approach for motion planning for a class of boundary controlled port-Hamiltonian systems with distributed parameters is presented. The goal is to achieve open-loop output tracking or finite-time transitions between steady states or operating profiles. Introducing new (fictious) boundary conditions in terms of so-called flat outputs, the port-Hamiltonian system is reformulated as a Cauchy problem in the spatial domain. The parametrization of any system variable and input by the flat output is computed using two different solution approaches. By assigning a suitable desired trajectory for the flat output, the input parametrization yields the feed forward control law to solve the motion planning task. The presented theory is applied to the wave equation with spatially varying parameters and is evaluated by numerical calculations and simulations.

The problem of trajectory tracking for nonlinear differentially flat systems is addressed in the paper. A novel event-based control methodology is developed for systems depending on unmeasurable disturbances. A standard flatness-based feedforward control is applied when the flat outputs are close to their desired values. If the error becomes too large, the feedforward controller parameters are updated based on the measurements of the flat outputs and on the estimates of their time-derivatives. The developed control strategy is applied to an autonomous underwater vehicle. Simulations show that the vehicle tracks the pre-defined reference trajectory both in healthy situation as well as in the case of certain mechanical faults.

The problem of output-feedback control for a class of semilinear unstable heat equations is addressed within the framework of dissipativity theory. It is shown that using a simple proportional output-feedback control in a collocated input-output pairing the closed-loop stability is ensured if the control gain is chosen sufficiently large and the nonlinearity satisfies a quadratic dissipativity condition. The approach is illustrated using numerical simulations.

The problem of state feedback control for a class of semilinear partial integro-differential equations is addressed within the framework of dissipativity theory. Adapting ideas from absolute stability theory the system is viewed as interconnection of a linear dynamic and a nonlinear static subsystem. Using this interpretation sufficient conditions for the stabilization of the zero solution by means of a backstepping state feedback controller are derived considering a class of nonlinearities satisfying a quadratic dissipativity condition. The approach is illustrated using numerical simulations for a representative case example.

The paper develops new sufficient conditions for synchronization of a network of $N$ nonlinearly coupled Chua oscillators interconnected via the first state coordinate only. The nonlinear coupling strength is governed by a function residing within a sector, i.e. it is bounded from above and below by linear functions. The derived sufficient conditions provide a trade-off between the characteristics of the sector and the interconnection topology of the network to guarantee the synchronization of the oscillators., Comment: 6 pages, 3 figures, submitted to IFAC Symposium on Nonlinear Control Systems (NOLCOS 2019)

Transient shape control of an artificial, actively actuated fishtail is considered to acquire an efficient, natural-like underwater locomotion. The fishtail’s body is made of silicon allowing for elastic bending motion. Two fluid chambers are integrated into the volume mimicking an antagonistic muscle pair if pressure is applied antisymmetrically. The mathematical model is determined by following an open source toolchain using the finite element method. Model order reduction in terms of modal truncation is applied to obtain a feasible system order. Based on the reduced order model a systematic motion planning methodology is developed for the elastomechanic structure taking into account the controllable canoical form. Simulation results are provided to evaluate the efficiency of the presented approach.