A Type of Set Membership Estimation Designed for Dynamic Flux Balance Models

Dynamic flux balance models (DFBM) are used in this study to infer metabolite concentrations that are difficult to measure online. The concentrations are estimated based on few available measurements. To account for uncertainty in initial conditions the DFBM is converted into a variable structure system based on a multiparametric linear programming (mpLP) where different regions of the state space are described by correspondingly different state space models. Using this variable structure system, a special set membership-based estimation approach is proposed to estimate unmeasured concentrations from few available measurements. For unobservable concentrations, upper and lower bounds are estimated. The proposed set membership estimation was applied to batch fermentation of E. coli based on DFBM.

The Synthesis of Variable Structure System for the Control of Quadrotor Spatial Motion

The method of the synthesis of multi-channel decentralized variable structure system for the control of quadrotor spatial motion is developed in this paper. The control law based on the formation of the sliding mode in the separate subsystems of each coordinates control is formed. Each subsystem includes two loops for Cartesian coordinates and relevant Euler angles control. The conditions of the existence of stable sliding mode are obtained. These conditions take into account essential dynamic reciprocal effect between all control channels. The application of proposed control law provides high control quality and maximal fast-action at any variations of the quadrotor parameters within given ranges. This control law does not require the identification of changing object parameters. Efficiency of synthesized control system is confirmed by numerical simulation results. The control system can be realized in the real time by simple technical means.

Discrete-Time Exponentially Stabilizing Fuzzy Sliding Mode Control via Lyapunov’s Method

The exponentially stabilizing state feedback control algorithm is developed by Lyapunov’s second method leading to the variable structure system with chattering free sliding modes. Linear time-invariant discrete-time second order plant is considered and the control law is obtained by using a simple fuzzy controller. The analytical structure of the proposed controller is derived and used to prove exponential stability of sliding subspace. Essentially, the control algorithm drives the system from an arbitrary initial state to a prescribed so-called sliding subspaceS, in finite time and with prescribed velocity estimate. Inside the sliding subspaceS, the system is switched to the sliding mode regime and stays in it forever. The proposed algorithm is tested on the real system in practice, DC servo motor, and simulation and experimental results are given.