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Some ideas concerning the application of methods of H-optimization theory in practice are discussed in this work. The problem of plasma current and shape stabilization system synthesis in tokamak ITER is considered as an application of discussed ideas.

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The paper is devoted to the problem of wheel angular velocity stabilization using encoder data. The differential drive robot with four wheels is used as a mobile robot. The left wheels and right wheels are controlled separately. This allows robot to move forward or backward if we apply equal control signal for both sides' wheels, or to turn left or right if the control for left and right wheels is different. It is well-known that for differential drive robots the robot wheels angular velocity is slightly different even if the same control input is applied for left and right wheels. This lead to the arc trajectories of the robot instead of straight lines. To overcome this problem it's necessary to use some internal low-level controller for wheels angular velocity stabilization. In order to stabilize angular velocity we need estimation of its current value, which can be obtained using encoder data. The algorithm for angular velocity estimation and stabilization using rough encoder data is proposed. The simulation study and practical real-time implementation for a particular differential drive robot are presented using Matlab and Arduino environment.

The problem of current and shape plasma stabilization in tokamaks is considered. The scheme of stabilization based on the H2 and H-infinity optimization problems solutions is proposed.The problem of plasma control in tokamaks is of significant interest in the area of controlled fusion nowadays. One of the main tasks usually arising in the framework of this problem is the development of plasma current and shape stabilization system. The control design scheme based on the H-2 and Hinfinity optimization problems solutions is proposed in this paper applied for current and shape plasma stabilization in tokamak ITER.The problems of H-2 and H-infinity optimization have a number of well-designed algorithms for computation of optimal solution, and the standard algorithms ([1], [2] etc.) based on matrix Riccati equations can be applied for statespace linear modelẋfor x ∈ E n , u ∈ E m , e ∈ E p , y ∈ E k , d ∈ E m d vectors of states, controls, regulated variables, measurements and external disturbances accordingly. All matrices have constant components.The problem of synthesis is to construct controller of the form u=W(s)y, minimizing the norm of the closed-loop system transfer matrix from d to ewhere H-2 or H-infinity norm of Hardy spaces is used, and Ω is a set of fractional-rational components such that characteristics polynomial of the closed-loop system is Hurwitz.The system (1) must satisfy some conditions (regularity conditions) to carry out controller design procedure on the base of H-2 and H-infinity optimization.Applying H-2 and H-infinity design standard procedures in practical task we need to take into account its specificity, precisely for example the base information and structure of vector of disturbances and dynamic requirements and constraints for regulated variables can result in violating of regularity conditions for nominal plant model in the form of (1). In order to use the algorithms of H-2 and H-infinity optimization in described situation it proposed to introduce some parameter vector h ∈ E N to modify the nominal model, varying the matrices G(h), F(h), L(h) and M(h), thus providing keeping of regularity conditions in modified plant.Satisfying of all dynamic requirements and constraints for the performance in the closed-loop system that can be presented in the formfor given J i0 , i = 1, K can be provided by solving the parameter optimization problemwhere f (h, J i0 ) ≥ 0 is the continuous function, and f (h, J i0 ) can equals to zero for fixed i only for such values of h that give (3) for this i, λ i ≥ 0 (i = 1, K) weight coefficients.Then the decision of problem (2) for any vector h =h solving the system (3) (if it exists) gives J(h) = 0 and the desired controller. Plasma current and shape control for ITER-FEAT tokamak for definite mode of plasma burning is based on the linear timeinvariant model of 11 order that is the reduced system from the full model formed of the plant model, power and filter systems and vertical controller, with full vector of states consisting of 100 components ([3], [4] e...