Issue 3 (189), article 2


Kibern. vyčisl. teh., 2017, Issue 3 (189), pp.

Zhiteckii L.S., PhD (Engineering), Acting Head of the Department of Intelligent Automatic Systems
Solovchuk K.Yu., Postgraduate Student
International Research and Training Center for Information Technologies and Systems of the NAS of Ukraine and Ministry of Education and Science of Ukraine,
Acad. Glushkova av., 40, Kiev, 03680, Ukraine


Introduction. The problem of controlling interconnected systems subjected to arbitrary unmeasurable disturbances remains actual up to now. It is important problem from both theoretical and practical points of view. During the last decades, the internal model control principle becomes popular among other methods dealing with an improvement of the control system. A perspective modification of the internal model control principle is the so-called model inverse approach. Unfortunately, the inverse model approach is quite unacceptable if the systems to be controlled are square but singular or if they are nonsquare. It turned out that the so-called pseudoinverse (generalized inverse) model approach can be exploited to cope with the noninevitability of singular square and also nonsquare system.
The purpose of the paper is to generalize the results obtained by the authors in their last works which are related to the asymptotic properties of the pseudoinverse model-based method for designing an efficient steady-state control of interconnected systems with uncertainties and arbitrary bounded disturbances and also to present some new results.
Results. In this paper, the main effort is focused on analyzing the asymptotic properties of the closed-loop systems containing the pseudoinverse model-based controllers. In the framework of the pseudoinversion concept, new theoretical results related to the asymptotic behavior of these systems are obtained. Namely, in the case of nonsingular gain matrices with known elements, the upper bounds on the ultimate norms of output and control input vectors are found. Next, in the case of nonsquare gain matrices whose elements are also known, the asymptotic behavior of the feedback control systems designed on the basis of pseudoinverse approach are studied. Further, the sufficient conditions guaranteeing the boundedness of the output and control input signals for the linear and certain class of nonlinear interconnected systems in the presence of uncertainties are derived.
Conclusion. It has been established that the pseudoinverse model-based concept can be used as a unified concept to deal with the steady-state regulation of the linear interconnected discrete-time systems and of some classes of nonlinear interconnected systems with possible uncertainties in the presence of arbitrary unmeasured but bounded disturbances.
Keywords: discrete time, feedback, pseudoinversion, interconnected systems, optimality, stability, uncertainty.

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Received 17.02.2017

Issue 185, article 3


KVT, 2016, Issue 185, pp.21-34

UDC 681.5


Zhiteckii L.S., Pilchevsky A.Yu., Solovchuk K.Yu.

International Research and Training Center for Information Technologies and Systems of the National Academy of Science of Ukraine and Ministry of Education and Sciences of Ukraine, Kiev, Ukraine , ,

Introduction. The optimal digital autopilot needed to control of the roll for an aircraft in the presence of an arbitrary unmeasured disturbances is addressed in this paper. This autopilot has to achieve a desired lateral motion control via minimizing the upper bound on the absolute value of the difference between the given and true roll angles. It is ensured by means of the two digital controllers. The inner controller is designed as the discrete-time PI controller in order to stabilize a given roll rate. This variable is formed by the external discrete-time P controller. To optimize this control system, the controller parameters are derived utilizing the so-called l1-optimization approach advanced in modern control theory. The motion parameters are assumed to be known.

The purpose of the paper is to synthesize a digital autopilot which is able to maintain a given roll orientation of an aircraft with a desired accuracy and to cope with an arbitrary external disturbance (a gust) whose bounds may be unknown.

Results. The necessary and sufficient conditions guaranteeing the stability of the two-circuit feedback discrete-time control system are established. First, the l1-optimal PI and P controller parameters are calculated simultaneously (in contrast with [14]). Second, the aileron servo dynamics are taken into account to establish the stability condition for optimizing the controller parameters. Third, random search algorithm is used to calculate the three optimal values of the autopilot parameters. To support the theoretical results obtained, in this work, several simulation experiments were conducted. We have established that the simultaneous l1-optimization of both controllers was more efficient than the sequential l1-optimization of inner and external controllers.

Conclusion. It was established that the two-circuit l1-optimal PI and P control laws can cope with the wind gust and ensure the desired roll orientation. This makes it possible to achieve the control objective which was stated. A distinguishing feature of the control algorithms is that they are sufficiently simple. This is important from the practical point of view.

Keywords: aircraft, lateral dynamics, digital control system, discrete time, stability, l1-optimization, random search algorithm.

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Received 01.06.16

ISSUE 181, article 4


Kibern. vyčisl. teh., 2015, Issue 181, pp.

Zhiteckii L.S., Nikolaienko S.A., Solovchuk K.Yu.

International Research and Training Center for Information Technologies and Systems of the National Academy of Science of Ukraine and Ministry of Education and Sciences of Ukraine, Kiev, Ukraine


Introduction. The paper deals with studying the asymptotical properties of the standard discrete-time gradient online learning algorithm in the two-layer neural network model of the uncertain nonlinear system to be identified. Also, the design of the discrete-time adaptive closed-loop system containing the linear multivariable memoryless plant with possibly singular but unknown matrix gain in the presence of unmeasurable bounded disturbances having the unknown bounds are addressed in this paper. It is assumed that the learning process in the neural network model is implemented in the stochastic environment whereas the adaptation of the plant model in the control system is based on the non-stochastic description of the external environment.
The purpose of the paper is to establish the global convergence conditions of the gradient online learning algorithm in the neural network model by utilizing the probabilistic asymptotic analysis and to derive the convergent adaptive control algorithm guaranteeing the boundedness of the signals in the closed-loop system which contains the multivariable memoryless plant with an arbitrary matrix gain in the presence of unmeasurable disturbances whose bounds are unknown.
Results. The Lyapunov function approach as the suitable tool for analyzing the asymptotic behavior both of the gradient learning algorithm in the neural network identification systems and of the adaptive gradient algorithm in the certain closed-loop control systems is utilized. Within this approach, the two groups of global sufficient conditions guaranteeing the convergence of the online gradient learning algorithm in neural network model with probability 1 are obtained. The first group of these conditions defines the requirements under which this algorithm will be convergent almost sure with a constant learning rate. Such an asymptotic property holds in the ideal case where the nonlinearity to be identified can exactly be described by a neural network model. The second group of convergence conditions shows that this property can also be achieved in non-ideal case. It turns out that adding a penalty term to the current error function is indeed not necessary to guarantee this property. It is established that in a worst case where the matrix gain of multivariable plant is unknown and may be singular, and the bounds on the arbitrary unmeasurable disturbances remain unknown, the convergence of the gradient adaptation algorithm and the boundedness of all signals in the adaptive closed-loop system can be ensured.
Conclusions. In order to guarantee the global convergence of the online learning algorithm in the neural network identification system with probability 1, the certain conditions should be satisfied. Also the boundedness of all signals in the closed-loop adaptive control system containing the multivariable memoryless plant whose matrix gain is unknown and possibly singular can be achieved even if the bounds on the unmeasurable disturbances are unknown.

Keywords: neural network, gradient learning algorithm, convergence, multivariable memoryless plant, adaptive control algorithm, boundedness of the signals.

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Received 06.07.2015