In this paper necessary and sufficient conditions are given which guarantee that there exists a realization of a set of nonlinear higher order differential input-output equations in the controller canonical form.Two cases are studied, corresponding respectively to linear and nonlinear output functions.The conditions are formulated in terms of certain sequence of vector spaces of differential 1-forms.The proofs suggest how to construct the transformations, necessary to obtain the specific state space realizations.Multiple examples are added, which describe different scenarios.

In this paper, we propose a new impulsive predator prey model with impulsive control at different fixed moments and analyze its interesting dynamic behaviors.Sufficient conditions for the globally asymptotical stability of the semi-trivial periodic solution and the permanence of the present model are obtained by Floquet theory of impulsive differential equation and small amplitude perturbation skills.Existences of the "infection-free" periodic solution and the "predator-free" solution are analyzed by bifurcation theory of impulsive differential equation.Finally, the analytical results presented in the work are validated by numerical simulation figures for this proposed model.

Complex dynamic regimes connected with the noise-induced mixed-mode oscillations in the thermochemical model of flow reactor are studied. It is revealed that the underlying reason of such excitability is in the high stochastic sensitivity of the equilibrium. The problem of stabilization of the excitable equilibrium regimes is investigated. We develop the control approach using feedback regulators which reduce the stochastic sensitivity and keep the randomly forced system near the stable equilibrium. We consider also a case when the information about system state is incomplete. Our new mathematical technique is applied to the stabilization of operating modes in the flow chemical reactors forced by random disturbances.

This article proposes a decentralized navigation controller for a group of differential mobile robots that yields autonomous navigation, which allows reaching a certain desired position with a specific desired orientation, while avoiding collisions with dynamic and static obstacles.The navigation controller is constituted by two control loops, the so-called external control loop is based on crowd dynamics, it brings autonomous navigation properties to the system, the internal control loop transforms the acceleration and velocity references, given by the external loop, into the driving translational and rotational control actions to command the robots.The controller physical application could be based on several onboard sensors information, in such a way that the control strategy can be programmed individually into a group of mobile robots, this allows a decentralized performance, rendering the crowd dynamics behavior.Each mobile robot is considered as an agent to which it is associated a comfort zone with a certain radius, that produces a repulsive force when it is trespassed by its environment or by another agent, this yields the necessary response to avoid collisions.Meanwhile, attractive forces drive the agents from their instantaneous position to the desired one.For collision-free navigation, Lyapunov stability method allows obtaining the stability conditions of the proposed controller and guarantees asymptotic convergence to the desired position and orientation.The navigation controller is tested by simulations, which supports the stability and convergence theoretical results.

The article is devoted to Markov reward chains in discrete-time setting with finite state spaces. Unfortunately, the usual optimization criteria examined in the literature on Markov decision chains, such as a total discounted, total reward up to reaching some specific state (called the first passage models) or mean (average) reward optimality, may be quite insufficient to characterize the problem from the point of a decision maker. To this end it seems that it may be preferable if not necessary to select more sophisticated criteria that also reflect variability-risk features of the problem. Perhaps the best known approaches stem from the classical work of Markowitz on mean variance selection rules, i. e. we optimize the weighted sum of average or total reward and its variance. The article presents explicit formulae for calculating the variances for transient and discounted models (where the value of the discount factor depends on the current state and action taken) for finite and infinite time horizon. The same result is presented for the long run average nondiscounted models where finding stationary policies minimizing the average variance in the class of policies with a given long run average reward is discussed.

This paper constructs and analyses a model for optimal production and emission covering of a real-life European steel company. The emissions may be covered by a combination of EUA and CER allowances and their derivatives. The company is assumed to be risk-averse, maximizing the Mean-CVaR criterion. The problem is analysed given continuum of risk-aversion coefficients and three scenarios of the demand. It is found that the production does not depend on the risk aversion and is always maximal, but the optimal composition of the (spot) allowances and their derivatives depends non-trivially on both the risk aversion and the demand. Out of all the derivatives, only futures are used. Surprisingly, options are never used.

This paper deals with a multistage stochastic programming portfolio selection problem with a new type of risk premium constraints.These risk premiums are constructed on the multistage scenario tree.Two ways of the construction are introduced and compared.The risk premiums are incorporated in the multistage stochastic programming portfolio selection problem.The problem maximizes the multivariate (multiperiod) utility function under condition that the multistage risk premiums are smaller than a prescribed level.The problem does not assume any separability of the multiperiod utility function.The performance of the suggested models is demonstrated for several kinds of multiperiod utility functions and several formulations of the multistage risk premium constraints.In all cases, including the risk premium constraints avoids the riskier positions.

Contrary to state space systems, there are different notions of controllability for linear time invariant descriptor systems due to the non smooth inputs and inconsistent initial conditions.A comprehensive study of different notions of controllability for linear descriptor systems is performed.Also, it is proved that reachable controllability for general linear time invariant descriptor system is equivalent to the controllability of some matrix pair under an assumption milder than impulse controllability.The whole theory has been developed by coining two new decompositions for system matrices.Examples are given to illustrate the presented theory.

In this paper, we discuss the distributed design for binary classification based on the nonlinear support vector machine in a time-varying multi-agent network when the training data sets are distributedly located and unavailable to all agents. In particular, the aim is to find a global large margin classifier and then enable each agent to classify any new input data into one of the two labels in the binary classification without sharing its all local data with other agents. We formulate the support vector machine problem into a distributed optimization problem in approximation and employ a distributed algorithm in a time-varying network to solve it. Our algorithm is a stochastic one with the high convergence rate and the low communication cost. With the jointly-connected connectivity condition, we analyze the consensus rate and the convergence rate of the given algorithm. Then some experimental results on various classification training data sets are also provided to illustrate the effectiveness of the given algorithm.

The paper presents fractional-order semilinear, continuous, finite-dimensional dynamical systems with multiple delays both in controls and nonlinear function $f$. The constrained relative controllability of the presented semilinear system and corresponding linear one are discussed. New criteria of constrained relative controllability for the fractional semilinear systems with delays under assumptions put on the control values are established and proved. The conical type constraints are considered. The results are illustrated by an example.