A discrete-time linear system with second-order integral control constraints is considered. The properties of the limit reachable and null-controllable sets of the system are investigated. Necessary and sufficient conditions for the boundedness of these sets are obtained, including for uncontrollable systems. It is proved that these sets are ellipsoids, when they are bounded, and their support function is constructed explicitly. Numerical simulations are performed.

This paper considers the problem of minimum-energy control of a linear singularly perturbed system with three groups of variables changing at significantly different rates. Asymptotic approximations to the solution of this problem are constructed in the form of open-loop control and feedback control. The main advantage is that the proposed computational procedures decompose the original problem into three unperturbed optimal control problems of lower dimension.

The problem of prescribed performance control under given constraints on the amplitude and rate of control signal is considered for dynamic systems with relative degree one in the presence of parametric uncertainty and external disturbances. Using the ideas of feedback design based on sat-function differentiable approximation and augmented perturbation estimation, a novel nonlinear robust control law is proposed, which, if the parameters are suitably chosen, provides a solution to the problem under consideration. The parameter calculation procedure is reduced to solving linear inequalities, which feasibility is proved analytically. Illustrative example corroborates theoretical results.

This paper considers the problem of fault accommodation in complex safety-critical discrete-event systems described by the fuzzy finite state automaton model. The problem is solved by forming control that ensures complete decoupling from fault-induced effects. The fault-tolerant control scheme contains several channels activated depending on the diagnosed fault. Each channel includes two main blocks: 1) an auxiliary deterministic finite state automaton (observer) estimating the fuzzy vector of possibilities of system transitions to various states and 2) a converter forming the input of the controlled system based on a new external input and the observer state. An integrated approach (the pair algebra of fuzzy coverings) is proposed to describe the blocks and the new input. A distinctive feature of this approach is the joint use of mathematical constructs of the pair algebra of coverings (system of sets) and fuzzy logic.

The problem of protecting a moving target from an attack by multiple pursuing attackers using an interceptor defender is considered. A rigorous mathematical formulation of the problem is presented, quality criteria for defense plans are introduced, and mathematical properties of the problem are formulated. Based on these properties, heuristic rules and algorithms for their application are proposed in order to construct suboptimal solutions.