A method for constructing an optimal control strategy in a linear terminal problem

This paper deals with an optimal control problem for a linear discrete system subject to unknown bounded disturbances, where the control goal is to steer the system with guarantees into a given terminal set while minimising the terminal cost function. We define an optimal control strategy which takes into account the state of the system at one future time instant and propose an efficient numerical method for its construction. The results of numerical experiments show an improvement in performance under the optimal control strategy in comparison to the optimal open-loop worst-case control while maintaining comparable computation times.

CONTROLLABILITY OF A LINEAR DISCRETE SYSTEM WITH CHANGE OF THE STATE VECTOR DIMENSION

The paper proposes an analysis of controllability of a linear discrete system with change of the state vector dimension. We offer necessary and sufficient conditions of controllability and design the control that guarantees the decision of a problem of moving of such system to an arbitrary final state. It provides functional stability of technological processes described by a linear discrete system with change of the state vector dimension.

Newton’s iterative formula for finding an equation solution as an abstract problem of the modal synthesis theory

A new approach to obtain an iterative Newton formula for finding an equation solution, by using modal control theory for linear discrete systems when solving problems of observation or identification is presented. The decomposition method as a modal control method, which allows obtaining analytical solutions, is used. Keywords Newton’s iterative formula; numerical solution of the equation; decomposition method of modal synthesis; linear discrete system

A closed-loop strategy in an optimal guaranteed control problem for a linear system

This paper deals with an optimal control problem for a linear discrete system subject to unknown bounded disturbances with the control goal being to steer the system with guarantees to a given target set while minimizing a given cost function. We define an optimal control strategy with one correction time instant, meaning taking into account information about one future state of the object, and propose an efficient numerical method for constructing it.

On a Decomposition Method in the Problem of Operation Speed for a Linear Discrete System with Bounded Control

The article presents the problem of operation speed for a linear discrete system with bounded control. For the case when the minimum number of steps necessary for the system to reach zero significantly exceeds the dimension of the phase space, a method of decomposition into scalar and two-dimensional subsystems is developed, based on the reduction of the state matrix to normal Jordan form. Moreover, due to the developed algorithm for adding two polyhedrons with linear complexity, it is possible to construct sets of 0-controllability for two-dimensional subsystems in an explicit form. A description of the main tools for solving the problem of operation speed is also presented, as well as the statement of the decomposition problem. Further, some properties of polyhedrons in the plane are formulated and proved, on the basis of which an algorithm for calculating the set of vertices of the sum of two polyhedrons in R2 in explicit form is developed. In conclusion, the main decomposition theorem is formulated and proved. And on the basis of the developed methods, the solution to the problem of the optimal damping speed of a high-rise structure located in the zone of seismic activity was constructed.