Algorithms of Optimization of Linear and Non-Linear Systems

Габасов, Р.; Glushenkov, V.S.; Кириллова, Ф. М.; Pokatayev, A.V.; Senko, A.A.; Tyatyushkin, A. I.

doi:10.1016/b978-0-08-029352-3.50053-2

Cited by 2 publications

(7 citation statements)

References 2 publications

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“…Its solution satisfies the linear system of algebraic equations (11) With the help of the solution to system (11) and α k = 1 -, the desired point on the plane is easily …”

Section: Convex Hull Methodmentioning

confidence: 99%

“…In [11] various adaptive methods for solving the general LP problem with interval constraints are con sidered and a detailed description is presented for algorithms intended for solving typical control problems with a large number of variables or inequality constraints to which control problems with state constraints are reduced. The multimethod technique as applied to finding their numerical solutions is also discussed.…”

Section: Solution Of Linear Problems With State Constraintsmentioning

confidence: 99%

“…When applied to the general prob lem with state constraints, this approach is associated with high computational costs caused by the neces sity of computing gradients at every time. Below, a method is described that reduces the linear problem with state constraints to a large scale LP problem, which is solved using special algorithms [11] that take into account the specific features of constrained LP problems.…”

Section: Solution Of Linear Problems With State Constraintsmentioning

confidence: 99%

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Numerical methods for control optimization in linear systems

Tyatyushkin

2015

Comput. Math. and Math. Phys.

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Numerical methods are considered for solving optimal control problems in linear systems, namely, terminal control problems with control and phase constraints and time optimal control prob lems. Several algorithms with various computer storage requirements are proposed for solving these problems. The algorithms are intended for finding an optimal control in linear systems having certain features, for example, when the reachable set of a system has flat faces.

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“…Its solution satisfies the linear system of algebraic equations (11) With the help of the solution to system (11) and α k = 1 -, the desired point on the plane is easily …”

Section: Convex Hull Methodmentioning

confidence: 99%

Section: Solution Of Linear Problems With State Constraintsmentioning

confidence: 99%

Section: Solution Of Linear Problems With State Constraintsmentioning

confidence: 99%

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Numerical methods for control optimization in linear systems

Tyatyushkin

2015

Comput. Math. and Math. Phys.

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“…In particular, the supporting control approach [10] can be used to produce the differential equations for the switching time functions τ (s, z) necessary to design the optimal controllers. In a similar manner to [6] it can be shown that these satisfy the following differential equations:…”

Section: I(y V W) I(y V W)mentioning

confidence: 99%

“…Now by using (6) we can rewrite the optimal problem considered here in the following integral form: (10) subject to the terminal conditions (4) and the control constraint (5). Also we can write …”

mentioning

confidence: 99%

Constrained Optimal Control Theory for Differential Linear Repetitive Processes

Dymkov

Rogers

Dymkou

et al. 2008

SIAM J. Control Optim.

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Abstract. Differential repetitive processes are a distinct class of continuous-discrete twodimensional linear systems of both systems theoretic and applications interest. These processes complete a series of sweeps termed passes through a set of dynamics defined over a finite duration known as the pass length, and once the end is reached the process is reset to its starting position before the next pass begins. Moreover the output or pass profile produced on each pass explicitly contributes to the dynamics of the next one. Applications areas include iterative learning control and iterative solution algorithms, for classes of dynamic nonlinear optimal control problems based on the maximum principle, and the modeling of numerous industrial processes such as metal rolling, long-wall cutting, etc. In this paper we develop substantial new results on optimal control of these processes in the presence of constraints where the cost function and constraints are motivated by practical application of iterative learning control to robotic manipulators and other electromechanical systems. The analysis is based on generalizing the well-known maximum and -maximum principles to them.Key words. two-dimensional systems, optimal control, constraints AMS subject classifications. 93C05, 93C15 DOI. 10.1137/060668298 1. Introduction. Repetitive processes are a distinct class of two-dimensional (2D) systems of both systems theoretic and applications interest. The unique characteristic of such a process is a series of sweeps, termed passes, through a set of dynamics defined over a fixed finite duration known as the pass length. On each pass an output, termed the pass profile, is produced which acts as a forcing function on, and hence contributes to, the dynamics of the next pass profile. This, in turn, leads to the unique control problem in that the output sequence of pass profiles generated can contain oscillations which increase in amplitude in the pass-to-pass direction.To introduce a formal definition, let α < +∞ denote the pass length (assumed constant). Then in a repetitive process the pass profile y k (t), 0 ≤ t ≤ α, generated on pass k acts as a forcing function on, and hence contributes to, the dynamics of the next pass profile y k+1 (t), 0 ≤ t ≤ α, k ≥ 0.Physical examples of repetitive processes include long-wall coal cutting and metalrolling operations (see, for example, the references cited in [17]). Also in recent years applications have arisen where adopting a repetitive process setting for analysis has distinct advantages over alternatives. Examples of these so-called algorithmic applications include classes of iterative learning control (ILC) schemes (see, for example, [13]) and iterative algorithms for solving nonlinear dynamic optimal control problems based on the maximum principle [15]. In the case of iterative learning control for the linear

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Algorithms of Optimization of Linear and Non-Linear Systems

Cited by 2 publications

References 2 publications

Numerical methods for control optimization in linear systems

Numerical methods for control optimization in linear systems

Constrained Optimal Control Theory for Differential Linear Repetitive Processes

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