Optimal Control of Non-stationary Differential Linear Repetitive Processes

Abstract

Abstract. Differential repetitive processes are a distinct class of continuousdiscrete 2D linear systems of both systems theoretic and applications interest. The feature which makes them distinct from other classes of such systems is the fact that information propagation in one of the two independent directions only occurs over a finite interval. 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 modelling of numerous industrial processes such as metal rolling, and long-wall cutting etc. The new results in is paper solve a general optimal problem in the presence of non-stationary dynamics.

Repetitive models in gas transportation networks

“…In accordance with [6] for the optimal control u 0 = {u 0 k (t), k ∈ K, t ∈ T } of the problem (25) -(28) the number δ 0 = J(u 0 ) is the smallest root of the equation Λ(δ) = 0 and u 0 = arg min u∈U (·)…”

“…Next we present optimality conditions for the processes described by (25) -(28). The solvability conditions and some properties of the optimization problem were studied in [6], also.…”

“…For a representative survey of these see, for example, [5]. The main elements of the theory of constructive optimization for the repetitive processes were developed in [6], [7]. Some aspects of control theory for multidimensional systems are investigated in [8], [9] and application of it to gas networks have been considered in [10].…”

Repetitive and 2-D systems theory approach for modeling in gas networks

“…In this paper the mathematical model and corresponding optimization problem of gas network units are introduced on the basis of the so-called repetitive processes [2] and the 2-D system theory setting [3], which is a starting point for the further investigation of complex networks and which provide a fairly well-established mathematical framework. Some aspects of control theory for multidimensional systems are investigated in [4,5] and application of it to gas networks have been considered in [6]. In this paper we develop substantial new results on optimal control of differential linear repetitive processes with constraints which we motivate from the introduced linearization gas pipeline model in the presence of constraints The analysis is based on generalizing the well known maximum and ε -maximum principles.…”

Modeling and control of a sorption process using 2D systems theory

“…Hence these processes fit under i) and ii) above as appropriate. Systems theory for these processes is well developed [2], [10], [11] and they do have applications areas such as iterative learning control where recently control laws have been experimentally validated on a gantry robot [12].…”