Synthesis of Optimal Discrete Control System

Optimal control of a rectilinear motion of a rocket

“…However, when the problem is difficult, direct discretization methods can be used for finding an approximate solution. In [15], the Cauchy formula for solving systems of linear differential equations is used to transform the linear optimal control problem into an equivalent problem, then discretization is performed to get a linear programming problem which is solved using the adaptive method. Recently in [16], the Cauchy formula is used with discretization to transform the original linear optimal control problem into a linear optimization problem which is solved with the hybrid direction algorithm proposed in [17].…”

Synthesis of Optimal Feedbacks for Linear Systems Under State Constraints

“…It is based on the fast algorithm of solving a linear OC problem with intermediate state constrained (Balashevich et al, 2001). Methodologically, the suggested implementation of optimal closed-loop control develops the approach (Gabasov et al, 1995;Gabasov et al, 2000). According to this approach, before starting the actual control process preliminary work to form the framework of the solution is performed, and then in the course of the control process preliminary results are getting more precise on the basis of the realized states.…”

Optimal Control of Non-stationary Differential Linear Repetitive Processes

“…Proof. Using Lemma 4.1 this reduces to a slight modification of the results in [3,5], and hence the details are again omitted here. Remark 4.3.…”

“…This is based on the so-called C-property of measurable functions [9] and, in fact, follows immediately on some routine modifications to that for continuous functions given in [5]. Hence the details are omitted here.…”

“…In particular, it is well known that the separation theorem, see e.g. [5] for convex sets is a useful method for studying a wide area of optimization problems and here we apply this method to establish optimality conditions in the form of the maximum principle for a differential non-stationary (in the along the pass direction) repetitive process with linear state dynamics and an additive nonlinear term to account for bounds on the available control input signal due, for example, to limited available control action. As motivation for this work, we next give a brief description of an optimal control problem in iterative learning control analysis and design.…”