We will study one-parameter families .Pu s /s∈[Þ;þ] of differentiable optimal control problems given by: P .s/  MinI u.s; x/ := ∫ b a L.s; t; x.t/; u.s; t// dt; where ẋ = F.s; t; x; u/ .t ∈ [a; b]/ H .s; t; x; u/ = 0 .t ∈ {t1 0 ; : : : ; t 0 }/ G.s; t; x; u; y/ ≥ 0; .y ∈ Y 1.s; t; x; u/; t ∈ [a; b]/ H b a .s; a; x.a/; u.s; a/; b; x.b/; u.s; b// = 0 Gb a.s; a; x.a/; u.s; a/; b...

In this article we use geometric optimal control to completely solve the problem of minimum-time transitions between thermal equilibrium and fixed average energy states of the quantum parametric oscillator, a system which has been extensively used to model quantum heat engines and refrigerators. We subsequently use the obtained results to find the minimum driving time for a quantum refrigerator...

Straight elastically supported beams of variable width under the action of a periodic axial force are considered. Two shape optimization problems for reducing parametric resonance zones are studied. In the first problem, the range of resonant frequencies is minimized for a given parametric resonance zone and a fixed amplitude of excitation. In the second problem, the minimal (critical) amplitud...

A methodology for combining multi-parametric programming and NCO tracking is presented in the case of linear dynamic systems. The resulting parametric controllers consist of (potentially nonlinear) feedback laws for tracking optimality conditions by exploiting the underlying optimal control switching structure. Compared to the classical multi-parametric MPC controller, this approach leads to a ...

This article presents a parametric approach to the optimal nonlinear control problem. This contribution is based on reducing the nonlinear optimal control problem to a sequence of linear time-varying ones and approaching the desired optimal control by a sequence of linear algebraic equations. This approach provides a solution which can be obtained in a simpler way than the usual one. Alternativ...

Methods of simplifying optimal control problems by decreasing the dimension space states are considered. For this purpose, transition to new phase coordinates or conversion class controls is used. The heat exchange and parametric oscillators given as examples: braking/swinging a pendulum changing length suspension variation energy molecules’ oscillations in crystal lattice state medium (exposur...