Decomposition Solution of Open-Loop 'Cheap' Control Problem

1993 ◽  
Author(s):  
S.X. Shen ◽  
V.G. Gourishankar ◽  
Q. Xia ◽  
M. Rao
Keyword(s):  
Control Problem ◽  
Open Loop ◽  
Cheap Control

Adjoint-Based Optimization Procedure for Active Vibration Control of Nonlinear Mechanical Systems

2017 ◽  
Vol 139 (8) ◽  
Author(s):  
Carmine M. Pappalardo ◽  
Domenico Guida
Keyword(s):  
Optimal Control ◽  
Control Theory ◽  
Control Problem ◽  
Numerical Solution ◽  
Optimal Control Theory ◽  
Numerical Procedure ◽  
Nonlinear Optimal Control ◽  
Open Loop ◽  
Adjoint Equations ◽  
Loop Control

In this paper, a new computational algorithm for the numerical solution of the adjoint equations for the nonlinear optimal control problem is introduced. To this end, the main features of the optimal control theory are briefly reviewed and effectively employed to derive the adjoint equations for the active control of a mechanical system forced by external excitations. A general nonlinear formulation of the cost functional is assumed, and a feedforward (open-loop) control scheme is considered in the analytical structure of the control architecture. By doing so, the adjoint equations resulting from the optimal control theory enter into the formulation of a nonlinear differential-algebraic two-point boundary value problem, which mathematically describes the solution of the motion control problem under consideration. For the numerical solution of the problem at hand, an adjoint-based control optimization computational procedure is developed in this work to effectively and efficiently compute a nonlinear optimal control policy. A numerical example is provided in the paper to show the principal analytical aspects of the adjoint method. In particular, the feasibility and the effectiveness of the proposed adjoint-based numerical procedure are demonstrated for the reduction of the mechanical vibrations of a nonlinear two degrees-of-freedom dynamical system.

scholarly journals Algorithm for solving optimal open-loop terminal control problem for spacecraft rendezvous with account of constraints on the state

2021 ◽  
Vol 20 (1) ◽  
pp. 46-64
Author(s):  
A. F. Shorikov ◽  
A. Yu. Goranov
Keyword(s):  
Control Problem ◽  
Nonlinear Differential Equations ◽  
Center Of Mass ◽  
Algebraic Method ◽  
Open Loop ◽  
Geometric Constraints ◽  
Linear Recurrence ◽  
Terminal Control ◽  
Finite Dimensional Vector Space ◽  
Maneuvering Spacecraft

The paper proposes an algorithm for solving the optimal open-loop terminal control problem of two spacecraft rendezvous with constraints on their states. A system of nonlinear differential equations that describes the dynamics of the active (maneuvering) spacecraft relative to the passive spacecraft (station) in the central gravitational field of the Earth in the orbital coordinate system of coordinates related to the passive spacecraft center-of-mass is considered as an initial model. The obtained nonlinear model of the active spacecraft dynamics is linearized relative to the specified reference state trajectory of the passive spacecraft, and then it is discretized and reduced to linear recurrence relations. Mathematical formalization of the spacecraft rendezvous problem under consideration is carried out at a specified final moment of time for the obtained discrete-time controlled dynamical system. The quality of solving the problem is estimated by a convex functional taking into account the geometric constraints on the active spacecraft states and the associated control actions in the form of convex polyhedral-compacts in the appropriate finite dimensional vector space. We propose a solution of the problem of optimal terminal control over the approach of the active spacecraft relative to the passive spacecraft in the form of a constructive algorithm on the basis of the general recursive algebraic method for constructing the availability domains of linear discrete controlled dynamic systems, taking into account specified conditions and constraints, as well as using the methods of direct and inverse constructions. In the final part of the paper, the computer modeling results are presented and conclusions about the effectiveness of the proposed algorithm are made.

scholarly journals Prospects on Solving an Optimal Control Problem with Bounded Uncertainties on Parameters using Interval Arithmetics

2021 ◽  
Author(s):  
Etienne Bertin ◽  
Elliot Brendel ◽  
Bruno Hérissé ◽  
Julien Alexandre dit Sandretto ◽  
Alexandre Chapoutot
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Closed Loop ◽  
Minimum Principle ◽  
Open Loop ◽  
Pontryagin Minimum Principle ◽  
Interval Method ◽  
Bounded Uncertainties ◽  
The Given

An interval method based on the Pontryagin Minimum Principle is proposed to enclose the solutions of an optimal control problem with embedded bounded uncertainties. This method is used to compute an enclosure of all optimal trajectories of the problem, as well as open loop and closed loop enclosures meant to enclose a concrete system using an optimal control regulator with inaccurate knowledge of the parameters. The differences in geometry of these enclosures are exposed, as well as some applications. For instance guaranteeing that the given optimal control problem will yield a satisfactory trajectory for any realization of the uncertainties or on the contrary that the problem is unsuitable and needs to be adjusted.

Coordination Concepts in Multilevel Hierarchical Differential Games

1977 ◽  
Vol 99 (3) ◽  
pp. 201-208 ◽  
Author(s):  
Guy Jumarie
Keyword(s):  
Game Theory ◽  
Control Problem ◽  
Control Systems ◽  
Coordination Mode ◽  
Closed Loop ◽  
Open Loop ◽  
Optimum Control ◽  
Differential Game Theory ◽  
Self Learning ◽  
Optimum Control Problem

This paper presents possible extensions of the usual differential game theory to the case where the players, say the supremal players do not completely govern the plant, but control it only via infimal players who have their own pay-off functions. One assumes that the internal structure of the game is given in the sense that the supremal players cannot define arbitrary decompositions for the system. One further assumes that these supremal players have given programming terminal objectives which they desire to attain. In this framework, the supremal players can only select suitable functions, which are the coordination controls, to coordinate the system for the best. It follows that the problem so defined is simultaneously an optimum control problem and a programming one. The direct coordination mode, the open-loop indirect coordination mode and the closed-loop indirect coordination mode are defined and are mainly based upon a direct reference to the overall system, together with a two-level optimization process. The explicit equations are given in the important case where the comparison criterion is defined in the form of an Euclidean norm, and an illustrative example is solved. This approach would be interesting to apply to the problem of learning and self-learning in optimum control systems for instance, via gradient techniques.

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