Mechanical Control Problems Research Articles

An approach to controlled mechanical systems based on the multiobjective optimization technique

This paper discusses the multiobjective optimization techniques for a class of optimal control problems in mechanics. We deal with constrained nonlinear control systems described by the Euler-Lagrange or Hamilton equations and study the variational structure of the solution of the corresponding boundary-value problems. We also reduce the original ''mechanical'' problem to an auxiliary multiobjective optimization problem. This approach makes it possible to apply the effective theoretical and computational results from multiobjective programming to the original problem. We consider first order computational schemes for optimal control problems governed by mechanical systems and examine some illustrative examples.

Optimal Control of Mechanical Systems

In the present work, we consider a class of nonlinear optimal control problems, which can be called “optimal control problems in mechanics.” We deal with control systems whose dynamics can be described by a system of Euler‐Lagrange or Hamilton equations. Using the variational structure of the solution of the corresponding boundary‐value problems, we reduce the initial optimal control problem to an auxiliary problem of multiobjective programming. This technique makes it possible to apply some consistent numerical approximations of a multiobjective optimization problem to the initial optimal control problem. For solving the auxiliary problem, we propose an implementable numerical algorithm.

Dynamics and control of mechanical systems in partly specified motion

The paper presents a systematic formulation for the dynamic analysis and synthesis of control of mechanical systems in partly specified motion. The motion specifications are modelled as program constraints on a controlled system, and the control that ensure their realization is determined. It is shown that program constraints may be realized by tangent control reactions with respect to the program constraint manifold, and this yields a very specific structure of the governing equations of the problem. The equations arise as DAEs, and the index of the DAEs may considerably exceed three. Index five and index 2n + 1 DAEs that describe control problems in mechanics are reported as illustrations. A method for analyzing the system motion consistent with the constraints and, based on the solution, synthesizing the program control is developed and applied to solve the mentioned case studies.

Structure of differential-algebraic equations for control problems in mechanics

A problem of control of a mechanical system in a partly specified motion is studied. It is shown that the structure of differential-algebraic equations (DAEs) describing the problem may essentially differ from the structure of governing equations for a constrained mechanical system. The control forces chosen to realize the program constraints may have arbitrary directions with respect to the constraint manifold, and, in the extreme, they may be tangent. Thus, the index of the original DAEs of the problem may exceed three and a special approach to the problem solution has to be undertaken. Such an approach is proposed; a systematic formulation is given for the transformation of the DAEs into index-one DAEs or ODEs. Criteria for solvability of the problem are included.