Optimal Control of Mechanical Systems

Abstract

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.

VISUAL MISER: An efficient user-friendly visual program for solving optimal control problems

“…With the advances of modern computers and the increasing emphasis on optimal design of large scale dynamical systems under scarce availability of resources, optimal control theory has become a useful tool for solving many engineering, industrial and management problems. For a brief selection, see [1,2,3,4,5,7,9,10,11,14,17,18,27,28,29,30,31,32,33,34,35,37,41,44,45,50,53,63,64,65,66]. The main theoretical tools for solving optimal control problems analytically are the famous Pontryagin's minimum principle [1,2,8,52] and the Hamilton-Jacobi-Bellman equation [4,59].…”

Self-Learning Variable Structure Control for a Class of Sensor-Actuator Systems

“…For Euler-lagrange system without nonholonomic constraints, the dimension of inputs are often equal to the dimension of output and the system are often able to be transformed into a double integrator system by employing feedback linearization [ 12 ]. Other methods, such as control Lyapunov function method [ 13 ], passivity based method [ 14 ], optimal control method [ 15 ], etc., are also successfully applied to the control of Euler-lagrange system without nonholonomic constraints. In contrast, as the dimension of inputs is lower than that of outputs, it is often impossible to directly transform the Euler-lagrange system subject to nonholonomic constraints to a linear system and thus feedback linearization fails to stabilize the system.…”