ABSTRACT
Mixed constraints imposed on both state and control variables of a dynamical system, as well as integral constraints imposed on the variables, are often present in applications. Energy and heat restrictions are usually reduced to integral constraints. All these constraints are essential for robots controlled by electric actuators. In this chapter, the author extends the well-known Kalman’s method originally developed for linear systems without control constraints to systems subject to mixed, state, and integral constraints. In Kalman’s approach, the open-loop control is formed as a linear combination of the natural modes of the system. The author derives sufficient controllability conditions which ensure that the obtained control satisfies all imposed constraints and brings our system to the prescribed terminal state in finite time. The proposed technique is applied to a dynamical system of the fourth order which is a model for mechanical systems controlled by electric drives.
