Abstract
The aim of this paper is to determine the feedforward and state feedback suboptimal time control for a subset of bilinear systems, namely, the control sequence and reaching time. This paper proposes a method that uses Block pulse functions as an orthogonal base. The bilinear system is projected along that base. The mathematical integration is transformed into a product of matrices. An algebraic system of equations is obtained. This system together with specified constraints is treated as an optimization problem. The parameters to determine are the final time, the control sequence, and the states trajectories. The obtained results via the newly proposed method are compared to known analytical solutions.
Highlights
Most engineering applications are aimed at solving complex mathematical models
Two examples of bilinear systems are presented to evaluate the effectiveness of our developed approach
The system needs to be shifted from x0 = 1 to the origin; the input u must be within interval [−1, 1]
Summary
Most engineering applications are aimed at solving complex mathematical models This usually comes with a computational burden and is of a major concern. Using Pontryagin maximum principle, the solution to this problem is known to be Bang-Bang, that is, control values switches between lower and upper boundaries This type of control is required in some types of systems such as the thermostat switching between the on- and off-position. Time optimal control problems’ aim is driving systems from an initial state to a desired final state in minimum time while satisfying given constraints. To this day, time optimal control problem still attracts interest among researchers [1,2,3]
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