Suboptimal Control of Nonlinear Dynamic System with Unlimited Transition Process Time

Abstract

Abstract In this paper, we consider the issue of synthesizing optimal control of nonlinear dynamic systems in case of a problem with an unspecified time of the transition process. To solve this problem, an algorithmic method for constructing a suboptimal control is suggested. The basis of this method is the behavior of the Hamiltonian on the optimal trajectory, which corresponds to the required condition of the optimal system. For the synthesis of suboptimal control, the original nonlinear model is replaced by an equivalent model with a linear structure with state-dependent parameters. The use of the quadratic quality functional allows to make the transition from solving the Hamilton-Jacobi-Bellman equation to the Riccati-type equation with state-dependent parameters. A computer simulation of a simple nonlinear system, for which the Riccati equation with state-dependent parameters can be solved, has been carried out. Also, for this system a suboptimal control was created with the use of a new algorithmic parametric optimization method. The simulation results confirm the effectiveness of the method. In addition, the constructed suboptimal control is close to the control obtained by solving the Riccati equation.