Uniform optimization method for nonlinear control systems with distributed parameters

È. Ya. Rapoport

Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, Tome 27 (2023) no. 2, pp. 270-291

Résumé

The problem of optimization of a nonlinear controlled system with distributed parameters, and uniformly estimated target sets is reduced to controlling a linear model of the object. This linear model incorporates an additional, a priori unknown spatiotemporal disturbance that compensates for the influence of discrepancies between the linear and nonlinear differential operators in the corresponding initial-boundary value problems. Partial differential equations of the parabolic type describe these problems. The specific form of the disturbance’s dependence on its arguments is identified based on the initial approximation at each step of the proposed convergent iterative procedure. This procedure is based on the results obtained in the previous step from solving the linear-quadratic programming optimal control problem using the developed alternance method. This problem includes a deterministic external input and requires the intermediate computation of the controlled state function of the nonlinear object using a digital model. It has been shown that the desired equations for the optimal regulators can be obtained from the known results of the iterative process used to find the program control. The control is represented as linear feedback algorithms based on the measured state of the object, which uses nonstationary transfer coefficients.

Détail

Keywords: nonlinear system with distributed parameters, linear-quadratic optimization problem, iterative procedure, alternance method, parameterization of control actions, software optimal control, optimal control synthesis.