Optimization of ship dynamic systems and technological processes in water transport using symbolic computing in MATLAB

The study aims to increase the efficiency and accuracy of solving optimal control problems for ship dynamic systems and technological processes in water transport under conditions of digital transformation using symbolic computing tools. The paper addresses the problem of optimal control of a nonlinear dynamic object by representing the system in symbolic mathematical form. The proposed computational algorithm provides an analytical solution of differential equations through linearization and integration in a standard matrix representation. Using the Hamiltonian approach, which ensures the transition from functional minimization to static optimization, a control vector is derived and the system of equations is transformed into symbolic form. Taking into account the syntax of symbolic functions, an analytical block describing system dynamics is identified, and a solver is constructed that includes the system dynamics and boundary conditions for state variables at the initial and final moments of the solution interval. As a result, equations for state and control variables are obtained, which can subsequently be converted into numerical form for quantitative evaluation and graphical interpretation. Using MATLAB programs, estimates of four boundary conditions are obtained and presented graphically. The proposed algorithmic solution of the boundary value problem differs from existing approaches by employing an analytical model expressed in symbolic terms. A discrete analogue of the model is obtained on the basis of the A. N. Krylov matrix with norm estimation and control representation in CVX format. The results confirm the correctness of the developed algorithms and software and demonstrate the expediency of combining analytical and numerical methods for modeling and optimization of dynamic systems.