Synthesis of ship systems optimal regulators based on matrix inequalities

Abstract

The output and state regulators synthesis for ship control systems based on linear matrix inequalities using the CVX software package for solving optimization problems by the method of semi-definite programming is considered. Estimates parameters for regulators providing asymptotically stable systems regimes on Lyapunov inequalities solutions sets are obtained. An algorithm for controlling the ship course using a robust regulator in state feedback, followed by the use of CVX technologies to implement the minimum energy consumption control algorithm, is presented. The control vector estimation is reduced to the minimization of the L2 norm and it is performed in two stages, namely, the best mode is first determined, and then the mode under constraints is defined. The use of Lyapunov inequalities with the calculations implementation in CVX format on proprietary solvers has allowed us to obtain compact program texts and expand the set of restrictions introduced. In the algorithm for solving the boundary value problem of controlling a discrete model of an object, in contrast to existing optimization methods, a mode of transfer from the initial state to the final one with the right boundary, not necessarily equal to zero, is implemented. For a class of observable and controllable time–invariant systems, using the Krylov’s function contained in the MATLAB gallery of functions, L2‑norms to be minimized are formed. Examples of regulator calculations with a given degree of stability and optimal systems, confirming proposed solutions correctness, are given.