Software for synthesizing robust controllers and observers in dynamical systems with incomplete measurements

Аuthors

Yakovleva A. A.

Moscow Aviation Institute (National Research University), 4, Volokolamskoe shosse, Moscow, А-80, GSP-3, 125993, Russia

e-mail: yakovlevaaa@mai.ru

Abstract

The evolution of the aerospace industry in modern conditions leads to an increasing demand for higher reliability, performance, and efficiency of control systems operating under uncertainty. Under such conditions, classical methods for the synthesis of controllers and observers, which rely on accurate models and complete information, prove to be ineffective.
Therefore, to maintain stability and the required control performance, it is necessary to develop new, more advanced approaches to the synthesis of controllers and observers. In this context, the most appropriate solution is the use of a robust approach, which accounts for the worst-case operating conditions of the system at the controller and observer design stage.
This paper presents a software package for the automated synthesis of robust controllers and state observers for linear (time-invariant and time-varying) and nonlinear dynamic systems that are linear in control and disturbance, under incomplete state-vector information and bounded uncertainties (external disturbances, measurement noise, and dispersion of initial conditions). The algorithms used in the study are based on proven sufficient optimality conditions applied in optimal control theory of dynamic systems and obtained using the extension principle.
The software has been developed in MATLAB and supplemented with a Python 3 module for solving controller synthesis problems for nonlinear systems linear in control and disturbance over a semi-infinite time interval. The software package has been successfully validated on benchmark models and applied control problems involving F-16 and Lockheed L-1011 aircraft, as well as the Raptor-90 helicopter. The paper also presents an example of applying the Python 3 module to the quadcopter stabilization problem.
The developed software can be used to solve a wide range of applied problems in robust control and observation, as well as in the design of flight control and stabilization systems.

Keywords:

software, robust control, H-infinity optimization, incomplete state information, H-infinity controller, H-infinity observer, Riccati equation, aircraft, MATLAB, Python, SDRE

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