Special Spectral Approach to Solutions of SISO LTI H-Optimization Problems

The paper is devoted to H-optimization problems for linear time invariant (LTI) systems with scalar control, external disturbance and measurement noise. All these problems can be numerically solved with the help of the well-known universal approaches based on Riccati equations, linear matrix inequalities (LMI) or maximum entropy technique. Nevertheless, in our opinion there exists a possibility to increase the computational efficiency of synthesis using a special spectral approach to the above mentioned problems in frequency domain. Some relevant details are discussed and efficient numerical algorithms are proposed for the practical implementation of spectral approach. One of its virtues is a possibility to present optimal solutions in a specific form, which is convenient for investigation.

[1]  Y. V. Knyazkin,et al.  H_2-Optimal synthesis problem with nonunique solution , 2016 .

[2]  Petko H. Petkov,et al.  Robust control design with MATLAB , 2005 .

[3]  Alexander Domahidi.  Methods and tools for embedded optimization and control , 2013 .

[4]  M. Grimble.  Robust Industrial Control Systems: Optimal Design Approach for Polynomial Systems , 1994 .

[5]  Efficient spectral approach to SISO problems of H_2-optimal synthesis , 2015 .

[6]  Suresh Thenozhi,et al.  Active Structural Control with Stable Fuzzy PID Techniques , 2015 .

[7]  Evgeny I. Veremey.  H∞-Approach to Wave Disturbance Filtering for Marine Autopilots , 2012 .

[8]  Stephen P. Boyd,et al.  Linear Matrix Inequalities in Systems and Control Theory , 1994 .

[9]  Fuwen Yang,et al.  Simultaneous H2/H∞ stabilization for chemical reaction systems based on orthogonal complement space , 2016, Int. J. Autom. Comput..

[10]  Michael Sylvester Packianather,et al.  Multi-objective invasive weed optimization of the LQR controller , 2017, Int. J. Autom. Comput..

[11]  Evgeny I. Veremey,et al.  Dynamical correction of control laws for marine ships’ accurate steering , 2014 .

[12]  V. Larin,et al.  Parametrization of sets of stabilizing controllers in mechanical systems , 2008 .

[13]  Daniel Liberzon,et al.  Calculus of Variations and Optimal Control Theory: A Concise Introduction , 2012 .

[14]  Evgeny I. Veremey.  Optimization of filtering correctors for autopilot control laws with special structures , 2016 .

[15]  Shankar P. Bhattacharyya,et al.  Linear Control Theory , 2009 .

[16]  Huibert Kwakernaak,et al.  H2-optimization - Theory and applications to robust control design , 2000, Annu. Rev. Control..

[17]  Bruce A. Francis,et al.  Feedback Control Theory , 1992 .

[18]  Algorithms for solving a class of problems of H∞-optimization of control systems , 2011 .

[19]  Vladimír Kučera.  Polynomial control: past, present, and future , 2007 .