Pseudo-PID tracking control for a class of output PDFs of general non-Gaussian stochastic systems

In this paper a pseudo-PID control strategy is presented for a class of non-Gaussian stochastic systems. To control the output probability density functions (PDFs) to track a given target function, the PID-type control structure is imposed a priori. Following the B-spline approximation on the measured output PDFs, the control objective is transferred into the tracking of given weights which correspond to the desired PDF. For systems with or without model uncertainties, it is shown that the solvability can be cast into a group of matrix inequalities. This leads to a feasible controller design procedure that can guarantee the required tracking convergence with enhanced robustness.

[1]  Michael J. Grimble,et al.  H∞ Controllers With a PID Structure , 1990 .

[2]  K. Åström.  Introduction to Stochastic Control Theory , 1970 .

[3]  E. Yaz.  Linear Matrix Inequalities In System And Control Theory , 1998, Proceedings of the IEEE.

[4]  Tong Heng Lee,et al.  On the design of multivariable PID controllers via LMI approach , 2002, Autom..

[5]  Karl Johan Åström,et al.  PID Controllers: Theory, Design, and Tuning , 1995 .

[6]  Hong Wang.  Model reference adaptive control of the output stochastic distributions for unknown linear stochastic systems , 1999, Int. J. Syst. Sci..

[7]  Massimiliano Mattei,et al.  Robust multivariable PID control for linear parameter varying systems , 2001, Autom..

[8]  Teuscher Gw,et al.  Prediction and control. , 1996 .

[9]  Min-Sen Chiu,et al.  Robust PID controller design via LMI approach , 2002 .

[10]  Zoran Gajic,et al.  Monotonicity of algebraic Lyapunov iterations for optimal control of jump parameter linear systems , 2000 .

[11]  Karl Johan Åström,et al.  Adaptive Control , 1989, Embedded Digital Control with Microcontrollers.

[12]  Z. K. Liu,et al.  Suboptimal design of regulators for jump linear system with time-multiplied quadratic cost , 2001, IEEE Trans. Autom. Control..

[13]  C. Zheng,et al.  ; 0 ; , 1951 .

[14]  Hong Wang,et al.  Bounded Dynamic Stochastic Systems , 2012 .

[15]  Hong Wang,et al.  Robust control of the output probability density functions for multivariable stochastic systems with guaranteed stability , 1999, IEEE Trans. Autom. Control..

[16]  Hong Wang,et al.  Robust control of the output probability density functions for multivariable stochastic systems , 1998, Proceedings of the 37th IEEE Conference on Decision and Control (Cat. No.98CH36171).