A neurodynamic optimization approach to robust pole assignment for synthesizing linear state feedback control systems

This paper presents a neurodynamic optimization approach to robust pole assignment for synthesizing linear control systems via state feedback. A pseudoconvex objective function is minimized as a robustness measure. A neurodynamic model is applied whose global convergence was theoretically proved for constrained pseudoconvex optimization. Compared with existing approaches on benchmark problems, the convergence of proposed neurodynamic approach to global optimal solutions can be guaranteed. Simulation results of the proposed neurodynamic approach is reported to demonstrate its superiority.

[1]  Jun Wang,et al.  Augmented gradient flows for on-line robust pole assignment via state and output feedback , 2002, Autom..

[2]  Jun Wang,et al.  Model Predictive Control of Unknown Nonlinear Dynamical Systems Based on Recurrent Neural Networks , 2012, IEEE Transactions on Industrial Electronics.

[3]  J. J. Hopfield,et al.  “Neural” computation of decisions in optimization problems , 1985, Biological Cybernetics.

[4]  Jun Wang,et al.  A recurrent neural network for nonlinear optimization with a continuously differentiable objective function and bound constraints , 2000, IEEE Trans. Neural Networks Learn. Syst..

[5]  Qingshan Liu,et al.  A one-layer recurrent neural network for constrained pseudoconvex optimization and its application for dynamic portfolio optimization , 2012, Neural Networks.

[6]  S. Nash,et al.  Approaches to robust pole assignment , 1989 .

[7]  Zheng Yan,et al.  Model Predictive Control for Tracking of Underactuated Vessels Based on Recurrent Neural Networks , 2012, IEEE Journal of Oceanic Engineering.

[8]  Jun Wang,et al.  A gradient flow approach to on-line robust pole assignment for synthesizing output feedback control systems , 2002, Autom..

[9]  Jun Wang,et al.  A general methodology for designing globally convergent optimization neural networks , 1998, IEEE Trans. Neural Networks.

[10]  Kimon P. Valavanis,et al.  Nonlinear Model Predictive Control With Neural Network Optimization for Autonomous Autorotation of Small Unmanned Helicopters , 2011, IEEE Transactions on Control Systems Technology.

[11]  N. Nichols,et al.  Robust pole assignment in linear state feedback , 1985 .

[12]  Youshen Xia,et al.  A recurrent neural network for nonlinear convex optimization subject to nonlinear inequality constraints , 2004, IEEE Trans. Circuits Syst. I Regul. Pap..

[13]  Abdellah Benzaouia,et al.  Robust Exact Pole Placement via an LMI-Based Algorithm , 2009, IEEE Transactions on Automatic Control.

[14]  Mauro Forti,et al.  Generalized neural network for nonsmooth nonlinear programming problems , 2004, IEEE Transactions on Circuits and Systems I: Regular Papers.

[15]  James Lam,et al.  Neural computation for robust approximate pole assignment , 1999, Neurocomputing.

[16]  A. Cambini,et al.  Generalized Convexity and Optimization: Theory and Applications , 2008 .

[17]  Qingshan Liu,et al.  A One-Layer Recurrent Neural Network for Pseudoconvex Optimization Subject to Linear Equality Constraints , 2011, IEEE Transactions on Neural Networks.

[18]  Xiaolin Hu,et al.  Design of General Projection Neural Networks for Solving Monotone Linear Variational Inequalities and Linear and Quadratic Optimization Problems , 2007, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[19]  Jane J. Ye,et al.  Optimizing Condition Numbers , 2009, SIAM J. Optim..

[20]  Jun Wang,et al.  A deterministic annealing neural network for convex programming , 1994, Neural Networks.

[21]  Jun Wang,et al.  A multilayer recurrent neural network for on-line synthesis of minimum-norm linear feedback control systems via pole assignment , 1996, Autom..

[22]  Eric King-Wah Chu,et al.  Pole assignment via the schur form , 2007, Syst. Control. Lett..

[23]  Qingshan Liu,et al.  A One-Layer Recurrent Neural Network With a Discontinuous Hard-Limiting Activation Function for Quadratic Programming , 2008, IEEE Transactions on Neural Networks.

[24]  A. Tits,et al.  Globally convergent algorithms for robust pole assignment by state feedback , 1996, IEEE Trans. Autom. Control..

[25]  Jianping Li,et al.  Notes on "Recurrent neural network model for computing largest and smallest generalized eigenvalue" , 2010, Neurocomputing.

[26]  Jun Wang Analysis and design of a recurrent neural network for linear programming , 1993 .

[27]  Leon O. Chua,et al.  Neural networks for nonlinear programming , 1988 .

[28]  Jun Wang,et al.  Model Predictive Control of Nonlinear Systems With Unmodeled Dynamics Based on Feedforward and Recurrent Neural Networks , 2012, IEEE Transactions on Industrial Informatics.

[29]  Xiaolin Hu,et al.  Solving Pseudomonotone Variational Inequalities and Pseudoconvex Optimization Problems Using the Projection Neural Network , 2006, IEEE Transactions on Neural Networks.

[30]  Jun Wang,et al.  Global exponential stability of recurrent neural networks for synthesizing linear feedback control systems via pole assignment , 2002, IEEE Trans. Neural Networks.

[31]  S. Bhattacharyya,et al.  Pole assignment via Sylvester's equation , 1982 .

[32]  Jun Wang,et al.  Multilayer recurrent neural networks for online robust pole assignment , 2003 .

[33]  James Lam,et al.  A gradient flow approach to the robust pole-placement problem , 1995 .

[34]  Jun Wang,et al.  Neurodynamic optimization approaches to robust pole assignment based on alternative robustness measures , 2013, The 2013 International Joint Conference on Neural Networks (IJCNN).

[35]  James Lam,et al.  Pole assignment with optimal spectral conditioning , 1997 .

[36]  Robin J. Evans,et al.  Robust pole assignment , 1987, Autom..

[37]  Jun Wang,et al.  Recurrent neural networks for nonlinear output regulation , 2001, Autom..

[38]  Mauro Forti,et al.  Convergence of Neural Networks for Programming Problems via a Nonsmooth Łojasiewicz Inequality , 2006, IEEE Transactions on Neural Networks.