Receding Horizon Robust Control for Nonlinear Systems Based on Linear Differential Inclusion of Neural Networks

In this paper, we present a new receding horizon neural robust control scheme for a class of nonlinear systems based on the linear differential inclusion (LDI) representation of neural networks. First, we propose a linear matrix inequality (LMI) condition on the terminal weighting matrix for a receding horizon neural robust control scheme. This condition guarantees the nonincreasing monotonicity of the saddle point value of the finite horizon dynamic game. We then propose a receding horizon neural robust control scheme for nonlinear systems, which ensures the infinite horizon robust performance and the internal stability of closed-loop systems. Since the proposed control scheme can effectively deal with input and state constraints in an optimization problem, it does not cause the instability problem or give the poor performance associated with the existing neural robust control schemes.

[1]  Wook Hyun Kwon,et al.  Stabilizing receding horizon H∞ controls for linear continuous time-varying systems , 2000, IEEE Trans. Autom. Control..

[2]  C.-L. Lin,et al.  Approach to adaptive neural net-based H∞ control design , 2002 .

[3]  Johan A. K. Suykens,et al.  Robust local stability of multilayer recurrent neural networks , 2000, IEEE Trans. Neural Networks Learn. Syst..

[4]  Kazuo Tanaka,et al.  An approach to stability criteria of neural-network control systems , 1996, IEEE Trans. Neural Networks.

[5]  Stephen Yurkovich,et al.  Fuzzy Control , 1997 .

[6]  W. Kwon,et al.  A modified quadratic cost problem and feedback stabilization of a linear system , 1977 .

[7]  Choon Ki Ahn,et al.  New results on stability margins of nonlinear discrete-time receding horizon h∞ control , 2013 .

[8]  Choon Ki Ahn,et al.  Takagi-Sugeno fuzzy receding horizon H∞ chaotic synchronization and its application to the Lorenz system , 2013 .

[9]  W. Kwon,et al.  Stabilizing state-feedback design via the moving horizon method† , 1983 .

[10]  A. N. Michel,et al.  Robustness analysis of a class of discrete-time recurrent neural networks under perturbations , 1999 .

[11]  Johan A. K. Suykens,et al.  Artificial Neural Networks for Modeling and Control of Non-Linear Systems , 1995 .

[12]  Tsai-Yuan Lin,et al.  An H∞ design approach for neural net-based control schemes , 2001, IEEE Trans. Autom. Control..

[13]  Wook Hyun Kwon,et al.  Advances in Nonlinear Predictive Control : A Survey on Stability and Optimality , 2004 .

[14]  Johan A. K. Suykens,et al.  Lur'e systems with multilayer perceptron and recurrent neural networks: absolute stability and dissipativity , 1999, IEEE Trans. Autom. Control..

[15]  Wook Hyun Kwon,et al.  ${\cal H}_{\infty}$ Finite Memory Controls for Linear Discrete-Time State-Space Models , 2007, IEEE Transactions on Circuits and Systems II: Express Briefs.

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

[17]  Choon Ki Ahn,et al.  Passive learning and input-to-state stability of switched Hopfield neural networks with time-delay , 2010, Inf. Sci..

[18]  C. Ahn.  An ℋ∞ approach to stability analysis of switched Hopfield neural networks with time-delay , 2010 .

[19]  J. Si,et al.  Neural network-based control design: an LMI approach , 1998, Proceedings of the 1998 American Control Conference. ACC (IEEE Cat. No.98CH36207).

[20]  Chun-Liang Lin,et al.  Neural Net-Based H∞ Control for a Class of Nonlinear Systems , 2004, Neural Processing Letters.

[21]  Wook Hyun Kwon,et al.  On stability of constrained receding horizon control with finite terminal weighting matrix , 1997, 1997 European Control Conference (ECC).

[22]  C. Ahn.  Delay-dependent state estimation for T-S fuzzy delayed Hopfield neural networks , 2010 .

[23]  Wook Hyun Kwon,et al.  On stabilizing receding horizon controls for linear continuous time-invariant systems , 2000, IEEE Trans. Autom. Control..

[24]  Chen-Chung Liu,et al.  Adaptively controlling nonlinear continuous-time systems using multilayer neural networks , 1994, IEEE Trans. Autom. Control..

[25]  Choon Ki Ahn,et al.  Robustness bound for receding horizon finite memory control: Lyapunov–Krasovskii approach , 2012, Int. J. Control.

[26]  Myo-Taeg Lim,et al.  Model predictive stabilizer for T–S fuzzy recurrent multilayer neural network models with general terminal weighting matrix , 2013, Neural Computing and Applications.

[27]  W. Kwon,et al.  On feedback stabilization of time-varying discrete linear systems , 1978 .

[28]  Alexander S. Poznyak,et al.  Stability analysis of dynamic neural control , 1998 .

[29]  Choon Ki Ahn,et al.  Output feedback ℋ∞ synchronization for delayed chaotic neural networks , 2009 .