Optimal Robust Control for Constrained Fuzzy Dynamic Systems: Semi-infinite Case

We consider a constrained state and constrained control design problem for fuzzy dynamic systems. The uncertainty in the system is time-varying and bounded, with the bound information prescribed by a fuzzy set. The control input of systems is also constrained to be one-sided (either positive or negative). An optimal design of a robust control is proposed. It is proven that the global solution to an optimal design problem always exists and is unique. Neither the system nor the control is fuzzy heuristic if-then rule-based.

[1]  Ye-Hwa Chen,et al.  Fractional robust control design for fuzzy dynamical systems: An optimal approach , 2015, J. Intell. Fuzzy Syst..

[2]  Thomas L. Vincent,et al.  Optimal Control of a Prey-Predator System* , 1974 .

[3]  George J. Klir,et al.  Fuzzy sets and fuzzy logic - theory and applications , 1995 .

[4]  T. K. Garrett,et al.  The Motor Vehicle , 1989 .

[5]  Liu Hsu,et al.  Achieving global convergence to an equilibrium population in predator-prey systems by the use of a discontinuous harvesting policy , 2000 .

[6]  Michio Sugeno,et al.  Fuzzy identification of systems and its applications to modeling and control , 1985, IEEE Transactions on Systems, Man, and Cybernetics.

[7]  Y. H. Chen,et al.  A New Approach to the Control Design of Fuzzy Dynamical Systems , 2011 .

[8]  Ye-Hwa Chen,et al.  Robust Control for Fuzzy Dynamical Systems: Uniform Ultimate Boundedness and Optimality , 2012, IEEE Transactions on Fuzzy Systems.

[9]  F. Fairman.  Introduction to dynamic systems: Theory, models and applications , 1979, Proceedings of the IEEE.

[10]  Ye-Hwa Chen,et al.  Optimal design of robust control for positive fuzzy dynamic systems with one-sided control constraint , 2017, J. Intell. Fuzzy Syst..

[11]  Wen-June Wang,et al.  Implementation of an Object-Grasping Robot Arm Using Stereo Vision Measurement and Fuzzy Control , 2015, Int. J. Fuzzy Syst..

[12]  Gerald Quirchmayr,et al.  Assignment of tasks to competing nodes when task duration times are fuzzy , 2000, J. Intell. Fuzzy Syst..

[13]  Ye-Hwa Chen,et al.  Optimal Design of Robust Control for Uncertain Systems: a Fuzzy Approach , 2001 .

[14]  M. Corless,et al.  Continuous state feedback guaranteeing uniform ultimate boundedness for uncertain dynamic systems , 1981 .

[15]  Chih-Lyang Hwang.  Decentralized Fuzzy Control of Nonlinear Interconnected Dynamic Delay Systems via Mixed $H_2/\!H_\infty$ Optimization With Smith Predictor , 2011, IEEE Transactions on Fuzzy Systems.

[16]  Chan-Gyun Kim,et al.  Positive Solutions for a Lotka–Volterra Prey–Predator Model with Cross-Diffusion of Fractional Type , 2014 .

[17]  Ye-Hwa Chen,et al.  Optimal Design of Constraint-Following Control for Fuzzy Mechanical Systems , 2016, IEEE Transactions on Fuzzy Systems.

[18]  Han Zhao,et al.  Optimal Robust Control for Rigid Serial Manipulators: A Fuzzy Approach , 2015 .

[19]  Chen-Yuan Kuo,et al.  Positive uncertain systems with one-sided robust control , 1997 .

[20]  David A. Kendrick,et al.  Stochastic control for economic models , 1981 .

[21]  Cheng-Hsiung Yang,et al.  Reduced Fuzzy Controllers for Lorenz–Stenflo System Control and Synchronization , 2015, Int. J. Fuzzy Syst..

[22]  Tingwen Huang,et al.  A new method to control chaos in an economic system , 2010, Appl. Math. Comput..

[23]  Delphine Picart,et al.  Optimal control in a multistage physiologically structured insect population model , 2014, Appl. Math. Comput..

[24]  George Leitmann,et al.  On ultimate boundedness control of uncertain systems in the absence of matching assumptions , 1982 .

[25]  Jyh-Horng Chou,et al.  Robust Quadratic-Optimal Control of TS-Fuzzy-Model-Based Dynamic Systems With Both Elemental Parametric Uncertainties and Norm-Bounded Approximation Error , 2009, IEEE Transactions on Fuzzy Systems.

[26]  Hong Guo,et al.  On the Foundations of Fuzzy Dynamical System Theory: Controllability and Observability , 2014 .

[27]  Ebrahim Mamdani,et al.  Applications of fuzzy algorithms for control of a simple dynamic plant , 1974 .