Nonlinear Synergetic Optimal Controllers

Optimality properties of synergetic controllers are analyzed using the Euler-Lagrange conditions and the Hamilton-Jacobi-Bellman equation. First, a synergetic control strategy is compared with the variable structure sliding mode control. The connections of synergetic control design methodology and the methods of variable structure sliding mode control are established. In fact, the methods of sliding surface design for the sliding mode control are essential for designing invariant manifolds in the synergetic control approach. It is shown that the synergetic control strategy can be derived using tools from the calculus of variations. The synergetic control laws have a simple structure because they are derived from the associated first-order differential equation. It is also shown that the synergetic controller for a certain class of linear quadratic optimal control problems has the same structure as the one generated using the linear quadratic regulator approach by solving the associated Riccati equation. The synergetic optimal control and sliding mode control methodologies are applied to the nonlinear control of the wing-rock suppression problem. Two different wing-rock dynamic models are used to test the design of the synergetic and sliding mode controllers. The performance of the closed-loop systems driven by these controllers is analyzed and compared.

[1]  B. Anderson,et al.  Optimal control: linear quadratic methods , 1990 .

[2]  B. L. Walcott,et al.  State observation of nonlinear control systems via the method of Lyapunov , 1990 .

[3]  S. Żak,et al.  Optimality of Synergetic Controllers , 2006 .

[4]  Weiping Li,et al.  Applied Nonlinear Control , 1991 .

[5]  S. Kahne,et al.  Optimal control: An introduction to the theory and ITs applications , 1967, IEEE Transactions on Automatic Control.

[6]  Giorgio Guglieri,et al.  Analytical and Experimental Analysis of Wing Rock , 2001 .

[7]  E B Lee,et al.  Foundations of optimal control theory , 1967 .

[8]  E. Santi,et al.  Synergetic control for m-parallel connected DC-DC buck converters , 2004, 2004 IEEE 35th Annual Power Electronics Specialists Conference (IEEE Cat. No.04CH37551).

[9]  R.A. Dougal,et al.  Synergetic control of power converters for pulse current charging of advanced batteries from a fuel cell power source , 2004, IEEE Transactions on Power Electronics.

[10]  Danil V. Prokhorov,et al.  Adaptive control on manifolds with RBF neural networks , 2000, Proceedings of the 39th IEEE Conference on Decision and Control (Cat. No.00CH37187).

[11]  A. N. Popov,et al.  Synergetic Control for Electromechanical Systems , 2022 .

[12]  Vadim I. Utkin,et al.  Sliding mode control in electromechanical systems , 1999 .

[13]  Antonello Monti,et al.  Synergetic Control For Power Electronics Applications: A Comparison With The Sliding Mode Approach , 2004, J. Circuits Syst. Comput..

[14]  Chih-Min Lin,et al.  Adaptive Decoupled Fuzzy Sliding-Mode Control of a Nonlinear Aeroelastic System , 2006 .

[15]  Christopher Edwards,et al.  Sliding mode control : theory and applications , 1998 .

[16]  A. Kolesnikov.  Synergetic Control of the Unstable Two-Mass System , 2022 .

[17]  S. R. Wells,et al.  Sliding mode control applied to reconfigurable flight control design , 2002 .

[18]  Robert E. Kalaba,et al.  Dynamic Programming and Modern Control Theory , 1966 .

[19]  Kevin M. Passino,et al.  Biomimicry for Optimization, Control and Automation , 2004, IEEE Transactions on Automatic Control.

[20]  David Downing,et al.  Discrete sliding mode control of wing rock , 1994 .

[21]  Kevin M. Passino,et al.  Direct adaptive control using dynamic structure fuzzy systems , 2000, Proceedings of the 2000 American Control Conference. ACC (IEEE Cat. No.00CH36334).

[22]  Dean T. Mook,et al.  Subsonic wing rock of slender delta wings , 1985 .

[23]  R. Decarlo,et al.  Variable structure control of nonlinear multivariable systems: a tutorial , 1988, Proc. IEEE.

[24]  Martin Corless,et al.  Control of uncertain systems with neglected dynamics , 1990 .

[25]  S. Żak.  Systems and control , 2002 .

[26]  Sarah K. Spurgeon,et al.  Sliding Mode Control , 1998 .

[27]  Vadim I. Utkin,et al.  Sliding Modes in Control and Optimization , 1992, Communications and Control Engineering Series.

[28]  Moshe Idan,et al.  Sliding-Mode Control for Integrated Missile Autopilot Guidance , 2004 .

[29]  Di Zhou,et al.  Adaptive Sliding-Mode Guidance of a Homing Missile , 1999 .

[30]  C. Hsu,et al.  Theory of wing rock , 1985 .

[31]  A. H. Nayfeh,et al.  Development of an analytical model of wing rock for slender delta wings , 1989 .

[32]  Vadim I. Utkin,et al.  Sliding mode control , 2004 .

[33]  David H. Owens.  Multivariable and Optimal Systems , 1982 .