Nonlinear controllers for nonlinear systems with input nonlinearities

We develop an optimality-based nonlinear control framework for nonlinear systems with time-invariant sector-bounded memoryless input nonlinearities. Specifically, using an optimal nonlinear control framework we develop a family of globally stabilizing controllers parametrized by the cost functional that is minimized. Furthermore, it is shown that the control Lyapunov function guaranteeing closed-loop stability over a prescribed set of input nonlinearities is a solution to the steady-state Hamilton-Jacobi-Bellman equation for the controlled system and thus guarantees stability and performance.

[1]  A. Glattfelder,et al.  Stability analysis of single loop control systems with saturation and antireset-windup circuits , 1983 .

[2]  M. Morari,et al.  Multivariable Anti-Windup and Bumpless Transfer: A General Theory , 1989, 1989 American Control Conference.

[3]  P.V. Kokotovic,et al.  Lean backstepping design for a jet engine compressor model , 1995, Proceedings of International Conference on Control Applications.

[4]  P. Kokotovic,et al.  Inverse Optimality in Robust Stabilization , 1996 .

[5]  Eduardo Sontag,et al.  Nonlinear output feedback design for linear systems with saturating controls , 1990, 29th IEEE Conference on Decision and Control.

[6]  Dennis S. Bernstein,et al.  Nonlinear Controllers for Positive Real Systems with Arbitrary Input Nonlinearities , 1993, 1993 American Control Conference.

[7]  Wassim M. Haddad,et al.  Robust nonlinear-nonquadratic feedback control via parameterdependent Lyapunov functions , 1997 .

[8]  W. Haddad,et al.  Fixed-architecture controller synthesis for systems with input–output time-varying nonlinearities , 1997 .

[9]  E. P. Ryan,et al.  Optimal Relay and Saturating Control System Synthesis , 1982 .

[10]  Robert L. Kosut,et al.  Design of Linear Systems with Saturating Linear Control and Bounded States , 1982, 1982 American Control Conference.

[11]  E. Gilbert,et al.  Computation of minimum-time feedback control laws for discrete-time systems with state-control constraints , 1987 .

[12]  Michel Kinnaert,et al.  Conditioning technique, a general anti-windup and bumpless transfer method , 1987, Autom..

[13]  Dennis S. Bernstein,et al.  Nonlinear controllers for positive real systems with arbitrary input nonlinearities , 1994 .

[14]  Isaac Horowitz,et al.  A synthesis theory for a class of saturating systems , 1983 .

[15]  Zongli Lin,et al.  Semi-global Exponential Stabilization of Linear Systems Subject to \input Saturation" via Linear Feedbacks , 1993 .

[16]  Chaouki T. Abdallah,et al.  A unification between nonlinear-nonquadratic optimal control and integrator backstepping , 1998 .

[17]  Dennis S. Bernstein,et al.  Anti-windup compensator synthesis for systems with saturation actuators , 1995 .

[18]  D. Bernstein,et al.  Nonlinear feedback control with global stabilization , 1995 .

[19]  B. Anderson,et al.  Nonlinear regulator theory and an inverse optimal control problem , 1973 .

[20]  A. Teel.  Semi-global stabilizability of linear null controllable systems with input nonlinearities , 1995, IEEE Trans. Autom. Control..

[21]  W. Haddad,et al.  Robust nonlinear feedback control with nonquadratic performance criteria , 1995, Proceedings of 1995 34th IEEE Conference on Decision and Control.

[22]  F. Moore,et al.  A Theory of Post-Stall Transients in Axial Compression Systems: Part I—Development of Equations , 1986 .

[23]  A. Teel.  Global stabilization and restricted tracking for multiple integrators with bounded controls , 1992 .