A receding horizon generalization of pointwise min-norm controllers

Control Lyapunov functions (CLFs) are used in conjunction with receding horizon control to develop a new class of receding horizon control schemes. In the process, strong connections between the seemingly disparate approaches are revealed, leading to a unified picture that ties together the notions of pointwise min-norm, receding horizon, and optimal control. This framework is used to develop a CLF based receding horizon scheme, of which a special case provides an appropriate extension of Sontag's formula. The scheme is first presented as an idealized continuous-time receding horizon control law. The issue of implementation under discrete-time sampling is then discussed as a modification. These schemes are shown to possess a number of desirable theoretical and implementation properties. An example is provided, demonstrating their application to a nonlinear control problem. Finally, stronger connections to both optimal and pointwise min-norm control are proved.

[1]  Z. Artstein.  Stabilization with relaxed controls , 1983 .

[2]  Wei Lin.  Input saturation and global stabilization by output feedback for affine systems , 1994, Proceedings of 1994 33rd IEEE Conference on Decision and Control.

[3]  A. Isidori.  Nonlinear Control Systems , 1985 .

[4]  L. Praly,et al.  Adding integrations, saturated controls, and stabilization for feedforward systems , 1996, IEEE Trans. Autom. Control..

[5]  Eduardo Sontag.  A universal construction of Artstein's theorem on nonlinear stabilization , 1989 .

[6]  Randy A. Freeman,et al.  Robust Nonlinear Control Design , 1996 .

[7]  J. Richalet,et al.  Model predictive heuristic control: Applications to industrial processes , 1978, Autom..

[8]  G. Martin,et al.  Nonlinear model predictive control , 1999, Proceedings of the 1999 American Control Conference (Cat. No. 99CH36251).

[9]  M. A. Henson,et al.  Receding horizon control and discontinuous state feedback stabilization , 1995 .

[10]  Manfred Morari,et al.  Model predictive control: Theory and practice , 1988 .

[11]  J. Doyle,et al.  Nonlinear games: examples and counterexamples , 1996, Proceedings of 35th IEEE Conference on Decision and Control.

[12]  H. Michalska,et al.  Receding horizon control of nonlinear systems , 1988, Proceedings of the 28th IEEE Conference on Decision and Control,.

[13]  Eduardo Sontag.  A Lyapunov-Like Characterization of Asymptotic Controllability , 1983, SIAM Journal on Control and Optimization.

[14]  Yu. S. Ledyaev,et al.  Asymptotic controllability implies feedback stabilization , 1997, IEEE Trans. Autom. Control..

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

[16]  Arthur E. Bryson,et al.  Applied Optimal Control , 1969 .

[17]  Randy A. Freeman,et al.  Integrator backstepping for rounded controls and control rates , 1998, IEEE Trans. Autom. Control..

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

[19]  R. Freeman,et al.  Control Lyapunov functions: new ideas from an old source , 1996, Proceedings of 35th IEEE Conference on Decision and Control.

[20]  D. Mayne,et al.  Receding horizon control of nonlinear systems , 1990 .

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

[22]  R.A. Freeman,et al.  Optimal nonlinear controllers for feedback linearizable systems , 1995, Proceedings of 1995 American Control Conference - ACC'95.

[23]  Manfred Morari,et al.  Model predictive control: Theory and practice - A survey , 1989, Autom..

[24]  D. Mayne,et al.  Robust receding horizon control of constrained nonlinear systems , 1993, IEEE Trans. Autom. Control..

[25]  J. Richalet,et al.  Industrial applications of model based predictive control , 1993, Autom..

[26]  James A. Primbs,et al.  A control lyapunov function based receding horizon methodology for input constrained nonlinear systems , 1999 .

[27]  Riccardo Marino,et al.  Nonlinear control design , 1995 .

[28]  Riccardo Scattolini,et al.  Stabilizing nonlinear receding horizon control via a nonquadratic terminal state penalty , 1996 .