Online Control Customization via Optimization‐Based Control

An advanced control technology that has had tremendous practical impact over the last two decades or so is model predictive control (MPC). By embedding an optimization solution in each sampling instant within the control calculation, MPC applications have demonstrated dramatic improvements in control performance. To date, this impact has largely been limited to the process industries. The reasons for the domain-specific benefit have to do with the relatively slow time constants of most industrial processes and their relatively benign dynamics (e.g., their open-loop stability). For aerospace systems to avail of the promise of MPC, research is needed in extending the technology so that it can be applied to systems with nonlinear, unstable, and fast dynamics. This chapter presents a new framework for MPC and optimization-based control for flight control applications. The MPC formulation replaces the traditional terminal constraint with a terminal cost based on a control Lyapunov function. This reduces computational requirements and allows proofs of stability under a variety of realistic assumptions on computation. The authors also show how differential flatness system can be used to computational advantage. (A system is differentially flat if, roughly, it can be modeled as a dynamical equation in one variable and its derivatives.) In this case the optimization can be done over a space of parametrized basis functions and a constrained nonlinear program can be solved using collocation points. A software package has been developed to implement these theoretical developments. There is an experimental component to this research as well. A tethered ducted fan testbed has been developed at Caltech that mimics the longitudinal dynamics of an aircraft. High-performance maneuvers can safely be flown with the ducted fan and an interface to high-end workstations

[1]  A. Schaft.  L2-Gain and Passivity Techniques in Nonlinear Control. Lecture Notes in Control and Information Sciences 218 , 1996 .

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

[3]  J. Hauser,et al.  On the geometry of optimal control: the inverted pendulum example , 2001, Proceedings of the 2001 American Control Conference. (Cat. No.01CH37148).

[4]  John Doyle,et al.  A receding horizon generalization of pointwise min-norm controllers , 2000, IEEE Trans. Autom. Control..

[5]  D. Mayne.  Nonlinear and Adaptive Control Design [Book Review] , 1996, IEEE Transactions on Automatic Control.

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

[7]  Richard M. Murray,et al.  Rapid Hover-to-Forward-Flight Transitions for a Thrust-Vectored Aircraft , 1998 .

[8]  Mark B. Milam,et al.  Inversion Based Constrained Trajectory Optimization , 2001 .

[9]  R. Murray,et al.  Real‐time trajectory generation for differentially flat systems , 1998 .

[10]  David Q. Mayne,et al.  Constrained model predictive control: Stability and optimality , 2000, Autom..

[11]  C. Hargraves,et al.  DIRECT TRAJECTORY OPTIMIZATION USING NONLINEAR PROGRAMMING AND COLLOCATION , 1987 .

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

[13]  M. Fliess,et al.  On Differentially Flat Nonlinear Systems , 1992 .

[14]  Carl de Boor,et al.  A Practical Guide to Splines , 1978, Applied Mathematical Sciences.

[15]  John R. Hauser,et al.  Applied receding horizon control of the Caltech Ducted Fan , 2002, Proceedings of the 2002 American Control Conference (IEEE Cat. No.CH37301).

[16]  William B. Dunbar,et al.  MODEL PREDICTIVE CONTROL OF A THRUST-VECTORED FLIGHT CONTROL EXPERIMENT , 2002 .

[17]  Hans Seywald,et al.  Trajectory optimization based on differential inclusion , 1994 .

[18]  L. Singh,et al.  Trajectory generation for a UAV in urban terrain, using nonlinear MPC , 2001, Proceedings of the 2001 American Control Conference. (Cat. No.01CH37148).

[19]  Richard M. Murray,et al.  REAL-TIME CONSTRAINED TRAJECTORY GENERATION APPLIED TO A FLIGHT CONTROL EXPERIMENT , 2002 .

[20]  P. Gill,et al.  Fortran package for nonlinear programming. User's Guide for NPSOL (Version 4. 0) , 1986 .

[21]  Chaouki T. Abdallah,et al.  Linear Quadratic Control: An Introduction , 2000 .

[22]  Richard M. Murray,et al.  Nonlinear Control of Mechanical Systems: A Lagrangian Perspective , 1995 .

[23]  P. Gill,et al.  User's Guide for SOL/NPSOL: A Fortran Package for Nonlinear Programming. , 1983 .

[24]  T. A. Badgwell,et al.  An Overview of Industrial Model Predictive Control Technology , 1997 .

[25]  Mark B. Milam,et al.  A new computational approach to real-time trajectory generation for constrained mechanical systems , 2000, Proceedings of the 39th IEEE Conference on Decision and Control (Cat. No.00CH37187).

[26]  A. Schaft.  On a state space approach to nonlinear H ∞ control , 1991 .

[27]  Richard M. Murray,et al.  A testbed for nonlinear flight control techniques: the Caltech ducted fan , 1999, Proceedings of the 1999 IEEE International Conference on Control Applications (Cat. No.99CH36328).

[28]  Lamberto Cesari,et al.  Optimization-Theory And Applications , 1983 .

[29]  Jie Yu,et al.  Unconstrained receding-horizon control of nonlinear systems , 2001, IEEE Trans. Autom. Control..

[30]  M. Bardi,et al.  Optimal Control and Viscosity Solutions of Hamilton-Jacobi-Bellman Equations , 1997 .

[31]  B. Paden,et al.  A different look at output tracking: control of a VTOL aircraft , 1994, Proceedings of 1994 33rd IEEE Conference on Decision and Control.

[32]  B. Dacorogna.  Direct methods in the calculus of variations , 1989 .