Explicit solutions to optimal control problems for constrained continuous-time linear systems

An algorithmic framework is presented for the derivation of the explicit optimal control policy for continuous-time linear dynamic systems that involve constraints on the process inputs and outputs. The control actions are usually computed by regularly solving an on-line optimisation problem in the discrete-time space based on a set of measurements that specify the current process state. A way to derive the explicit optimal control law, thereby, eliminating the need for rigorous on-line computations has already been reported in the literature, but it is limited to discrete-time linear dynamic systems. The currently presented approach derives the optimal state-feedback control law off-line for a continuous-time dynamic plant representation. The control law is proved to be nonlinear piecewise differentiable with respect to the system state and does not require the repetitive solution of on-line optimisation problems. Hence, the on-line implementation is reduced to a sequence of function evaluations. The key advantages of the proposed algorithm are demonstrated via two illustrative examples.

[1]  Arthur E. Bryson,et al.  OPTIMAL PROGRAMMING PROBLEMS WITH INEQUALITY CONSTRAINTS , 1963 .

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

[3]  Huibert Kwakernaak,et al.  Linear Optimal Control Systems , 1972 .

[4]  Babu Joseph,et al.  On‐line optimization of constrained multivariable chemical processes , 1987 .

[5]  Robert F. Stengel,et al.  Optimal Control and Estimation , 1994 .

[6]  R.W.H. Sargent,et al.  Robust receding horizon optimal control , 1996 .

[7]  Linda R. Petzold,et al.  Numerical solution of initial-value problems in differential-algebraic equations , 1996, Classics in applied mathematics.

[8]  C. Kravaris,et al.  Controller synthesis for time-varying systems by input/output linearization , 1997 .

[9]  Frank Allgöwer,et al.  A quasi-infinite horizon nonlinear model predictive control scheme with guaranteed stability , 1997, 1997 European Control Conference (ECC).

[10]  D. Mayne,et al.  Min-max feedback model predictive control for constrained linear systems , 1998, IEEE Trans. Autom. Control..

[11]  Carla I.C. Pinheiro,et al.  Model predictive control of reactor temperature in a CSTR pilot plant operating at an unstable steady-state , 1999 .

[12]  M. Egerstedt,et al.  On the regularization of Zeno hybrid automata , 1999 .

[13]  Lorenz T. Biegler,et al.  Interior-point methods for reduced Hessian successive quadratic programming , 1999 .

[14]  S. Palanki,et al.  A feedback-based implementation scheme for batch process optimization , 2000 .

[15]  Lorenz T. Biegler,et al.  On-line implementation of nonlinear MPC: an experimental case study , 2000 .

[16]  Francis J. Doyle,et al.  Robust H∞ glucose control in diabetes using a physiological model , 2000 .

[17]  M. Morari,et al.  On-line optimization via off-line parametric optimization tools , 2000 .

[18]  Xiaolong Wang,et al.  Optimal control of batch electrochemical reactor using K-L expansion , 2001 .

[19]  Helmut Maurer,et al.  Sensitivity Analysis for Optimal Control Problems Subject to Higher Order State Constraints , 2001, Ann. Oper. Res..

[20]  Panagiotis D. Christofides,et al.  Robust near-optimal output feedback control of non-linear systems , 2001 .

[21]  N. El‐Farra,et al.  Integrating robustness, optimality and constraints in control of nonlinear processes , 2001 .

[22]  Helmut Maurer,et al.  Computational Sensitivity Analysis for State Constrained Optimal Control Problems , 2001, Ann. Oper. Res..

[23]  D. Chmielewski,et al.  On constrained infinite-time nonlinear optimal control , 2002 .

[24]  M. Diehl,et al.  Real-time optimization and nonlinear model predictive control of processes governed by differential-algebraic equations , 2000 .

[25]  Alberto Bemporad,et al.  The explicit linear quadratic regulator for constrained systems , 2003, Autom..