A Riccati approach to equality constrained Linear Quadratic Optimal control

A Riccati based approach is proposed to solve Linear Quadratic Optimal control problems subject to linear equality path constraints including mixed state-control and state-only constraints. The proposed algorithm requires computations that scale linearly with the horizon length. It can be used as the key sub-problem to build effective iterative methodologies that tackle general inequality constrained and nonlinear optimal control problems.

[1]  J. Bobrow,et al.  A Fast Sequential Linear Quadratic Algorithm for Solving Unconstrained Nonlinear Optimal Control Problems , 2005 .

[2]  A. Bryson,et al.  A SUCCESSIVE SWEEP METHOD FOR SOLVING OPTIMAL PROGRAMMING PROBLEMS , 1965 .

[3]  Jacques Vlassenbroeck,et al.  A chebyshev polynomial method for optimal control with state constraints , 1988, Autom..

[4]  Athanasios Sideris,et al.  An active set method for constrained linear quadratic optimal control , 2010, Proceedings of the 2010 American Control Conference.

[5]  Basil Kouvaritakis,et al.  Efficient MPC Optimization using Pontryagin's Minimum Principle , 2006, CDC.

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

[7]  Wook Hyun Kwon,et al.  LQ tracking controls with fixed terminal states and their application to receding horizon controls , 2008, Syst. Control. Lett..

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

[9]  James E. Bobrow,et al.  An efficient sequential linear quadratic algorithm for solving nonlinear optimal control problems , 2005, Proceedings of the 2005, American Control Conference, 2005..

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

[11]  George M. Siouris,et al.  Applied Optimal Control: Optimization, Estimation, and Control , 1979, IEEE Transactions on Systems, Man, and Cybernetics.

[12]  Hussein Jaddu,et al.  Spectral method for constrained linear-quadratic optimal control , 2002, Math. Comput. Simul..

[13]  José A. De Doná,et al.  Solution of the input-constrained LQR problem using dynamic programming , 2007, Syst. Control. Lett..

[14]  R. E. Kalman,et al.  Contributions to the Theory of Optimal Control , 1960 .

[15]  Anil V. Rao,et al.  Practical Methods for Optimal Control Using Nonlinear Programming , 1987 .