NDLI: A parsimonious algorithm for the solution of continuous-time constrained LQR problems with guaranteed convergence

Content Provider	IEEE Xplore Digital Library
Author	Pannocchia, G. Mayne, D.Q. Rawlings, J.B. Mancuso, G.M.
Copyright Year	2013
Description	Author affiliation: Dept. of Civil & Ind. Eng. (DICI), Univ. of Pisa, Pisa, Italy (Pannocchia, G.) \|\| Dept. of Electr. & Electron. Eng., Imperial Coll. London, London, UK (Mayne, D.Q.) \|\| Scuola Superiore Sant'Anna, Pisa, Italy (Mancuso, G.M.) \|\| Dept. of Chem. & Biol. Eng., Univ. of Wisconsin, Madison, WI, USA (Rawlings, J.B.)
Abstract	This paper presents an efficient computational method for solving the input-constrained, continuous time, infinite horizon, linear quadratic regulator problem to within a user specified tolerance. The infinite dimensional input trajectory is approximated with a piecewise linear function on a finite time discretization to ensure input constraint satisfaction. This approximate problem is then a standard finite dimensional quadratic program and is solved by conventional methods, generating an upper bound for the optimal value function. The finite time discretization is then refined by subdividing the intervals estimated to cause the largest decrease in the cost function. Convergence of the solution of this discretized problem towards the optimal continuous-time solution, as the discretization is refined, is proved. Exploiting the strict convexity of the original infinite dimensional problem, the gradient of the cost function with respect to the continuous-time input can be computed to generate a lower bound for the optimal cost. For computational efficiency, a lower bound for the solution of the discretized control at a very fine discretization can be used instead. The algorithm terminates when the difference between the upper and lower bounds meets a user supplied tolerance.
Starting Page	1553
Ending Page	1558
File Size	364257
Page Count	6
File Format	PDF
ISBN	9783033039629
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2013-07-17
Publisher Place	Switzerland
Access Restriction	Subscribed
Rights Holder	EUCA
Subject Keyword	Heuristic algorithms Computational modeling Optimal control Cost function Trajectory Convergence Predictive control
Content Type	Text
Resource Type	Article

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