On constrained infinite-time linear quadratic optimal control

Chmielewski, Donald J.; Manousiouthakis, Vasilios I.

doi:10.1109/cdc.1996.572684

Cited by 58 publications

(105 citation statements)

References 14 publications

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“…LQR can be easily derived by solving a Riccati equation. The resulting MPC control law, with the corresponding terminal weight and the terminal constraint, is indeed an optimal feedback controller for the infinite horizon problem if the terminal constraint remains inactive [25][26][27]. If the terminal constraint does become active, it loses the optimality property as it implies that the computed moves may be different from the optimal ones without the constraint.…”

Section: Stability Resultsmentioning

confidence: 98%

Model predictive control: Review of the three decades of development

Lee

2011

Int. J. Control Autom. Syst.

550

254

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Three decades have passed since milestone publications by several industrialists spawned a flurry of research and industrial / commercial activities on model predictive control (MPC). This article reviews major developments and achievements during the three decades and attempts to put a perspective on them. The first decade is characterized by the fast-growing industrial adoption of the technology, primarily in the refining and petrochemical sectors, which sparked much interest and also confusion among the academicians. The second decade saw a number of significant advances in understanding the MPC from a control theoretician's viewpoint, which included state-space interpretations / formulations and stability proofs. These theoretical triumphs contributed to the makings of the second generation of commercial software, which was significantly enhanced in generality and rigor. The third decade's main focus has been on the development of "fast MPC," a term chosen to collectively describe the various efforts to bring orders-of-magnitude improvement in the efficiency of the on-line computation so that the technology can be applied to systems requiring very fast sampling rates. Throughout the three decades of the development, theory and practice supported each other quite effectively, a primary reason for the fast and steady rise of the technology.

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Section: Stability Resultsmentioning

confidence: 98%

Model predictive control: Review of the three decades of development

Lee

2011

Int. J. Control Autom. Syst.

550

254

View full text Add to dashboard Cite

show abstract

“…So depending on the stability properties of the chosen MPC, switching may or may not occur, and if it occurs, it can take place near or far from the origin. Finally, we note that the notion of "switching" from a predictive to an unconstrained LQR controller, for times beyond a ÿnite control horizon, has been used in Sznaier and Damborg (1987), Chmielewski and Manousiouthakis (1996), and Scokaert and Rawlings (1998), in the context of determining a ÿnite horizon that solves the inÿnite horizon constrained LQR problem.…”

Section: Switching Using Advanced Mpc Formulationsmentioning

confidence: 99%

“…An important issue in the practical implementation of MPC is the selection of the horizon length. It is well known that this selection can have a profound e ect on nominal closed-loop stability, and results are available in the literature that establish, under certain assumptions, the existence of "su ciently large" ÿnite horizons that ensure stability (e.g., Rawlings & Muske, 1993;Chmielewski & Manousiouthakis, 1996). However, a priori knowledge (without closed-loop simulations) of the minimum horizon length that guarantees feasibility or closed-loop stability, from an arbitrary initial condition, is currently not available.…”

Section: Switching Using Advanced Mpc Formulationsmentioning

confidence: 99%

Uniting bounded control and MPC for stabilization of constrained linear systems

2004

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“…This realization, together with the prevalence of hard constraints in control applications, has consequently fostered a large and growing body of research work on control of systems subject to input constraints. Examples include results on constrained optimal quadratic control [6,7], model predictive control [8] and feedback stabilization [9][10][11][12]. The GSP for linear systems without delays has been solved in existing literature, whereas a solution to the linear systems with time delay is not known to our knowledge.…”

Section: Introductionmentioning

confidence: 98%