Optimal infinite-horizon control and the stabilization of linear discrete-time systems: State-control constraints and nonquadratic cost functions

Keerthi, S.S.; Gilbert, Éric

doi:10.1109/tac.1986.1104237

Cited by 10 publications

(5 citation statements)

References 5 publications

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“…To improve the conditioning of the optimization, we parameterize the input as u k = Lx k +r k , where L is a linear stabilizing feedback gain for A; B 11,20 The original formulation 1 , 2 can be recovered from 4 , 5 by making the following substitutions into the second formulation:…”

Section: Introductionmentioning

confidence: 99%

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Application of Interior-Point Methods to Model Predictive Control

Rao

Wright

Rawlings

1998

Journal of Optimization Theory and Applications

471

395

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We present a structured interior-point method for the e cient solution of the optimal control problem in model predictive control MPC . The cost of this approach is linear in the horizon length, compared with cubic growth for a naive approach. We use a discrete-time Riccati recursion to solve the linear equations e ciently at each iteration of the interior-point method, and show that this recursion is numerically stable. We demonstrate the e ectiveness of the approach b y applying it to three process control problems.

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Section: Introductionmentioning

confidence: 99%

“…In the language of linear algebra, our modi cation of the block-elimination approach proceeds by partitioning the coe cient matrix in 38 as T 11 : 56…”

mentioning

confidence: 99%

Application of Interior-Point Methods to Model Predictive Control

Rao

Wright

Rawlings

1998

Journal of Optimization Theory and Applications

471

395

View full text Add to dashboard Cite

show abstract

“…If A is unstable, the Riccati recursion might not provide the correct solution to (19). To avoid this, we pre-stabilize the state-space equations using state feedback control, see [26], [27], [28]. That is, we let…”

Section: A Unstable Modelmentioning

confidence: 99%

An ADMM algorithm for solving ℓ<inf>1</inf> regularized MPC

Annergren

Hansson

Wahlberg

2012

2012 IEEE 51st IEEE Conference on Decision and Control (CDC)

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We present an Alternating Direction Method of Multipliers (ADMM) algorithm for solving optimization problems with an 1 regularized least-squares cost function subject to recursive equality constraints. The considered optimization problem has applications in control, for example in 1 regularized MPC. The ADMM algorithm is easy to implement, converges fast to a solution of moderate accuracy, and enables separation of the optimization problem into sub-problems that may be solved in parallel. We show that the most costly step of the proposed ADMM algorithm is equivalent to solving an LQ regulator problem with an extra linear term in the cost function, a problem that can be solved efficiently using a Riccati recursion. We apply the ADMM algorithm to an example of 1 regularized MPC. The numerical examples confirm fast convergence to moderate accuracy and a linear complexity in the MPC prediction horizon.

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“…The optimal control problem is not, however, transformed into a convex problem, because the transformed control and state constraint sets and the transformed cost are no longer necessarily convex. [43,44] employ linear transformation (x(k + 1) = Ax + Buis replaced byx(k + 1) = (A + BK )x + Bv, where v : = u − Kx is the re-parameterized control) to improve conditioning of the optimal control problem solved on-line.…”

Section: Finite Horizon Nmpcmentioning

confidence: 99%

Discrete-Time Model Predictive Control

Li¹,

Xia²,

Fu³

et al. 2012

Advances in Discrete Time Systems

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Optimal infinite-horizon control and the stabilization of linear discrete-time systems: State-control constraints and nonquadratic cost functions

Cited by 10 publications

References 5 publications

Application of Interior-Point Methods to Model Predictive Control

Application of Interior-Point Methods to Model Predictive Control

An ADMM algorithm for solving ℓ<inf>1</inf> regularized MPC

Discrete-Time Model Predictive Control

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Optimal infinite-horizon control and the stabilization of linear discrete-time systems: State-control constraints and nonquadratic cost functions

Cited by 10 publications

References 5 publications

Application of Interior-Point Methods to Model Predictive Control

Application of Interior-Point Methods to Model Predictive Control

An ADMM algorithm for solving &#x2113;<inf>1</inf> regularized MPC

Discrete-Time Model Predictive Control

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An ADMM algorithm for solving ℓ<inf>1</inf> regularized MPC