Admissible sets and feedback control for discrete-time linear dynamical systems with bounded controls and states

Gutman, Per‐Olof; Ćwikel, Michael

doi:10.1109/cdc.1984.272428

Cited by 54 publications

(95 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…It is worth to note that the proposed parametrization recovers the parametrization proposed in [4] whenever S is a controlled (1, λ)-contractive set, i.e., a standard controlled λ-contractive set.…”

Section: A Periodic Conewise Linear Control Lawsmentioning

confidence: 99%

“…The corresponding values were found to be k = 3 and λ = 0.99. The simplicial decompositions {D s i } s∈N [1,4] T can be seen in Figure 4. Moreover, the control effort d t := π(z t − z s ) + d s for the zero initial state, where π(·) corresponds to the control law (19), (20), is shown in Figure 5.…”

Section: Remarkmentioning

confidence: 99%

“…The concept of controlled λ-contractive sets was utilized in several methods for synthesis of stabilizing control laws for constrained linear systems. Most of these methods generate either conewise linear control laws [4], [5], which require the solution of a point location problem at every time instant, or vertex-interpolation control laws, which require the solution of a linear program at every time instant [6]- [9].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

On constrained stabilization of discrete-time linear systems

Αθανασόπουλος

Doban

Lazăr

2013

21st Mediterranean Conference on Control and Automation

View full text Add to dashboard Cite

Section: A Periodic Conewise Linear Control Lawsmentioning

confidence: 99%

Section: Remarkmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

On constrained stabilization of discrete-time linear systems

Αθανασόπουλος

Doban

Lazăr

2013

21st Mediterranean Conference on Control and Automation

View full text Add to dashboard Cite

“…In [14] it has been proved that, if the region defined by the set of feasible state + input vectors is bounded and contains the final state + input in its interior, an infinite horizon problem may be reduced to a finite horizon problem by appropriately choosing a finite value of N . In such a case the optimal control law after the finite horizon is taken equal to the unconstrained infinite horizon LQR problem with weights Q and R.…”

Section: Explicit Mpc -Finite Horizonmentioning

confidence: 99%

Optimal Model Predictive Control of Timed Continuous Petri Nets

Mahulea

Giua

Recalde

et al. 2008

IEEE Trans. Automat. Contr.

View full text Add to dashboard Cite

This paper addresses the optimal control problem of timed continuous Petri nets under infinite servers semantics. In particular, our goal is to find a control input optimizing a certain cost function that permits the evolution from an initial marking (state) to a desired steady-state. The solution we propose is based on a particular discrete-time representation of the controlled continuous Petri net system, as a certain linear constrained system. An upper bound on the sample period is given in order to preserve important information of the timed continuous net, in particular the positiveness of the markings. The reachability space of the sampled system in relation to autonomous continuous Petri nets is also studied.Based on the resulting linear constrained model, the optimal control problem is studied through Model Predictive Control (MPC). Implicit and explicit procedures are presented together with a comparison between the two schemes. Stability of the closed-loop system is also studied.

show abstract

“…This article proposes a different approach to stabilization of large scale linear systems, which is based on a recent relaxation of the standard control Lyapunov function (CLF) notion , i.e., finite-time control Lyapunov functions. Similarly to standard synthesis methods based on polyhedral CLFs, see, e.g., (Gutman and Cwikel, 1986), finite-time polyhedral CLFs can be employed to compute stabilizing periodic vertex-control laws, while the actual control law is obtained by periodic interpolation among the vertexcontrol laws . However, in contrast to the standard CLF case, any choice within the class of Minkowski (or gauge) functions of proper C-sets provides a valid finite-time CLF candidate.…”

Section: Introductionmentioning

confidence: 99%

Scalable Stabilization of Large Scale Discrete-time Linear Systems via the 1-norm

Αθανασόπουλος

Lazăr

2013

IFAC Proceedings Volumes

View full text Add to dashboard Cite

This article reconsiders the stabilizing controller synthesis problem for discrete-time linear systems with a focus on systems of large scale. In this case, existing solutions are either not scalable, and thus, not tractable, or conservative. This motivates us to exploit finite-time control Lyapunov functions (CLFs), i.e., a relaxation of the standard CLF concept, to obtain a nonconservative and scalable synthesis method. The main idea is to employ Minkowski functions of a particular family of polytopic sets, which includes the hyper-rhombus induced by the 1-norm, as candidate finite-time CLFs. This choice results in explicit periodic vertex-interpolation control laws, which are globally stabilizing. The vertex-control laws can be computed offline using distributed optimization, in a scalable fashion, while the actual control law comes in an explicit, distributed form. Large scale illustrative examples demonstrate the effectiveness of the proposed approach.

show abstract

Admissible sets and feedback control for discrete-time linear dynamical systems with bounded controls and states

Cited by 54 publications

References 0 publications

On constrained stabilization of discrete-time linear systems

On constrained stabilization of discrete-time linear systems

Optimal Model Predictive Control of Timed Continuous Petri Nets

Scalable Stabilization of Large Scale Discrete-time Linear Systems via the 1-norm

Contact Info

Product

Resources

About