Optimized State Space Grids for Abstractions

Weber, Alexander; Rungger, Matthias; Reißig, Gunther

doi:10.1109/tac.2016.2642794

Cited by 20 publications

(12 citation statements)

References 25 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…A common first step for symbolic controller synthesis requires abstracting the control system with a continuous state and input space into one with discrete states and inputs. However, this abstraction step has been cited as a key bottleneck in benchmarks for higher-dimensional systems [1] [2]. Many abstraction procedures implemented in current tools traverse the state space in a brute force manner and suffer from an exponential runtime with respect to the sum of state and input dimensions.…”

Section: Introductionmentioning

confidence: 99%

Sparsity-aware finite abstraction

Gruber¹,

Kim²,

Arcak³

2017

2017 IEEE 56th Annual Conference on Decision and Control (CDC)

View full text Add to dashboard Cite

Abstraction of a continuous-space model into a finite state and input dynamical model is a key step in formal controller synthesis tools. To date, these software tools have been limited to systems of modest size (typically ≤ 6 dimensions) because the abstraction procedure suffers from an exponential runtime with respect to the sum of state and input dimensions. We present a simple modification to the abstraction algorithm that dramatically reduces the computation time for systems exhibiting a sparse interconnection structure. This modified procedure recovers the same abstraction as the one computed by a brute force algorithm that disregards the sparsity. Examples highlight speed-ups from existing benchmarks in the literature, synthesis of a safety supervisory controller for a 12-dimensional and abstraction of a 51-dimensional vehicular traffic network.

show abstract

Section: Introductionmentioning

confidence: 99%

Sparsity-aware finite abstraction

Gruber¹,

Kim²,

Arcak³

2017

2017 IEEE 56th Annual Conference on Decision and Control (CDC)

View full text Add to dashboard Cite

show abstract

“…Then, from Lemma 4, there exists q ∈ ∆(q 0 , u 0 ) such that q = (x(τ ), z(τ )) Q0 . By, (14) we also get that q ∈ dom(Θ), which in turn implies by (12) that (x(τ ), z(τ )) ∈ dom(g). Hence, the completeness condition (CC) is satisfied.…”

Section: Proofmentioning

confidence: 88%

“…∀q ∈ dom(Θ), ∀v ∈ Θ(q), ∆(q, v) ⊆ dom(Θ). (14) Let the control map g : X × Z ⇒ U be given by (12). Then, Σ |= s C andΣ satisfies (CC).…”

Section: Proofmentioning

confidence: 99%

See 1 more Smart Citation

Contract-Based Design of Symbolic Controllers for Safety in Distributed Multiperiodic Sampled-Data Systems

Saoud

Girard

Fribourg

2021

IEEE Trans. Automat. Contr.

View full text Add to dashboard Cite

This paper presents a symbolic control approach to the design of distributed safety controllers for a class of continuous-time nonlinear systems. More precisely, we consider systems made of components where each component is equipped with a sampled-data controller with its own sampling period, resulting globally in a distributed multiperiodic sampled-data system. Moreover, controllers receive partial information on the state of the other components. We propose a component-based approach to controller synthesis, which relies on the use of abstractions and continuous-time assume-guarantee contracts. The abstractions describe the dynamics of the system from the point of view of each component based on the information structure, while assume-guarantee contracts specify guarantees that a component must satisfy if assumptions on the other components are met. We show that our approach makes it possible to decompose a global safety control problem into local ones that can be solved independently. We then show how symbolic control techniques can be used to synthesize controllers that enforce the local control objectives. Illustrative applications in building automation and vehicle platooning are shown.

show abstract

“…While the problem is found with all discretization based methods to solve (7), several strategies to somewhat relieve the computational burden that have been proposed, e.g. [53]- [55], could potentially be extended to our setting.…”

Section: Comments On Computational Complexitymentioning

confidence: 99%

Symbolic Optimal Control

Reißig

Rungger

2019

IEEE Trans. Automat. Contr.

Self Cite

View full text Add to dashboard Cite

We present novel results on the solution of a class of leavable, undiscounted optimal control problems in the minimax sense for nonlinear, continuous-state, discrete-time plants. The problem class includes entry-(exit-)time problems as well as minimum time, pursuit-evasion and reach-avoid games as special cases. We utilize auxiliary optimal control problems ("abstractions") to compute both upper bounds of the value function, i.e., of the achievable closed-loop performance, and symbolic feedback controllers realizing those bounds. The abstractions are obtained from discretizing the problem data, and we prove that the computed bounds and the performance of the symbolic controllers converge to the value function as the discretization parameters approach zero. In particular, if the optimal control problem is solvable on some compact subset of the state space, and if the discretization parameters are sufficiently small, then we obtain a symbolic feedback controller solving the problem on that subset. These results do not assume the continuity of the value function or any problem data, and they fully apply in the presence of hard state and control constraints.

show abstract

Optimized State Space Grids for Abstractions

Cited by 20 publications

References 25 publications

Sparsity-aware finite abstraction

Sparsity-aware finite abstraction

Contract-Based Design of Symbolic Controllers for Safety in Distributed Multiperiodic Sampled-Data Systems

Symbolic Optimal Control

Contact Info

Product

Resources

About