# Arithmetic-Geometric Mean Robustness for Control from Signal Temporal Logic Specifications

@article{Mehdipour2019ArithmeticGeometricMR, title={Arithmetic-Geometric Mean Robustness for Control from Signal Temporal Logic Specifications}, author={N. Mehdipour and C. Vasile and C. Belta}, journal={2019 American Control Conference (ACC)}, year={2019}, pages={1690-1695} }

We present a new average-based robustness for Signal Temporal Logic (STL) and a framework for optimal control of a dynamical system under STL constraints. By averaging the scores of different specifications or subformulae at different time points, our definition highlights the frequency of satisfaction as well as how robustly each specification is satisfied. Its usefulness in control synthesis problems is illustrated through case studies.

#### 33 Citations

Average-based Robustness for Continuous-Time Signal Temporal Logic

- Computer Science
- 2019 IEEE 58th Conference on Decision and Control (CDC)
- 2019

A new robustness score for continuous-time Signal Temporal Logic specifications is proposed, which uses average scores to extract more information from the signal, emphasizing robust satisfaction of all the specifications’ subformulae over their entire time interval domains. Expand

Control from Signal Temporal Logic Specifications with Smooth Cumulative Quantitative Semantics

- Computer Science
- 2019 IEEE 58th Conference on Decision and Control (CDC)
- 2019

This work proposes a novel smooth STL quantitative semantics called cumulative robustness, and efficiently compute control policies through a series of smooth optimization problems that are solved using gradient ascent algorithms. Expand

A Smooth Robustness Measure of Signal Temporal Logic for Symbolic Control

- Computer Science, Engineering
- IEEE Control Systems Letters
- 2021

This work proposes a novel robustness approximation that is smooth everywhere, sound, and asymptotically complete, while enabling an explicit tradeoff between conservativeness and completeness. Expand

Control Synthesis using Signal Temporal Logic Specifications with Integral and Derivative Predicates

- Computer Science, Engineering
- 2021 American Control Conference (ACC)
- 2021

This paper extends the expressiveness of Signal Temporal Logic (STL) by introducing predicates that can define rich properties related to the integral and derivative of a signal. Expand

On Robustness Metrics for Learning STL Tasks

- Computer Science, Engineering
- 2020 American Control Conference (ACC)
- 2020

It is shown that various desirable properties restrict the form of potential metrics, and a new one is introduced based on the results, and the effectiveness of this new robustness metric for accelerating the learning procedure is demonstrated. Expand

Recurrent Neural Network Controllers for Signal Temporal Logic Specifications Subject to Safety Constraints

- Computer Science, Engineering
- IEEE Control Systems Letters
- 2020

We propose a framework based on Recurrent Neural Networks (RNNs) to determine an optimal control strategy for a discrete-time system that is required to satisfy specifications given as Signal… Expand

Signal Temporal Logic Synthesis as Probabilistic Inference

- Computer Science
- ArXiv
- 2021

The notion of random STL~(RSTL), which extends deterministic STL with random predicates is introduced, which leads to a synthesis-as-inference approach and allows for differentiable, gradient-based synthesis while extending the class of possible uncertain semantics. Expand

Resilient Abstraction-Based Controller Design

- Computer Science
- 2020 59th IEEE Conference on Decision and Control (CDC)
- 2020

This work constructs abstractions which model the impact of occasional high disturbance spikes on the system via so called disturbance edges and shows that the application of resilient reactive synthesis techniques to these abstract models results in closed loop systems which are optimally resilient to these occasionalhigh disturbance spikes. Expand

Efficient Automata-based Planning and Control under Spatio-Temporal Logic Specifications

- Computer Science
- 2020 American Control Conference (ACC)
- 2020

This work considers efficient automata-based planning for continuous-time systems under signal interval temporal logic specifications, an expressive fragment of signal temporal logic. Expand

Trajectory Optimization for High-Dimensional Nonlinear Systems Under STL Specifications

- Computer Science, Engineering
- IEEE Control Systems Letters
- 2021

This letter presents a new trajectory optimization approach for STL synthesis based on Differential Dynamic Programming (DDP), well known that DDP scales well to extremely high-dimensional nonlinear systems like robotic quadrupeds and humanoids, and proves the soundness of the proposed approach and the scalability of the approach. Expand

#### References

SHOWING 1-10 OF 22 REFERENCES

Model predictive control with signal temporal logic specifications

- Computer Science
- 53rd IEEE Conference on Decision and Control
- 2014

This work describes the use of STL to specify a wide range of properties of these systems, including safety, response and bounded liveness, and encode STL specifications as mixed integer-linear constraints on the system variables in the optimization problem at each step of a model predictive control framework. Expand

Reactive synthesis from signal temporal logic specifications

- Engineering, Computer Science
- HSCC
- 2015

We present a counterexample-guided inductive synthesis approach to controller synthesis for cyber-physical systems subject to signal temporal logic (STL) specifications, operating in potentially… Expand

Robust control for signal temporal logic specifications using discrete average space robustness

- Computer Science
- Autom.
- 2019

A robust and computationally efficient model predictive control framework for signal temporal logic specifications is proposed and discrete average space robustness is introduced, a novel quantitative semantic for signalporal logic, that is directly incorporated into the cost function of the model predictive controller. Expand

Robust Satisfaction of Temporal Logic over Real-Valued Signals

- Computer Science
- FORMATS
- 2010

We consider temporal logic formulae specifying constraints in continuous time and space on the behaviors of continuous and hybrid dynamical system admitting uncertain parameters. We present several… Expand

Smooth operator: Control using the smooth robustness of temporal logic

- Computer Science, Mathematics
- 2017 IEEE Conference on Control Technology and Applications (CCTA)
- 2017

This work formalizes the requirements as formulas in Metric Temporal Logic (MTL), and designs a controller that maximizes the robustness of the MTL formula, thus enabling the use of powerful gradient descent optimizers. Expand

Sampling-based synthesis of maximally-satisfying controllers for temporal logic specifications

- Computer Science
- 2017 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS)
- 2017

This work presents an incremental sampling-based algorithm that synthesizes a motion control policy satisfying a bounded Signal Temporal Logic formula over properties of a given environment using a quantitative measure of how well the best path in the current tree of samples satisfies the specification. Expand

An MILP approach for real-time optimal controller synthesis with Metric Temporal Logic specifications

- Mathematics, Computer Science
- 2016 American Control Conference (ACC)
- 2016

The fundamental idea of this work is to synthesize reactive controllers such that closed-loop execution trajectories of the system satisfies desired specifications that ensure correct system… Expand

Monitoring Temporal Properties of Continuous Signals

- Computer Science
- FORMATS/FTRTFT
- 2004

A variant of temporal logic tailored for specifying desired properties of continuous signals, based on a bounded subset of the real-time logic mitl, augmented with a static mapping from continuous domains into propositions is introduced. Expand

Time Robustness in MTL and Expressivity in Hybrid System Falsification

- Computer Science, Mathematics
- CAV
- 2015

AvSTL, an extension of metric interval temporal logic by averaged temporal operators, helps solving falsification problems (searching for a critical path in hybrid system models) by communicating a designer’s intention more faithfully to the stochastic optimization engine employed in a falsification solver. Expand

Linear temporal logic motion planning for teams of underactuated robots using satisfiability modulo convex programming

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

An efficient algorithm for multi-robot motion planning from linear temporal logic (LTL) specifications is presented that is more than one order of magnitude faster than state-of-the-art sampling-based techniques for high-dimensional state spaces while supporting complex missions. Expand