Sound and Automated Synthesis of Digital Stabilizing Controllers for Continuous Plants

Modern control is implemented with digital microcontrollers, embedded within a dynamical plant that represents physical components. We present a new algorithm based on counter-example guided inductive synthesis that automates the design of digital controllers that are correct by construction. The synthesis result is sound with respect to the complete range of approximations, including time discretization, quantization effects, and finite-precision arithmetic and its rounding errors. We have implemented our new algorithm in a tool called DSSynth, and are able to automatically generate stable controllers for a set of intricate plant models taken from the literature within minutes.Comment: 10 page

Formal Verification of a Rover Anti-collision System

In this paper, we integrate inductive proof, bounded model checking, test case generation and equivalence proof techniques to verify an embedded system. This approach is implemented using Systerel Smart Solver (S3) toolset. It is applied to verify properties at system, software, and code levels. The verification process is illustrated on an anti-collision system (ARP for Automatic Rover Protection) implemented on-board a rover. Focus is placed on the verification of safety and functional properties and the proof of equivalence between the design model and the generated code

Automated formal synthesis of provably safe digital controllers for continuous plants

Abstract: We present a sound and automated approach to synthesizing safe, digital controllers for physical plants represented as time-invariant models. Models are linear differential equations with inputs, evolving over a continuous state space. The synthesis precisely accounts for the effects of finite-precision arithmetic introduced by the controller. The approach uses counterexample-guided inductive synthesis: an inductive generalization phase produces a controller that is known to stabilize the model but that may not be safe for all initial conditions of the model. Safety is then verified via bounded model checking: if the verification step fails, a counterexample is provided to the inductive generalization, and the process further iterates until a safe controller is obtained. We demonstrate the practical value of this approach by automatically synthesizing safe controllers for physical plant models from the digital control literature

Closed loop analysis of control command software

International audienceRecent work addressing the stability analysis of controllers at code level has been mainly focused on the controller alone. However, most of the properties of interest of control software lie in how they interact with their environment. We introduce an extension of the analysis framework to reason on the stability of closed loop systems, i.e., controllers along with a model of their physical environment, the plant. The proposed approach focuses on the closed loop stability of discrete linear control systems with saturations, interacting with a discrete linear plant. The analysis is performed in the state space domain using Lyapunov-based quadratic invariants. We specifically address the automatic synthesis of such invariants and the treatment of floating-point imprecision