Controller synthesis with inductive proofs for piecewise linear systems: An SMT-based algorithm

Huang, Zhengxu; Wang, Yu; Mitra, Sayan; Dullerud, Geir E.; Chaudhuri, Swarat

doi:10.1109/cdc.2015.7403394

Cited by 17 publications

(15 citation statements)

References 23 publications

(28 reference statements)

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“…Bessa et al [12] employed DSVerifier to find FWL problems in controllers implementations in direct-and delta-form realizations. Recent studies [10], [33], [34] apply SMT-based verification to controllers synthesis.…”

Section: Related Workmentioning

confidence: 99%

Formal Non-Fragile Stability Verification of Digital Control Systems with Uncertainty

Bessa

Ismail²,

Palhares

et al. 2017

IEEE Trans. Comput.

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A verification methodology is described and evaluated to formally determine uncertain linear systems stability in digital controllers with considerations to the implementation aspects. In particular, this methodology is combined with the digital-system verifier (DSVerifier), which is a verification tool that employs Bounded Model Checking based on Satisfiability Modulo Theories to check the stability of digital control systems with uncertainty. DSVerifier determines the control system stability, considering all the plant interval variation set, together with the Finite Word-length (FWL) effects in the digital controller implementation; DSVerifier checks the robust non-fragile stability of a given closed-loop system. The proposed methodology and respective tool are evaluated considering non-fragile control examples from literature. Experimental results show that the approach used in this study is able to foresee fragility problems in robust controllers, which could be overlooked by other existing approaches due to underestimating of FWL effects.

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Section: Related Workmentioning

confidence: 99%

Formal Non-Fragile Stability Verification of Digital Control Systems with Uncertainty

Bessa

Ismail²,

Palhares

et al. 2017

IEEE Trans. Comput.

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show abstract

“…In most of these methods, the control input has a fixed form. This fixed form can be a polynomial (in state variables) which yields a static feedback controller [29,12] or a control table [14].…”

Section: Related Workmentioning

confidence: 99%

“…This model is input to a RCLF synthesis tool to generate coefficients of V . After acquiring V , offline computations are needed to compute the minimum dwell time δ and check Equations (14) and (15).…”

Section: Controller Synthesismentioning

confidence: 99%

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Robust controller synthesis of switched systems using counterexample guided framework

Ravanbakhsh

Sankaranarayanan

2016

Proceedings of the 13th International Conference on Embedded Software

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We investigate the problem of synthesizing robust controllers that ensure that the closed loop satisfies an input reach-while-stay specification, wherein all trajectories starting from some initial set I, eventually reach a specified goal set G, while staying inside a safe set S. Our plant model consists of a continuous-time switched system controlled by an external switching signal and plant disturbance inputs. The controller uses a state feedback law to control the switching signal in order to ensure that the desired correctness properties hold, regardless of the disturbance actions. Our approach uses a proof certificate in the form of a robust control Lyapunov-like function (RCLF) whose existence guarantees the reach-while-stay specification. A counterexample guided inductive synthesis (CEGIS) framework is used to find a RCLF by solving a ∃∀∃∀ formula iteratively using quantifier free SMT solvers. We compare our synthesis scheme against a common approach that fixes disturbances to nominal values and synthesizes the controller, ignoring the disturbance. We demonstrate that the latter approach fails to yield a robust controller over some benchmark examples, whereas our approach does. Finally, we consider the problem of translating the RCLF synthesized by our approach into a control implementation. We outline the series of offline and real-time computation steps needed. The synthesized controller is implemented and simulated using the Matlab(tm)/Simulink(tm) model-based design framework, and illustrated on some examples.

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“…The policy synthesis problem asks for a controller that satisfies a given formal specification. This problem has been considered through many formal synthesis approaches in the recent past [22], [16], [6], [27], [21]. In the subsequent section, we will describe the specific setup considered in this paper.…”

Section: Introductionmentioning

confidence: 99%

Formal Policy Learning from Demonstrations for Reachability Properties

Ravanbakhsh

Sankaranarayanan

Seshia

2019

2019 International Conference on Robotics and Automation (ICRA)

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We consider the problem of learning structured, closed-loop policies (feedback laws) from demonstrations in order to control under-actuated robotic systems, so that formal behavioral specifications such as reaching a target set of states are satisfied. Our approach uses a "counterexample-guided" iterative loop that involves the interaction between a policy learner, a demonstrator and a verifier. The learner is responsible for querying the demonstrator in order to obtain the training data to guide the construction of a policy candidate. This candidate is analyzed by the verifier and either accepted as correct, or rejected with a counterexample. In the latter case, the counterexample is used to update the training data and further refine the policy.The approach is instantiated using receding horizon modelpredictive controllers (MPCs) as demonstrators. Rather than using regression to fit a policy to the demonstrator actions, we extend the MPC formulation with the gradient of the cost-to-go function evaluated at sample states in order to constrain the set of policies compatible with the behavior of the demonstrator. We demonstrate the successful application of the resulting policy learning schemes on two case studies and we show how simple, formally-verified policies can be inferred starting from a complex and unverified nonlinear MPC implementations. As a further benefit, the policies are many orders of magnitude faster to implement when compared to the original MPCs.

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Controller synthesis with inductive proofs for piecewise linear systems: An SMT-based algorithm

Cited by 17 publications

References 23 publications

Formal Non-Fragile Stability Verification of Digital Control Systems with Uncertainty

Formal Non-Fragile Stability Verification of Digital Control Systems with Uncertainty

Robust controller synthesis of switched systems using counterexample guided framework

Formal Policy Learning from Demonstrations for Reachability Properties

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