Counter-Example Guided Synthesis of control Lyapunov functions for switched systems

Ravanbakhsh, Hadi; Sankaranarayanan, Sriram

doi:10.1109/cdc.2015.7402879

Cited by 34 publications

(49 citation statements)

References 30 publications

(50 reference statements)

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“…for the DC-DC boost converter the authors of [33] had to iteratively add barrier functions by hand before a solution was found. Moreover, in our benchmarks we synthesize sampled-data controllers with a larger sampling time than the minimum dwell-times presented in [33,49]. Finally, we are not able to find sampled-data controllers for all systems in Table 1 (systems 3 and 4) as opposed to our previous work [38].…”

Section: Discussionmentioning

confidence: 84%

Formal Controller Synthesis via Genetic Programming

Verdier

Mazo

2017

IFAC-PapersOnLine

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This paper proposes a framework for automatic formal controller synthesis for general hybrid systems with a subset of safety and reachability specifications. The framework uses genetic programming to automatically co-synthesize controllers and candidate Lyapunov-like functions. These candidate Lyapunov-like functions are used to formally verify the control specification, and their correctness is proven using a Satisfiability Modulo Theories solver. The advantages of this approach are: no restriction is made to polynomial systems, the synthesized controllers are expressed as compact expressions, and no explicit solution structure has to be specified beforehand. We demonstrate the effectiveness of the proposed framework in several case studies, including nonpolynomial systems, sampled-data systems, systems with bounded uncertainties, switched systems, and systems with jumps.

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Section: Discussionmentioning

confidence: 84%

Formal Controller Synthesis via Genetic Programming

Verdier

Mazo

2017

IFAC-PapersOnLine

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“…In the setting of this paper, however, the use of a MPC scheme as a demonstrator allows us to use faster LP solvers and provide convergence guarantees. Empirically, we are able to demonstrate the successful inference of CLFs on systems with up to eight state variables, whereas previous work in this space has been restricted to much smaller problems [77].…”

Section: Counter-example Guided Inductive Synthesismentioning

confidence: 84%

“…Sontag formula can be extended to systems with saturated inputs where U is an n-ball [53] or a polytope [91]. Also switching-based feedback is possible, under some mild assumptions (to avoid Zeno behavior) [22,77]. We assume dynamics are affine in control and use these results which reduce Problem 1 to that of finding a control Lyapunov function V .…”

Section: Definition 3 (Control Lyapunov Function(clf))mentioning

confidence: 99%

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Learning control lyapunov functions from counterexamples and demonstrations

Ravanbakhsh

Sankaranarayanan

2018

Auton Robot

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We present a technique for learning control Lyapunov-like functions, which are used in turn to synthesize controllers for nonlinear dynamical systems that can stabilize the system, or satisfy specifications such as remaining inside a safe set, or eventually reaching a target set while remaining inside a safe set. The learning framework uses a demonstrator that implements a black-box, untrusted strategy presumed to solve the problem of interest, a learner that poses finitely many queries to the demonstrator to infer a candidate function, and a verifier that checks whether the current candidate is a valid control Lyapunov function. The overall learning framework is iterative, eliminating a set of candidates on each iteration using the counterexamples discovered by the verifier and the demonstrations over these counterexamples. We prove its convergence using ellipsoidal approximation techniques from convex optimization. We also implement this scheme using nonlinear MPC controllers to serve as demonstrators for a set of state and trajectory stabilization problems for nonlinear dynamical systems. We show how the verifier can be constructed efficiently using convex relaxations of the verification problem for polynomial systems to semi-definite programming (SDP) problem instances. Our approach is able to synthesize relatively simple polynomial control Lyapunov functions, and in that process replace the MPC using a guaranteed and computationally less expensive controller.

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“…In the second phase, a counterexample guided inductive synthesis (CEGIS) framework [26], -an approach that uses SMT solvers at its core -is used to discover such control certificates. However, this procedure is used off the shelf, building upon the previous work of Ravanbakhsh et al [22]. This procedure uses a specialized solver for finding a certificate of a given parametric form that handles quantified formulas by alternating between a series of quantifier free formulas using existing SMT solvers [18,3].…”

Section: Introductionmentioning

confidence: 99%

A Class of Control Certificates to Ensure Reach-While-Stay for Switched Systems

Ravanbakhsh

Sankaranarayanan

2017

Electron. Proc. Theor. Comput. Sci.

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In this article, we consider the problem of synthesizing switching controllers for temporal properties through the composition of simple primitive reach-while-stay (RWS) properties. Reach-while-stay properties specify that the system states starting from an initial set I, must reach a goal (target) set G in finite time, while remaining inside a safe set S. Our approach synthesizes switched controllers that select between finitely many modes to satisfy the given RWS specification. To do so, we consider control certificates, which are Lyapunov-like functions that represent control strategies to achieve the desired specification. However, for RWS problems, a control Lyapunov-like function is often hard to synthesize in a simple polynomial form. Therefore, we combine control barrier and Lyapunov functions with an additional compatibility condition between them. Using this approach, the controller synthesis problem reduces to one of solving quantified nonlinear constrained problems that are handled using a combination of SMT solvers. The synthesis of controllers is demonstrated through a set of interesting numerical examples drawn from the related work, and compared with the state-of-theart tool SCOTS. Our evaluation suggests that our approach is computationally feasible, and adds to the growing body of formal approaches to controller synthesis.

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Counter-Example Guided Synthesis of control Lyapunov functions for switched systems

Cited by 34 publications

References 30 publications

Formal Controller Synthesis via Genetic Programming

Formal Controller Synthesis via Genetic Programming

Learning control lyapunov functions from counterexamples and demonstrations

A Class of Control Certificates to Ensure Reach-While-Stay for Switched Systems

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