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A characterization of convex problems in decentralized control

by Michael Rotkowitz, Sanjay Lall - IEEE Transactions on Automatic Control
"... Abstract—We consider the problem of constructing optimal decentralized controllers. We formulate this problem as one of minimizing the closed-loop norm of a feedback system subject to constraints on the controller structure. We define the notion of quadratic invariance of a constraint set with respe ..."
Abstract - Cited by 133 (24 self) - Add to MetaCart
Abstract—We consider the problem of constructing optimal decentralized controllers. We formulate this problem as one of minimizing the closed-loop norm of a feedback system subject to constraints on the controller structure. We define the notion of quadratic invariance of a constraint set

Loop invariant synthesis in a combined domain

by Shengchao Qin, Guanhua He, Chenguang Luo, Wei-ngan Chin - IN: ICFEM , 2010
"... Automated verification of memory safety and functional correctness for heap-manipulating programs has been a challenging task, especially when dealing with complex data structures with strong invariants involving both shape and numerical properties. Existing verification systems usually rely on us ..."
Abstract - Cited by 5 (3 self) - Add to MetaCart
information. Our loop invariant synthesis is conducted automatically by a fixpoint iteration process, equipped with newly designed abstraction mechanism, and join and widening operators. Initial experiments have confirmed that we can synthesise loop invariants with non-trivial constraints.

Refinement and Term Synthesis in Loop Invariant Generation

by Ewen Maclean, Andrew Irel, Robert Atkey, Lucas Dixon - 2nd International Workshop on Invariant Generation (WING’09 , 2009
"... We present a technique for refining incorrect or insufficiently strong loop invariants in correctness proofs for imperative programs. We rely on previous work [16] in combining program analysis and Proof Planning, and exploit IsaPlanner’s use of meta-variables and goal-naming to generate correct loo ..."
Abstract - Cited by 3 (2 self) - Add to MetaCart
We present a technique for refining incorrect or insufficiently strong loop invariants in correctness proofs for imperative programs. We rely on previous work [16] in combining program analysis and Proof Planning, and exploit IsaPlanner’s use of meta-variables and goal-naming to generate correct

Loop Invariant Synthesis in a Combined Abstract Domain

by Shengchao Qin, Guanhua He , Chenguang Luo , Wei-ngan Chin , Xin Chen , 2012
"... Automated verification of memory safety and functional correctness for heap-manipulating programs has been a challenging task, especially when dealing with complex data structures with strong invariants involving both shape and numerical properties. Existing verification systems usually rely on user ..."
Abstract - Cited by 1 (0 self) - Add to MetaCart
on users to supply annotations to guide the verification, which can be cumbersome and error-prone by hand and can significantly restrict the usability of the verification system. In this paper, we reduce the need for some user annotations by automatically inferring loop invariants over an abstract domain

Termination analysis of integer linear loops

by Aaron R. Bradley, Zohar Manna, Henny B. Sipma - In CONCUR , 2005
"... Abstract. Usually, ranking function synthesis and invariant generation over a loop with integer variables involves abstracting the loop to have real variables. Integer division and modulo arithmetic must be soundly abstracted away so that the analysis over the abstracted loop is sound for the origin ..."
Abstract - Cited by 34 (3 self) - Add to MetaCart
Abstract. Usually, ranking function synthesis and invariant generation over a loop with integer variables involves abstracting the loop to have real variables. Integer division and modulo arithmetic must be soundly abstracted away so that the analysis over the abstracted loop is sound

Linear ranking with reachability

by Aaron R. Bradley, Zohar Manna, Henny B. Sipma - In CAV , 2005
"... Abstract. We present a complete method for synthesizing lexicographic linear ranking functions supported by inductive linear invariants for loops with linear guards and transitions. Proving termination via linear ranking functions often requires invariants; yet invariant generation is expensive. Thu ..."
Abstract - Cited by 76 (10 self) - Add to MetaCart
Abstract. We present a complete method for synthesizing lexicographic linear ranking functions supported by inductive linear invariants for loops with linear guards and transitions. Proving termination via linear ranking functions often requires invariants; yet invariant generation is expensive

Automatic Synthesis of Piecewise Linear Quadratic Invariants for Programs?

by Assalé Adjé, Pierre-loïc Garoche
"... Abstract. Among the various critical systems that worth to be for-mally analyzed, a wide set consists of controllers for dynamical systems. Those programs typically execute an infinite loop in which simple com-putations update internal states and produce commands to update the system state. Those sy ..."
Abstract - Cited by 1 (0 self) - Add to MetaCart
Abstract. Among the various critical systems that worth to be for-mally analyzed, a wide set consists of controllers for dynamical systems. Those programs typically execute an infinite loop in which simple com-putations update internal states and produce commands to update the system state. Those

Internal quadratic invariance and decentralized control

by Laurent Lessard , Sanjay Lall - In American Control Conference , 2010
"... Abstract For decentralized control systems with quadratically invariant information constraints, the set of achievable closed-loop maps is affine, and thus the associated minimum-norm controller synthesis problem is amenable to a convex programming approach. In this paper, we show that a strictly b ..."
Abstract - Cited by 3 (3 self) - Add to MetaCart
Abstract For decentralized control systems with quadratically invariant information constraints, the set of achievable closed-loop maps is affine, and thus the associated minimum-norm controller synthesis problem is amenable to a convex programming approach. In this paper, we show that a strictly

A Transformational Approach for Generating Non-Linear Invariants

by S. Bensalem, M. Bozga, J.-C. Fernandez, L. Ghirvu, Y. Lakhnech - IN STATIC ANALYSIS SYMPOSIUM (JUNE 2000 , 2000
"... Computing invariants is the key issue in the analysis of infinite-state systems whether analysis means testing, verification or parameter synthesis. In particular, methods that allow to treat combinations of loops are of interest. We present a set of algorithms and methods that can be applied to cha ..."
Abstract - Cited by 7 (0 self) - Add to MetaCart
Computing invariants is the key issue in the analysis of infinite-state systems whether analysis means testing, verification or parameter synthesis. In particular, methods that allow to treat combinations of loops are of interest. We present a set of algorithms and methods that can be applied

The polyranking principle

by Aaron R. Bradley, Zohar Manna, Henny B. Sipma - In ICALP , 2005
"... Abstract. Although every terminating loop has a ranking function, not every loop has a ranking function of a restricted form, such as a lexicographic tuple of polynomials over program variables. The polyranking principle is proposed as a generalization of polynomial ranking for analyzing termination ..."
Abstract - Cited by 50 (3 self) - Add to MetaCart
termination of loops. We define lexicographic polyranking functions in the context of loops with parallel transitions consisting of polynomial assertions, including inequalities, over primed and unprimed variables. Next, we address synthesis of these functions with a complete and automatic method
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