Optimal Control Strategies for Robust Certification

Leyendecker, Sigrid; Lucas, Leonard J.; Owhadi, Houman; Ortiz, Michael

doi:10.1115/1.4001375

Cited by 6 publications

(3 citation statements)

References 16 publications

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“…5 This is in contrast to other approaches in robust optimal control, where, for example, the probability of a state constraint violation is required to be less than some small, but given probability, which is then included as an inequality constraint or as new single objective function in the optimal control problem (see e.g. [94]). Instead, Equation (3.8) is treated as an additional objective functional in the optimal control problem.…”

Section: Optimal Control With Uncertaintymentioning

confidence: 96%

Methods of Improving the Dependability of Self-optimizing Systems

Dorociak

Gausemeier

2014

Lecture Notes in Mechanical Engineering

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Abstract. Various methods have been developed in the Collaborative ResearchCenter 614 which can be used to improve the dependability of self-optimizing systems. These methods are presented in this chapter. They are sorted into two categories with regard to the development process of self-optimizing systems. On one hand, there are methods which can be applied during the Conceptual Design Phase. On the other hand, there are methods that are applicable during Design and Development.There are domain-spanning methods as well as methods that have been specifically developed for particular domains, e.g., software engineering or control engineering. The methods address different attributes of dependability, such as reliability, availability or safety.Each section is prefaced with a short overview of the classification of the described method regarding the corresponding domain(s), as well as its dependability attributes, to provide the reader with a brief outline of the methods' areas of application. Information about independently applicable methods or existing relationships and interactions with other methods or third-party literature is also provided.The development process for self-optimizing mechatronic systems which was introduced in Chap. 2 consists of two main phases: Conceptual Design and Design and Development. The main result of the Conceptual Design is the Principle Solution, which includes all information required for the concrete development during the second phase. Conceptual Design PhaseEven as early as during the specification of the Principle Solution, the dependability of self-optimizing mechatronic systems can be evaluated and improved by employing appropriate methods. The result is an improved Principle Solution, as such methods take the whole system into account before splitting it up into domain-specific tasks for the following development phase.

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Section: Optimal Control With Uncertaintymentioning

confidence: 96%

Methods of Improving the Dependability of Self-optimizing Systems

Dorociak

Gausemeier

2014

Lecture Notes in Mechanical Engineering

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“…This problem is solved numerically using a simulated annealing algorithm for the optimisation and discretising the dynamics (2) via a variational integrator, see [2].…”

Section: Concentration-of-measure Inequalities For Uncertainty Quantimentioning

confidence: 99%

Certification with optimal control strategies

Leyendecker

Lucas

Owhadi

et al. 2010

Proc Appl Math and Mech

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The optimal control methodology called concentration-of-measure optimal control (COMOC), seeks to minimise a concentration-of-measure upper bound on the probability of failure of an uncertain system. This bound is computed for a system characterised by a single performance measure depending on random inputs.This work considers controlled multibody dynamics taking place in an uncertain environment. The goal is to quantify uncertainty in a controlled robot manoeuvre and to minimise the probability of failure with regard to a performance measure. First, a deterministic optimal control problem is solved, yielding state and control trajectories that minimise an objective function. Boundary conditions for the optimal control problem are chosen such that the system performs ideally in the sense of the performance measure. Secondly, the obtained manoeuvre is reconsidered in the presence of uncertainty. Using a concentration-of-measure inequality, a rigorous upper bound for the probability of failure is derived. Finally, an optimisation is performed that searches for a control sequence (in the neighbourhood of the given one), that minimises the probability of failure.

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“…Our approximate approach to estimate DOS of SAT instances exploits the concentration of measure inequalities (Boucheron, Lugosi, & Massart, 2013). These inequalities provide bounds on the tails of the distributions of random functions and have been used to construct the theory of generalization in machine learning (Abu-Mostafa, Magdon-Ismail, & Lin, 2012), compute optimal bounds on uncertainty (Owhadi, Scovel, Sullivan, McKerns, & Ortiz, 2013), certify systems (Leyendecker, Lucas, Owhadi, & Ortiz, 2010), compute bias of statistical estimators (Gourgoulias, Katsoulakis, Rey-Bellet, & Wang, 2017), and derive results in random matrix theory (Tao, 2012).…”

Section: Introductionmentioning

confidence: 99%

Estimating the Density of States of Boolean Satisfiability Problems on Classical and Quantum Computing Platforms

Sahai¹,

Mishra²,

Pasini³

et al. 2019

Preprint

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Given a Boolean formula φ(x) in conjunctive normal form (CNF), the density of states counts the number of variable assignments that violate exactly e clauses, for all values of e. Thus, the density of states is a histogram of the number of unsatisfied clauses over all possible assignments. This computation generalizes both maximum-satisfiability (MAX-SAT) and model counting problems and not only provides insight into the entire solution space, but also yields a measure for the hardness of the problem instance. Consequently, in real-world scenarios, this problem is typically infeasible even when using state-of-the-art algorithms. While finding an exact answer to this problem is a computationally intensive task, we propose a novel approach for estimating density of states based on the concentration of measure inequalities. The methodology results in a quadratic unconstrained binary optimization (QUBO), which is particularly amenable to quantum annealing-based solutions. We present the overall approach and compare results from the D-Wave quantum annealer against the best-known classical algorithms such as the Hamze-de Freitas-Selby (HFS) algorithm and satisfiability modulo theory (SMT) solvers.

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Optimal Control Strategies for Robust Certification

Cited by 6 publications

References 16 publications

Methods of Improving the Dependability of Self-optimizing Systems

Methods of Improving the Dependability of Self-optimizing Systems

Certification with optimal control strategies

Estimating the Density of States of Boolean Satisfiability Problems on Classical and Quantum Computing Platforms

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