Physical Interpretations of Negative Imaginary Systems Theory

This paper presents some physical interpretations of recent stability results on the feedback interconnection of negative imaginary systems. These interpretations involve spring mass damper systems coupled together by springs or RLC electrical networks coupled together via inductors or capacitors.Comment: To appear in the Proceedings of the 10th ASIAN CONTROL CONFERENCE 201

The Dynamics of Group Codes: Dual Abelian Group Codes and Systems

Fundamental results concerning the dynamics of abelian group codes (behaviors) and their duals are developed. Duals of sequence spaces over locally compact abelian groups may be defined via Pontryagin duality; dual group codes are orthogonal subgroups of dual sequence spaces. The dual of a complete code or system is finite, and the dual of a Laurent code or system is (anti-)Laurent. If C and C^\perp are dual codes, then the state spaces of C act as the character groups of the state spaces of C^\perp. The controllability properties of C are the observability properties of C^\perp. In particular, C is (strongly) controllable if and only if C^\perp is (strongly) observable, and the controller memory of C is the observer memory of C^\perp. The controller granules of C act as the character groups of the observer granules of C^\perp. Examples of minimal observer-form encoder and syndrome-former constructions are given. Finally, every observer granule of C is an "end-around" controller granule of C.Comment: 30 pages, 11 figures. To appear in IEEE Trans. Inform. Theory, 200

Structured singular value of implicit systems

Implicit systems provide a general framework in which many important properties of dynamic systems can be studied. Implicit systems are especially relevant to behavioural systems theory, the analysis and synthesis of complex interconnected systems, systems identification and robust control. By incorporating algebraic constraints, implicit models provide additional versatility relative to the standard input–output framework. Problems of robust stability in implicit systems lead in a natural way to non‐standard structured singular value (μ) formulations. In this note, it is shown that for a class of uncertainty structures involving repeated scalar parameters, these problems reduce to a standard μ problem which is well studied and for the solution of which several numerical algorithms are available. Our results are based on a matrix dilation technique and the redefinition of the uncertainty structure of the transformed problem. The main results of the paper are illustrated with a numerical example

Distributionally Robust Chance Constrained Data-enabled Predictive Control

We study the problem of finite-time constrained optimal control of unknown stochastic linear time-invariant systems, which is the key ingredient of a predictive control algorithm -- albeit typically having access to a model. We propose a novel distributionally robust data-enabled predictive control (DeePC) algorithm which uses noise-corrupted input/output data to predict future trajectories and compute optimal control inputs while satisfying output chance constraints. The algorithm is based on (i) a non-parametric representation of the subspace spanning the system behaviour, where past trajectories are sorted in Page or Hankel matrices; and (ii) a distributionally robust optimization formulation which gives rise to strong probabilistic performance guarantees. We show that for certain objective functions, DeePC exhibits strong out-of-sample performance, and at the same time respects constraints with high probability. The algorithm provides an end-to-end approach to control design for unknown stochastic linear time-invariant systems. We illustrate the closed-loop performance of the DeePC in an aerial robotics case study

Shaping adolescent heterosexual romantic experiences : contributions of same- and other-sex friendships

Contributing through the skills and capacities that they foster as well as through the quality of them, friendships have been identified as a powerful source of influence on adolescents’ romantic experiences. Unlike same-sex friendships, the influence of adolescents’ other-sex friendships on romantic relationships remains largely under-researched (Monsour, 2002; Sippola, 1999). In the current study I examined unique longitudinal and concurrent contributions of adolescents’ experiences of relational authenticity and intimacy in other-sex friendships to adolescents’ romantic intimacy and competence, while controlling for the influence of same-sex friendships. Ninety-seven participants rated their perception of relational authenticity and relationship intimacy in Grade 9. In Grade 11 they rated their perception of friendship and romantic intimacy, as well as romantic competence. The present longitudinal findings showed that adolescents’ earlier perception of relational authenticity in other-sex friendships predicted their subsequent perception of romantic intimacy and competence. The corresponding experience in same-sex friendships predicted only romantic competence in Grade 11 and only when the influence of other-sex friendships was not being considered. Although same-sex friendship intimacy in Grade 9 also demonstrated unique links to romantic intimacy in Grade 11, other-sex friendship intimacy in Grade 9 showed no such links. With regard to concurrent findings in Grade 11, experiences of intimacy in same- and other-sex friendships both predicted romantic intimacy in Grade 11. A discussion of possible explanations to the present research results is offered. Future research is suggested

Contract Composition for Dynamical Control Systems: Definition and Verification using Linear Programming

Designing large-scale control systems to satisfy complex specifications is hard in practice, as most formal methods are limited to systems of modest size. Contract theory has been proposed as a modular alternative to formal methods in control, in which specifications are defined by assumptions on the input to a component and guarantees on its output. However, current contract-based methods for control systems either prescribe guarantees on the state of the system, going against the spirit of contract theory, or can only support rudimentary compositions. In this paper, we present a contract-based modular framework for discrete-time dynamical control systems. We extend the definition of contracts by allowing the assumption on the input at a time $k$ to depend on outputs up to time $k-1$, which is essential when considering the feedback connection of an unregulated dynamical system and a controller. We also define contract composition for arbitrary interconnection topologies, under the pretence of well-posedness, and prove that this notion supports modular design, analysis and verification. This is done using graph theory methods, and specifically using the notions of topological ordering and backward-reachable nodes. Lastly, we use $k$-induction to present an algorithm for verifying vertical contracts, which are claims of the form "the conjugation of given component-level contracts is a stronger specification than a given contract on the integrated system". These algorithms are based on linear programming, and scale linearly with the number of components in the interconnected network. A numerical example is provided to demonstrate the scalability of the presented approach, as well as the modularity achieved by using it.Comment: 17 pages, 6 figure