Passivity Degradation In Discrete Control Implementations: An Approximate Bisimulation Approach

In this paper, we present some preliminary results for compositional analysis of heterogeneous systems containing both discrete state models and continuous systems using consistent notions of dissipativity and passivity. We study the following problem: given a physical plant model and a continuous feedback controller designed using traditional control techniques, how is the closed-loop passivity affected when the continuous controller is replaced by a discrete (i.e., symbolic) implementation within this framework? Specifically, we give quantitative results on performance degradation when the discrete control implementation is approximately bisimilar to the continuous controller, and based on them, we provide conditions that guarantee the boundedness property of the closed-loop system.Comment: This is an extended version of our IEEE CDC 2015 paper to appear in Japa

Predictability and Fairness in Load Aggregation with Deadband

Virtual power plants and load aggregation are becoming increasingly common. There, one regulates the aggregate power output of an ensemble of distributed energy resources (DERs). Marecek et al. [Automatica, Volume 147, January 2023, 110743, arXiv:2110.03001] recently suggested that long-term averages of prices or incentives offered should exist and be independent of the initial states of the operators of the DER, the aggregator, and the power grid. This can be seen as predictability, which underlies fairness. Unfortunately, the existence of such averages cannot be guaranteed with many traditional regulators, including the proportional-integral (PI) regulator with or without deadband. Here, we consider the effects of losses in the alternating current model and the deadband in the controller. This yields a non-linear dynamical system (due to the non-linear losses) exhibiting discontinuities (due to the deadband). We show that Filippov invariant measures enable reasoning about predictability and fairness while considering non-linearity of the alternating-current model and deadband.Comment: arXiv admin note: substantial text overlap with arXiv:2110.0300

Compositional Synthesis of Control Barrier Certificates for Networks of Stochastic Systems against ω\omega-Regular Specifications

This paper is concerned with a compositional scheme for the construction of control barrier certificates for interconnected discrete-time stochastic systems. The main objective is to synthesize switching control policies against $\omega$-regular properties that can be described by accepting languages of deterministic Streett automata (DSA) along with providing probabilistic guarantees for the satisfaction of such specifications. The proposed framework leverages the interconnection topology and a notion of so-called control sub-barrier certificates of subsystems, which are used to compositionally construct control barrier certificates of interconnected systems by imposing some dissipativity-type compositionality conditions. We propose a systematic approach to decompose high-level $\omega$-regular specifications into simpler tasks by utilizing the automata corresponding to the complement of specifications. In addition, we formulate an alternating direction method of multipliers (ADMM) optimization problem in order to obtain suitable control sub-barrier certificates of subsystems while satisfying compositionality conditions. We also provide a sum-of-squares (SOS) optimization problem for the computation of control sub-barrier certificates and local control policies of subsystems. Finally, we demonstrate the effectiveness of our proposed approaches by applying them to a physical case study