Variable Sampling MPC via Differentiable Time-Warping Function

Designing control inputs for a system that involves dynamical responses in multiple timescales is nontrivial. This paper proposes a parameterized time-warping function to enable a non-uniformly sampling along a prediction horizon given some parameters. The horizon should capture the responses under faster dynamics in the near future and preview the impact from slower dynamics in the distant future. Then a variable sampling MPC (VS-MPC) strategy is proposed to jointly determine optimal control and sampling parameters at each time instant. VS-MPC adapts how it samples along the horizon and determines optimal control accordingly at each time instant without any manual tuning or trial and error. A numerical example of a wind farm battery energy storage system is also provided to demonstrate that VS-MPC outperforms the uniform sampling MPC

Distributed Optimization via Kernelized Multi-armed Bandits

Multi-armed bandit algorithms provide solutions for sequential decision-making where learning takes place by interacting with the environment. In this work, we model a distributed optimization problem as a multi-agent kernelized multi-armed bandit problem with a heterogeneous reward setting. In this setup, the agents collaboratively aim to maximize a global objective function which is an average of local objective functions. The agents can access only bandit feedback (noisy reward) obtained from the associated unknown local function with a small norm in reproducing kernel Hilbert space (RKHS). We present a fully decentralized algorithm, Multi-agent IGP-UCB (MA-IGP-UCB), which achieves a sub-linear regret bound for popular classes for kernels while preserving privacy. It does not necessitate the agents to share their actions, rewards, or estimates of their local function. In the proposed approach, the agents sample their individual local functions in a way that benefits the whole network by utilizing a running consensus to estimate the upper confidence bound on the global function. Furthermore, we propose an extension, Multi-agent Delayed IGP-UCB (MAD-IGP-UCB) algorithm, which reduces the dependence of the regret bound on the number of agents in the network. It provides improved performance by utilizing a delay in the estimation update step at the cost of more communication

A Distributed Algorithm for Multi-Agent Optimization under Edge-Agreements

Generalized from the concept of consensus, this paper considers a group of edge agreements, i.e. constraints defined for neighboring agents, in which each pair of neighboring agents is required to satisfy one edge agreement constraint. Edge agreements are defined locally to allow more flexibility than a global consensus. This work formulates a multi-agent optimization problem under edge agreements and proposes a continuous-time distributed augmented Lagrangian algorithm. Both analytical proof and numerical examples are provided to validate the effectiveness of the proposed distributed algorithm

How retroactivity impacts the robustness of genetic networks

This paper studies how retroactivity impacts the robustness of gene transcription networks against parameter perturbations. By employing the linearization technique and the real stability radius, we provide comparisons of the robustness between gene transcription networks with retroactivity and ones without retroactivity. Both numerical and analytical results show that retroactivity tends to decrease such robustness. This finding in turn implies that modular genetic networks tend to be more robust against parameter perturbations.National Science Foundation (U.S.) (NSF-CCF-I058127

Resilience for Distributed Consensus with Constraints

This paper proposes a new approach that enables multi-agent systems to achieve resilient \textit{constrained} consensus in the presence of Byzantine attacks, in contrast to existing literature that is only applicable to \textit{unconstrained} resilient consensus problems. The key enabler for our approach is a new device called a \textit{$(\gamma_i,\alpha_i)$-resilient convex combination}, which allows normal agents in the network to utilize their locally available information to automatically isolate the impact of the Byzantine agents. Such a resilient convex combination is computable through linear programming, whose complexity scales well with the size of the overall system. By applying this new device to multi-agent systems, we introduce network and constraint redundancy conditions under which resilient constrained consensus can be achieved with an exponential convergence rate. We also provide insights on the design of a network such that the redundancy conditions are satisfied. Finally, numerical simulations and an example of safe multi-agent learning are provided to demonstrate the effectiveness of the proposed results.Comment: 15 page