30,197 research outputs found

    A Bayesian perspective on classical control

    Full text link
    The connections between optimal control and Bayesian inference have long been recognised, with the field of stochastic (optimal) control combining these frameworks for the solution of partially observable control problems. In particular, for the linear case with quadratic functions and Gaussian noise, stochastic control has shown remarkable results in different fields, including robotics, reinforcement learning and neuroscience, especially thanks to the established duality of estimation and control processes. Following this idea we recently introduced a formulation of PID control, one of the most popular methods from classical control, based on active inference, a theory with roots in variational Bayesian methods, and applications in the biological and neural sciences. In this work, we highlight the advantages of our previous formulation and introduce new and more general ways to tackle some existing problems in current controller design procedures. In particular, we consider 1) a gradient-based tuning rule for the parameters (or gains) of a PID controller, 2) an implementation of multiple degrees of freedom for independent responses to different types of signals (e.g., two-degree-of-freedom PID), and 3) a novel time-domain formalisation of the performance-robustness trade-off in terms of tunable constraints (i.e., priors in a Bayesian model) of a single cost functional, variational free energy.Comment: 8 pages, Accepted at IJCNN 202

    Log-Concave Duality in Estimation and Control

    Full text link
    In this paper we generalize the estimation-control duality that exists in the linear-quadratic-Gaussian setting. We extend this duality to maximum a posteriori estimation of the system's state, where the measurement and dynamical system noise are independent log-concave random variables. More generally, we show that a problem which induces a convex penalty on noise terms will have a dual control problem. We provide conditions for strong duality to hold, and then prove relaxed conditions for the piecewise linear-quadratic case. The results have applications in estimation problems with nonsmooth densities, such as log-concave maximum likelihood densities. We conclude with an example reconstructing optimal estimates from solutions to the dual control problem, which has implications for sharing solution methods between the two types of problems

    Optimal Charging of Electric Vehicles in Smart Grid: Characterization and Valley-Filling Algorithms

    Full text link
    Electric vehicles (EVs) offer an attractive long-term solution to reduce the dependence on fossil fuel and greenhouse gas emission. However, a fleet of EVs with different EV battery charging rate constraints, that is distributed across a smart power grid network requires a coordinated charging schedule to minimize the power generation and EV charging costs. In this paper, we study a joint optimal power flow (OPF) and EV charging problem that augments the OPF problem with charging EVs over time. While the OPF problem is generally nonconvex and nonsmooth, it is shown recently that the OPF problem can be solved optimally for most practical power networks using its convex dual problem. Building on this zero duality gap result, we study a nested optimization approach to decompose the joint OPF and EV charging problem. We characterize the optimal offline EV charging schedule to be a valley-filling profile, which allows us to develop an optimal offline algorithm with computational complexity that is significantly lower than centralized interior point solvers. Furthermore, we propose a decentralized online algorithm that dynamically tracks the valley-filling profile. Our algorithms are evaluated on the IEEE 14 bus system, and the simulations show that the online algorithm performs almost near optimality (<1<1% relative difference from the offline optimal solution) under different settings.Comment: This paper is temporarily withdrawn in preparation for journal submissio
    • …
    corecore