30,197 research outputs found
A Bayesian perspective on classical control
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
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
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 ( relative difference from the offline optimal solution) under
different settings.Comment: This paper is temporarily withdrawn in preparation for journal
submissio
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