23,807 research outputs found
Control of Complex Dynamic Systems by Neural Networks
This paper considers the use of neural networks (NN's) in controlling a nonlinear, stochastic system with unknown process equations. The NN is used to model the resulting unknown control law. The approach here is based on using the output error of the system to train the NN controller without the need to construct a separate model (NN or other type) for the unknown process dynamics. To implement such a direct adaptive control approach, it is required that connection weights in the NN be estimated while the system is being controlled. As a result of the feedback of the unknown process dynamics, however, it is not possible to determine the gradient of the loss function for use in standard (back-propagation-type) weight estimation algorithms. Therefore, this paper considers the use of a new stochastic approximation algorithm for this weight estimation, which is based on a 'simultaneous perturbation' gradient approximation that only requires the system output error. It is shown that this algorithm can greatly enhance the efficiency over more standard stochastic approximation algorithms based on finite-difference gradient approximations
Active Classification for POMDPs: a Kalman-like State Estimator
The problem of state tracking with active observation control is considered
for a system modeled by a discrete-time, finite-state Markov chain observed
through conditionally Gaussian measurement vectors. The measurement model
statistics are shaped by the underlying state and an exogenous control input,
which influence the observations' quality. Exploiting an innovations approach,
an approximate minimum mean-squared error (MMSE) filter is derived to estimate
the Markov chain system state. To optimize the control strategy, the associated
mean-squared error is used as an optimization criterion in a partially
observable Markov decision process formulation. A stochastic dynamic
programming algorithm is proposed to solve for the optimal solution. To enhance
the quality of system state estimates, approximate MMSE smoothing estimators
are also derived. Finally, the performance of the proposed framework is
illustrated on the problem of physical activity detection in wireless body
sensing networks. The power of the proposed framework lies within its ability
to accommodate a broad spectrum of active classification applications including
sensor management for object classification and tracking, estimation of sparse
signals and radar scheduling.Comment: 38 pages, 6 figure
Actor-Critic Reinforcement Learning for Control with Stability Guarantee
Reinforcement Learning (RL) and its integration with deep learning have
achieved impressive performance in various robotic control tasks, ranging from
motion planning and navigation to end-to-end visual manipulation. However,
stability is not guaranteed in model-free RL by solely using data. From a
control-theoretic perspective, stability is the most important property for any
control system, since it is closely related to safety, robustness, and
reliability of robotic systems. In this paper, we propose an actor-critic RL
framework for control which can guarantee closed-loop stability by employing
the classic Lyapunov's method in control theory. First of all, a data-based
stability theorem is proposed for stochastic nonlinear systems modeled by
Markov decision process. Then we show that the stability condition could be
exploited as the critic in the actor-critic RL to learn a controller/policy. At
last, the effectiveness of our approach is evaluated on several well-known
3-dimensional robot control tasks and a synthetic biology gene network tracking
task in three different popular physics simulation platforms. As an empirical
evaluation on the advantage of stability, we show that the learned policies can
enable the systems to recover to the equilibrium or way-points when interfered
by uncertainties such as system parametric variations and external disturbances
to a certain extent.Comment: IEEE RA-L + IROS 202
Analytic Regularity and GPC Approximation for Control Problems Constrained by Linear Parametric Elliptic and Parabolic PDEs
This paper deals with linear-quadratic optimal control problems constrained by a parametric or stochastic elliptic or parabolic PDE. We address the (difficult) case that the state equation depends on a countable number of parameters i.e., on with , and that the PDE operator may depend non-affinely on the parameters. We consider tracking-type functionals and distributed as well as boundary controls. Building on recent results in [CDS1, CDS2], we show that the state and the control are analytic as functions depending on these parameters . We
establish sparsity of generalized polynomial chaos (gpc) expansions of both, state and control, in terms of the stochastic coordinate sequence of the random inputs, and prove convergence rates of best -term truncations of these expansions. Such truncations are the key for subsequent computations since they do {\em not} assume that the stochastic input data has a finite expansion. In the follow-up paper [KS2], we explain two methods how such best -term truncations can practically be computed, by greedy-type algorithms
as in [SG, Gi1], or by multilevel Monte-Carlo methods as in
[KSS]. The sparsity result allows in conjunction with adaptive wavelet Galerkin schemes for sparse, adaptive tensor discretizations of control problems constrained by linear elliptic and parabolic PDEs developed in [DK, GK, K], see [KS2]
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