scholarly journals Leveraging Stochasticity for Open Loop and Model Predictive Control of Spatio-Temporal Systems

Entropy ◽  
2021 ◽  
Vol 23 (8) ◽  
pp. 941
Author(s):  
George I. Boutselis ◽  
Ethan N. Evans ◽  
Marcus A. Pereira ◽  
Evangelos A. Theodorou
Keyword(s):  
Wave Function ◽  
Predictive Control ◽  
Hilbert Spaces ◽  
Wide Class ◽  
Quantum Systems ◽  
Open Loop ◽  
Control Problems ◽  
Optimization Framework ◽  
Spatio Temporal ◽  
Theoretic Description

Stochastic spatio-temporal processes are prevalent across domains ranging from the modeling of plasma, turbulence in fluids to the wave function of quantum systems. This letter studies a measure-theoretic description of such systems by describing them as evolutionary processes on Hilbert spaces, and in doing so, derives a framework for spatio-temporal manipulation from fundamental thermodynamic principles. This approach yields a variational optimization framework for controlling stochastic fields. The resulting scheme is applicable to a wide class of spatio-temporal processes and can be used for optimizing parameterized control policies. Our simulated experiments explore the application of two forms of this approach on four stochastic spatio-temporal processes, with results that suggest new perspectives and directions for studying stochastic control problems for spatio-temporal systems.

On closed-loop equilibrium strategies for mean-field stochastic linear quadratic problems

2020 ◽  
Vol 26 ◽  
pp. 41
Author(s):  
Tianxiao Wang
Keyword(s):  
Optimal Control ◽  
Closed Loop ◽  
Optimal Control Problems ◽  
Mean Field ◽  
Open Loop ◽  
Time Inconsistency ◽  
Control Problems ◽  
Linear Quadratic ◽  
Linear Quadratic Optimal Control ◽  
Equilibrium Strategies

This article is concerned with linear quadratic optimal control problems of mean-field stochastic differential equations (MF-SDE) with deterministic coefficients. To treat the time inconsistency of the optimal control problems, linear closed-loop equilibrium strategies are introduced and characterized by variational approach. Our developed methodology drops the delicate convergence procedures in Yong [Trans. Amer. Math. Soc. 369 (2017) 5467–5523]. When the MF-SDE reduces to SDE, our Riccati system coincides with the analogue in Yong [Trans. Amer. Math. Soc. 369 (2017) 5467–5523]. However, these two systems are in general different from each other due to the conditional mean-field terms in the MF-SDE. Eventually, the comparisons with pre-committed optimal strategies, open-loop equilibrium strategies are given in details.

A Geometric Approach to Dynamically Feasible, Real-Time Formation Control

2011 ◽  
Vol 133 (2) ◽  
Author(s):  
D. H. A. Maithripala ◽  
D. H. S. Maithripala ◽  
S. Jayasuriya
Keyword(s):  
Real Time ◽  
Wide Class ◽  
Formation Control ◽  
Geometric Approach ◽  
Control Problems ◽  
Multi Agent Systems ◽  
Individual Agent ◽  
Planning Algorithm ◽  
Explicit Consideration ◽  
Multi Agent

We propose a framework for synthesizing real-time trajectories for a wide class of coordinating multi-agent systems. The class of problems considered is characterized by the ability to decompose a given formation objective into an equivalent set of lower dimensional problems. These include the so called radar deception problem and the formation control problems that fall under formation keeping and/or formation reconfiguration tasks. The decomposition makes the approach scalable, computationally economical, and decentralized. Most importantly, the designed trajectories are dynamically feasible, meaning that they maintain the formation while satisfying the nonholonomic and saturation type velocity and acceleration constraints of each individual agent. The main contributions of this paper are (i) explicit consideration of second order dynamics for agents, (ii) explicit consideration of nonholonomic and saturation type velocity and acceleration constraints, (iii) unification of a wide class of formation control problems, and (iv) development of a real-time, distributed, scalable, computationally economical motion planning algorithm.

Model Predictive Control and Controller Parameter Optimisation of Combustion Instabilities

2019 ◽  
Vol 36 (2) ◽  
pp. 185-194 ◽  
Author(s):  
I. Yazar ◽  
F. Caliskan ◽  
R. Vepa
Keyword(s):  
Model Predictive Control ◽  
Predictive Control ◽  
Closed Loop ◽  
Combustion Process ◽  
Open Loop ◽  
Loop Model ◽  
Parameter Optimisation ◽  
Direct Adaptive Control ◽  
The Cost ◽  
Adaptive Control Algorithm

Abstract In this paper the application of model predictive control (MPC) to a two-mode model of the dynamics of the combustion process is considered. It is shown that the MPC by itself does not stabilize the combustor and the control gains obtained by applying the MPC algorithms need to be optimized further to ensure that the phase difference between the two modes is also stable. The results of applying the algorithm are compared with the open loop model amplitude responses and to the closed loop responses obtained by the application of a direct adaptive control algorithm. It is shown that the MPC coupled with the cost parameter optimisation proposed in the paper, always guarantees the closed loop stability, a feature that may not always be possible with an adaptive implementations.

scholarly journals Uncertainty Quantification in Control Problems for Flocking Models

2015 ◽  
Vol 2015 ◽  
pp. 1-14 ◽  
Author(s):  
Giacomo Albi ◽  
Lorenzo Pareschi ◽  
Mattia Zanella
Keyword(s):  
Optimal Control ◽  
Predictive Control ◽  
Polynomial Chaos ◽  
Point Of View ◽  
Type Model ◽  
Control Problems ◽  
Threshold Effects ◽  
Random Parameters ◽  
Random Inputs ◽  
Generalized Polynomial

The optimal control of flocking models with random inputs is investigated from a numerical point of view. The effect of uncertainty in the interaction parameters is studied for a Cucker-Smale type model using a generalized polynomial chaos (gPC) approach. Numerical evidence of threshold effects in the alignment dynamic due to the random parameters is given. The use of a selective model predictive control permits steering of the system towards the desired state even in unstable regimes.

TOWARDS A THEORY OF DECOHERENCE

2004 ◽  
Vol 18 (04n05) ◽  
pp. 643-654 ◽  
Author(s):  
GIANFAUSTO DELL'ANTONIO
Keyword(s):  
Wave Function ◽  
Quantum Mechanics ◽  
Quantum Particle ◽  
Small Mass ◽  
Quantum Systems ◽  
Classical Description ◽  
Large Quantum

Consider a quantum particle of mass M in R3, described at time 0 by a wave function ϕ(x) with dispersion Δ, interacting independently with a collection of N particles of mass m. Using only Schroedinger's Quantum Mechanics we prove that when N becomes large and m/M becomes small, and if the information at time t>0 about the N particles of small mass in negleted, the system admits a "classical" description, i.e. a description in which the coherence of the wave function over distances of the order of mM-1N-1Δ have disappeared. We consider this a first step towards proving that most "sufficiently large" quantum systems interacting with an uncontrolled environment admit a classical description at least for position measurements.

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