The Modified MSA, a Gradient Flow and Convergence

The modified Method of Successive Approximations (MSA) is an iterative scheme for approximating solutions to stochastic control problems in continuous time based on Pontryagin Optimality Principle which, starting with an initial open loop control, solves the forward equation, the backward adjoint equation and then performs a static minimization step. We observe that this is an implicit Euler scheme for a gradient flow system. We prove that appropriate interpolations of the iterates of the modified MSA converge to a gradient flow with rate $\tau$. We then study the convergence of this gradient flow as time goes to infinity. In the general (non-convex) case we prove that the gradient term itself converges to zero. This is a consequence of an energy identity which shows that the optimization objective decreases along the gradient flow. Moreover, in the convex case, when Pontryagin Optimality Principle provides a sufficient condition for optimality, we prove that the optimization objective converges at rate $\tfrac{1}{S}$ to its optimal value and at exponential rate under strong convexity. The main technical difficulties lie in obtaining appropriate properties of the Hamiltonian (growth, continuity). These are obtained by utilising the theory of Bounded Mean Oscillation (BMO) martingales required for estimates on the adjoint Backward Stochastic Differential Equation (BSDE)

Real-time control of WECs based on NAR, NARX and LSTM artificial neural network

In this study, we aim to improve WECs’ performance for maximizing energy absorption through a sub-optimal method of phase control by latching is applied to the device. The forecasting of future wave force is required for the optimal control command deducted. An artificial neural network, namely LSTM (Long Short-Term Memory) is proposed to accurately predict the short-term wave force. The hydrodynamic properties of a point absorber is analyzed based on the 3D potential flow theory in frequency-domain. Cummin’s equation and a 4th-order state-space model are used to efficiently represent the hydrodynamic behavior of the WEC under irregular waves in time-domain. The Nonlinear Autoregressive artificial neural network(NAR-ANN) and NARx network are used to verify the method proposed in this paper. The simulation results show that the mean square error value, root mean square error value and R2 value based on the LSTM prediction model are better than those of the NAR prediction model. The prediction performance of LSTM is more suitable for processing the time series

An investigation of air and water dual adjustment decoupling control of surface heat exchanger

The terminal equipment of central cooling system accounts for a significant proportion of the total system's energy consumption. Therefore, it is important to reduce the terminal equipment energy consumption in central air conditioning system. In this study, the difference of the effect of the chilled water flow rate and air supply rate on the surface cooler during the heat transfer process is taken into full account. Matlab/Simulink simulation software is used to model and simulate the heat transfer of surface cooler of the main terminal equipment of air conditioning system. Simulation tests and experimental validations are conducted by using variable chilled water flow rate and variable air supply rate control mode separately. The experiment results show that the simulation model can effectively predict the heat transfer performance of heat exchanger. Further, the study introduced a dual feedback control mode, which synchronously regulates the chilled water flow rate and air supply rate. Also, under certain conditions, the complex heat transfer process of the surface cooler can be decoupled, and single variable control pattern is used to separately regulate the chilled water flow rate and air supply rate. This can effectively shorten the system regulation time, reduce overshoot and improve control performance

Power Control Optimization of an Underwater Piezoelectric Energy Harvester

Over the past few years, it has been established that vibration energy harvesters with intentionally designed components can be used for frequency bandwidth enhancement under excitation for sufficiently high vibration amplitudes. Pipelines are often necessary means of transporting important resources such as water, gas, and oil. A self-powered wireless sensor network could be a sustainable alternative for in-pipe monitoring applications. A new control algorithm has been developed and implemented into an underwater energy harvester. Firstly, a computational study of a piezoelectric energy harvester for underwater applications has been studied for using the kinetic energy of water flow at four different Reynolds numbers Re = 3000, 6000, 9000, and 12,000. The device consists of a piezoelectric beam assembled to an oscillating cylinder inside the water of pipes from 2 to 5 inches in diameter. Therefore, unsteady simulations have been performed to study the dynamic forces under different water speeds. Secondly, a new control law strategy based on the computational results has been developed to extract as much energy as possible from the energy harvester. The results show that the harvester can efficiently extract the power from the kinetic energy of the fluid. The maximum power output is 996.25 mu W and corresponds to the case with Re = 12,000.The funding from the Government of the Basque Country and the University of the Basque Country UPV/EHU through the SAIOTEK (S-PE11UN112) and EHU12/26 research programs, respectively, is gratefully acknowledged. The authors are very grateful to SGIker of UPV/EHU and European funding (ERDF and ESF) for providing technical and human

Method And System For Dynamic Stochastic Optimal Electric Power Flow Control

A dynamic stochastic optimal power flow (DSOPF) control system is described for performing multi-objective optimal control capability in complex electrical power systems. The DSOPF system and method replaces the traditional adaptive critic designs (ACDs) and secondary voltage control, and provides a coordinated AC power flow control solution to the smart grid operation in an environment with high short-term uncertainty and variability. The DSOPF system and method is used to provide nonlinear optimal control, where the control objective is explicitly formulated to incorporate power system economy, stability and security considerations. The system and method dynamically drives a power system to its optimal operating point by continuously adjusting the steady-state set points sent by a traditional optimal power flow algorithm.Clemson UniversityGeorgia Tech Research CorporationThe Curators Of The University Of Missour