Sufficient conditions for the optimality of a stochastic control.
Sufficient conditions for optimal stochastic control of diffusion processes governed by vector equations satisfying local Lipschitz conditions
OPTIMAL CONTROL↗
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Bilinear dynamic mode decomposition for quantum control
Abstract Data-driven methods for establishing quantum optimal control (QOC) using time-dependent control pulses tailored to specific quantum dynamical systems and desired control objectives are critical for many emerging quantum technologies. We develop a data-driven regression procedure, bilinear dynamic mode decomposition (biDMD), that leverages time-series measurements to establish quantum system identification for QOC. The biDMD optimization framework is a physics-informed regression that makes use of the known underlying Hamiltonian structure. Further, the biDMD can be modified to model both fast and slow sampling of control signals, the latter by way of stroboscopic sampling strategies. The biDMD method provides a flexible, interpretable, and adaptive regression framework for real-time, online implementation in quantum systems. Further, the method has strong theoretical connections to Koopman theory, which approximates nonlinear dynamics with linear operators. In comparison with many machine learning paradigms minimal data is needed to construct a biDMD model, and the model is easily updated as new data is collected. We demonstrate the efficacy and performance of the approach on a number of representative quantum systems, showing that it also matches experimental results.
97 MATHEMATICS AND COMPUTING↗
Optimal output feedback control of linear systems in presence of forcing and measurement noise
The problem of obtaining an optimal control law, which is constrained to be a linear feedback of the available measurements, for both continuous and discrete time linear systems subjected to additive white process noise and measurement noise was Necessary conditions are obtained for minimizing a quadratic performance function for both finite and infinite terminal time cases. The feedback gains are constrained to be time invariant for the infinite terminal time cases. For all the cases considered, algorithms are derived for generating sequences of feedback gain matrices which successively improve the performance function. A continuous time numerical example is included for the purpose of demonstration.
Joshi, S. M.↗
Optimal Traffic Signal Control Using Priority Metric Based on Real-Time Measured Traffic Information
Optimizing traffic control systems at traffic intersections can reduce network-wide fuel consumption as well as improve traffic flow. While traffic signals have conventionally been controlled based on predetermined schedules, various adaptive control systems have been developed recently using advanced sensors such as cameras, radars, and LiDARs. By utilizing rich traffic information enabled by the advanced sensors, more efficient or optimal traffic signal control is possible in response to varying traffic conditions. This paper proposes an optimal traffic signal control method to minimize network-wide fuel consumption utilizing real-time traffic information provided by advanced sensors. This new method employs a priority metric calculated by a weighted sum of various factors, including the total number of vehicles, total vehicle speed, vehicle waiting time, and road preference. Genetic Algorithm (GA) is used as a global optimization method to determine the optimal weights in the priority metric. In order to evaluate the effectiveness of the proposed method, a traffic simulation model is developed in a high-fidelity traffic simulation environment called SUMO, based on a real-world traffic network. The traffic flow within this model is simulated using actual measured traffic data from the traffic network, enabling a comprehensive assessment of the novel optimal traffic signal control method in realistic conditions. The simulation results show that the proposed priority metric-based real-time traffic signal control algorithm can significantly reduce network-wide fuel consumption compared to the conventional fixed-time control and coordinated actuated control methods that are currently used in the modeled network. Additionally, incorporating truck priority in the priority metric leads to further improvements in fuel consumption reduction.
47 OTHER INSTRUMENTATION↗
Spline approximations for nonlinear hereditary control systems
A sline-based approximation scheme is discussed for optimal control problems governed by nonlinear nonautonomous delay differential equations. The approximating framework reduces the original control problem to a sequence of optimization problems governed by ordinary differential equations. Convergence proofs, which appeal directly to dissipative-type estimates for the underlying nonlinear operator, are given and numerical findings are summarized.
Daniel, P. L.↗
Experimental Validation of an Integrated Controls-Structures Design Methodology
The first experimental validation of an integrated controls-structures design methodology for a class of large order, flexible space structures is described. Integrated redesign of the controls-structures-interaction evolutionary model, a laboratory testbed at NASA Langley, was described earlier. The redesigned structure was fabricated, assembled in the laboratory, and experimentally tested against the original structure. Experimental results indicate that the structure redesigned using the integrated design methodology requires significantly less average control power than the nominal structure with control-optimized designs, while maintaining the required line-of-sight pointing performance. Thus, the superiority of the integrated design methodology over the conventional design approach is experimentally demonstrated. Furthermore, amenability of the integrated design structure to other control strategies is evaluated, both analytically and experimentally. Using Linear-Quadratic-Guassian optimal dissipative controllers, it is observed that the redesigned structure leads to significantly improved performance with alternate controllers as well.
Maghami, Peiman G.↗
Some theoretical considerations arising in guidance analysis.
Optimal control and estimation theory application to space navigation, noting random disturbance
SPACE NAVIGATION↗
Some theoretical considerations arising in guidance analysis.
Optimal control and estimation theory application to space navigation, noting random disturbance
SPACE NAVIGATION↗
Dynamic optimization with flexible heat integration of a solar parabolic trough collector plant with thermal energy storage used for industrial process heat
There is an increasing need to reduce fossil fuel consumption used for industrial process heat to slow the effects of climate change. Using solar thermal heat is a viable way to replace fossil fuel use, but solar industrial process heat plants have limited implementation due to large upfront costs and inefficiencies from the inherent variability from solar energy. Having more flexible and optimized control over these plants can enable them to be more efficient. Here in this work, a solar industrial process heat plant with thermal energy storage that can flexibly collect and deliver heat to two industrial processes (flexible heat integration) is dynamically modeled with control setpoints found by a dynamic optimization method. The optimized case can increase the solar efficiency of the plant by 7.5% on average relative to a base case. The results show that it is best to collect heat at lower temperatures for all but ideal solar conditions, only medium to high quality heat should be stored in large quantities, and exchanging heat with a lower temperature heat sink is generally more efficient. The optimized case is able to reduce the levelized cost of heat of the plant to $31.83/MWh th compared to a base case value of $34.10/MWh th . The optimized case can reduce emissions by 22.2% compared to a plant which uses only natural gas. This work shows that dynamic optimization with flexible heat integration can be a cost-effective way to increase efficiency so that more of these types of plants can be implemented.
14 SOLAR ENERGY↗
Predicting plug loads with occupant count data through a deep learning approach
Predictive control has gained increasing attention for its ability to reduce energy consumption and improve occupant comfort in buildings. The plug loads prediction is a key component for the predictive building controls, as plug loads is a major source of internal heat gains in buildings. This study proposed a novel method to apply the Long-Short-Term-Memory (LSTM) Network, a special form of Recurrent Neural Network, to predict plug loads. The occupant count and the time have been confirmed to drive the plug load profile and thus selected as the features for the plug load prediction. The LSTM network was trained and tested with ground truth occupant count data collected from a real office building in Berkeley, California. Results from the LSTM network markedly improve the prediction accuracy compared with traditional linear regression methods and the classical Artificial Neural Network. 95% of 1-hour predictions from LSTM network are within ±1 kW of the actual plug loads, given the average plug loads during the office hour is 8.6 kW. The CV(RMSE) of the predicted plug load is 11% for the next hour, and 20% for the next eight hours. Lastly, we compared four prediction approaches with the office building we monitored: LSTM vs. ARIMA, with occupant counts vs. without occupant counts. It was found, the prediction error of the LSTM approach is around 4% less than the ARIMA approach. Using occupant counts as an exogenous input could further reduce the prediction error by 5%-6%. The findings of this paper could shed light on the plug load prediction for building control optimizations such as model-predictive control.
Occupant count↗
Data-Enabled Predictive Control for Building HVAC Systems
Model predictive control is widely used as a control technology for the computation of optimal control inputs of building heating, ventilating, and air conditioning (HVAC) systems. However, both the benefits and widespread adoption of model predictive control (MPC) are hindered by the effort of model creation, calibration, and accuracy of the predictions. In this paper, we apply the data-enabled predictive control (DeePC) algorithm for designing controls for building HVAC systems. The algorithm solely depends on input/output data from the system to predict future state trajectories without the need for system identification. The algorithm relies on the idea that a vector space of all input–output trajectories of a discrete-time linear time-invariant (LTI) system is spanned by time-shifts of a single measured trajectory, given the input signal is persistently exciting. Closed-loop simulations using EnergyPlus are performed to demonstrate the approach. The simulated building modeled in EnergyPlus is a modified commercial large office prototype building served by an air handling unit-variable air volume HVAC system. Temperature setpoints of zones are used as control variables to minimize the HVAC energy cost of the building considering a time-of-use electricity rate structure. Furthermore, sensitivity analysis is conducted to gain insights into the effect of parameter tuning on DeePC performance. Simulation results are used to illustrate the performance of the algorithm and compare the algorithm with model-based MPC and occupancy-based setpoint controller. Overall, DeePC achieves similar performance compared to MPC for lower engineering effort.
32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
On optimization and the guidance problem for systems with transport lags.
Terminal guidance problem involving optimal control for deviations in systems with transport lag
TIME DELAY↗
Prediction of pilot opinion ratings using an optimal pilot model
A brief review of some of the more pertinent applications of analytical pilot models to the prediction of aircraft handling qualities is undertaken. The relative ease with which multiloop piloting tasks can be modeled via the optimal control formulation makes the use of optimal pilot models particularly attractive for handling qualities research. To this end, a rating hypothesis is introduced which relates the numerical pilot opinion rating assigned to a particular vehicle and task to the numerical value of the index of performance resulting from an optimal pilot modeling procedure as applied to that vehicle and task. This hypothesis is tested using data from piloted simulations and is shown to be reasonable. An example concerning a helicopter landing approach is introduced to outline the predictive capability of the rating hypothesis in multiaxis piloting tasks.
Hess, R. A.↗
Algebraic methods for the solution of some linear matrix equations
The characterization of polynomials whose zeros lie in certain algebraic domains (and the unification of the ideas of Hermite and Lyapunov) is the basis for developing finite algorithms for the solution of linear matrix equations. Particular attention is given to equations PA + A'P = Q (the Lyapunov equation) and P - A'PA = Q the (discrete Lyapunov equation). The Lyapunov equation appears in several areas of control theory such as stability theory, optimal control (evaluation of quadratic integrals), stochastic control (evaluation of covariance matrices) and in the solution of the algebraic Riccati equation using Newton's method.
Djaferis, T. E.↗
Pilot model hypothesis testing
The aircraft control time history predicted by the optimal control pilot model and actual pilot tracking data obtained from NASA Langley's differential maneuvering simulator (DMS) are analyzed. The analysis is performed using a hypothesis testing scheme modified to allow for changes in the true hypothesis. A finite number of pilot models, each with different hypothesized internal model representations of the aircraft dynamics, are constructed. The hypothesis testing scheme determines the relative probability that each pilot model best matches the DMS data. By observing the changes in probabilities, it is possible to determine when the pilot changes control strategy and which hypothesized pilot model best represent's the pilot's control behavior.
Broussard, J. R.↗
Application of an adaptive blade control algorithm to a gust alleviation system
The feasibility of an adaptive control system designed to alleviate helicopter gust induced vibration was analytically investigated for an articulated rotor system. This control system is based on discrete optimal control theory, and is composed of a set of measurements (oscillatory hub forces and moments), an identification system using a Kalman filter, a control system based on the minimization of the quadratic performance function, and a simulation system of the helicopter rotor. The gust models are step and sinusoidal vertical gusts. Control inputs are selected at the gust frequency, subharmonic frequency, and superharmonic frequency, and are superimposed on the basic collective and cyclic control inputs. The response to be reduced is selected to be that at the gust frequency because this is the dominant response compared with sub- and superharmonics. Numerical calculations show that the adaptive blade pitch control algorithm satisfactorily alleviates the hub gust response. Almost 100% reduction of the perturbation thrust response to a step gust and more than 50% reduction to a sinusoidal gust are achieved in the numerical simulations.
Saito, S.↗
Application of an adaptive blade control algorithm to a gust alleviation system
The feasibility of an adaptive control system designed to alleviate helicopter gust induced vibration was analytically investigated for an articulated rotor system. This control system is based on discrete optimal control theory, and is composed of a set of measurements (oscillatory hub forces and moments), an identification system using a Kalman filter, a control system based on the minimization of the quadratic performance function, and a simulation system of the helicopter rotor. The gust models are step and sinusoidal vertical gusts. Control inputs are selected at the gust frequency, subharmonic frequency, and superharmonic frequency, and are superimposed on the basic collective and cyclic control inputs. The response to be reduced is selected to be that at the gust frequency because this is the dominant response compared with sub- and superharmonics. Numerical calculations show that the adaptive blade pitch control algorithm satisfactorily alleviates the hub gust response. Almost 100 percent reduction of the perturbation thrust response to a step gust and more than 50 percent reduction to a sinusoidal gust are achieved in the numerical simulations.
Saito, S.↗
Control of space stations
A study is made to develop controllers for the NASA-JSC Triangular Space Station and evaluate their performances to make recommendations for structural design and/or control alternatives. The control system design assumes the rigid body of the Space Station and developes the lumped parameter control system by using the Inverse Optimal Control Theory. In order to evaluate the performance of the control system, a Parameter Estimation algorithm is being developed which will be used in modeling an equivalent but simpler Space Station model. Finally, a scaled version of the Space Station is being built for the purpose of physical experiments to evaluate the control system performance.
Lee, K. Y.↗