Online-Computation Approach to Optimal Control of Noise-Affected Nonlinear Systems with Continuous State and Control Spaces

© 2007 EUCA.A novel online-computation approach to optimal control of nonlinear, noise-affected systems with continuous state and control spaces is presented. In the proposed algorithm, system noise is explicitly incorporated into the control decision. This leads to superior results compared to state-of-the-art nonlinear controllers that neglect this influence. The solution of an optimal nonlinear controller for a corresponding deterministic system is employed to find a meaningful state space restriction. This restriction is obtained by means of approximate state prediction using the noisy system equation. Within this constrained state space, an optimal closed-loop solution for a finite decision-making horizon (prediction horizon) is determined within an adaptively restricted optimization space. Interleaving stochastic dynamic programming and value function approximation yields a solution to the considered optimal control problem. The enhanced performance of the proposed discrete-time controller is illustrated by means of a scalar example system. Nonlinear model predictive control is applied to address approximate treatment of infinite-horizon problems by the finite-horizon controller

Finite-Horizon Optimal State Feedback Control of Nonlinear Stochastic Systems Based on a Minimum Principle

In this paper, an approach to the finite-horizon optimal state-feedback control problem of nonlinear, stochastic, discrete-time systems is presented. Starting from the dynamic programming equation, the value function will be approximated by means of Taylor series expansion up to second-order derivatives. Moreover, the problem will be reformulated, such that a minimum principle can be applied to the stochastic problem. Employing this minimum principle, the optimal control problem can be rewritten as a two-point boundary-value problem to be solved at each time step of a shrinking horizon. To avoid numerical problems, the two-point boundary-value problem will be solved by means of a continuation method. Thus, the curse of dimensionality of dynamic programming is avoided, and good candidates for the optimal state-feedback controls are obtained. The proposed approach will be evaluated by means of a scalar example system. © 2006 IEEE

Risk and Uncertainty in Environmental Economics: From Theory to Policy

A lack of awareness and understanding of risk and uncertainty can lead to poor decision making and higher costs for policy providers, as not accounting for them may produce policy which is inflexible and with a negative effect on welfare. Further, misunderstanding of and/or failure to account for risk and uncertainty can inhibit research and development for policy to which environmental economics can contribute (for example, in developing effective measures of sustainability). The aim of this project is to develop guidelines for ‘Best Practice’ approaches to risk and uncertainty in environmental economics for guiding policy development and implementation, taking into account key issues such as costs, irreversibility, adaptation and dynamics. These guidelines are developed by examining the frameworks commonly used by environmental economists to account for risk and uncertainty (such as the Precautionary Principle and Cost Benefit Analysis) as well as specifically developed theories (e.g. Quiggin’s Rank Dependent Utility Theory), borrowing from other disciplines (e.g. Prospect Theory) and drawing attention to lesser known ideas (e.g. Shackle’s Model).Environmental Economics and Policy,

Online-Computation Approach to Optimal Control of Noise-Affected Nonlinear Systems with Continuous State and Control Spaces

A novel online-computation approach to optimal control of nonlinear, noise-affected systems with continuous state and control spaces is presented. In the proposed algorithm, system noise is explicitly incorporated into the control decision. This leads to superior results compared to state-of-the-art nonlinear controllers that neglect this influence. The solution of an optimal nonlinear controller for a corresponding deterministic system is employed to find a meaningful state space restriction. This restriction is obtained by means of approximate state prediction using the noisy system equation. Within this constrained state space, an optimal closed-loop solution for a finite decisionmaking horizon (prediction horizon) is determined within an adaptively restricted optimization space. Interleaving stochastic dynamic programming and value function approximation yields a solution to the considered optimal control problem. The enhanced performance of the proposed discrete-time controller is illustrated by means of a scalar example system. Nonlinear model predictive control is applied to address approximate treatment of infinite-horizon problems by the finite-horizon controller

Development of Biomimetic-Based Controller Design Methods for Advanced Energy Systems

A biologically inspired optimal control strategy, denoted as BIO-CS, is proposed for advanced energy systems applications. This strategy combines the ant\u27s rule of pursuit idea with multi-agent and optimal control concepts. The BIO-CS algorithm employs gradient-based optimal control solvers for the intermediate problems associated with the leader-follower agents\u27 local interactions. The developed BIO-CS is integrated with an Artificial Neural Network (ANN)-based adaptive component for further improvement of the overall framework. In particular, the ANN component captures the mismatch between the controller and the plant models by using a single-hidden-layer technique with online learning capabilities to augment the baseline BIO-CS control laws. The resulting approach is a unique combination of biomimetic control and data-driven methods that provides optimal solutions for dynamic systems.;The applicability of the proposed framework is illustrated via an Integrated Gasification Combined Cycle (IGCC) process with carbon capture as an advanced energy system example. Specifically, a multivariable control structure associated with a subsystem of the IGCC plant simulation in DYNSIMRTM software platform is addressed. The proposed control laws are derived in MATLAB RTM environment, while the plant models are built in DYNSIM RTM, and a previously developed MATLABRTM-DYNSIM RTM link is employed for implementation purposes. The proposed integrated approach improves the overall performance of the process up to 85% in terms of reducing the output tracking error when compared to stand-alone BIO-CS and Proportional-Integral (PI) controller implementations, resulting in faster setpoint tracking.;Other applications of BIO-CS addressed include: i) a nonlinear fermentation process to produce ethanol; and ii) a transfer function model derived from the cyber-physical fuel cell-gas turbine hybrid power system that is part of the Hybrid Performance (HYPER) project at the National Energy Technology Laboratory (NETL). Other theoretical developments in this work correspond to the integration of the BIO-CS approach with Multi-Agent Optimization (MAO) techniques and casting BIO-CS as a Model Predictive Controller (MPC). These developments are demonstrated by revisiting the fermentation process example. The proposed biologically-inspired approaches provide a promising alternative for advanced control of energy systems of the future

OPTIMAL CONTROL OF ION EXCHANGE PROCESS FOR CHROMATE REMOVAL AND PROTEIN A CHROMATOGRAPHY FOR ANTIBODY EXTRACTION

Ion exchange resins are widely used in the extraction of hazardous chemicals as well as the recovery of precious molecules. Therefore, an early breakthrough from the resin system can lead to toxic compounds affecting the drinking water quality or inefficient use of costly resins. Hence, accurate modeling of the ion exchange process and control strategy can enable decisions that assist in avoiding leakage when facing fluctuations in the inlet contaminant concentrations. In this work, the ion exchange process is modeled via the method of moments where the system uncertainties are captured via stochastic modeling using Ito processes. The flow rate is controlled to optimize the resin performance by maximizing its dynamic removal efficiency. The process runs more efficiently with a well-controlled varying flow rate rather than a constant flow, a standard industrial practice. The optimal control reveals that introducing the feed at a high flow rate followed by a decreasing flow can achieve significant removal of the target molecules and increase the efficiency of the purification process. This work has wide applicability ranging from chromate removal from water to extracting antibodies with a costly affinity chromatography resin