270 research outputs found

    Hybrid System Identification of Manual Tracking Submovements in Parkinson\u27s Disease

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    Seemingly smooth motions in manual tracking, (e.g., following a moving target with a joystick input) are actually sequences of submovements: short, open-loop motions that have been previously learned. In Parkinson\u27s disease, a neurodegenerative movement disorder, characterizations of motor performance can yield insight into underlying neurological mechanisms and therefore into potential treatment strategies. We focus on characterizing submovements through Hybrid System Identification, in which the dynamics of each submovement, the mode sequence and timing, and switching mechanisms are all unknown. We describe an initialization that provides a mode sequence and estimate of the dynamics of submovements, then apply hybrid optimization techniques based on embedding to solve a constrained nonlinear program. We also use the existing geometric approach for hybrid system identification to analyze our model and explain the deficits and advantages of each. These methods are applied to data gathered from subjects with Parkinson\u27s disease (on and off L-dopa medication) and from age-matched control subjects, and the results compared across groups demonstrating robust differences. Lastly, we develop a scheme to estimate the switching mechanism of the modeled hybrid system by using the principle of maximum margin separating hyperplane, which is a convex optimization problem, over the affine parameters describing the switching surface and provide a means o characterizing when too many or too few parameters are hypothesized to lie in the switching surface

    International Conference on Continuous Optimization (ICCOPT) 2019 Conference Book

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    The Sixth International Conference on Continuous Optimization took place on the campus of the Technical University of Berlin, August 3-8, 2019. The ICCOPT is a flagship conference of the Mathematical Optimization Society (MOS), organized every three years. ICCOPT 2019 was hosted by the Weierstrass Institute for Applied Analysis and Stochastics (WIAS) Berlin. It included a Summer School and a Conference with a series of plenary and semi-plenary talks, organized and contributed sessions, and poster sessions. This book comprises the full conference program. It contains, in particular, the scientific program in survey style as well as with all details, and information on the social program, the venue, special meetings, and more

    Statistical Machine Learning for Modeling and Control of Stochastic Structured Systems

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    Machine learning and its various applications have driven innovation in robotics, synthetic perception, and data analytics. The last decade especially has experienced an explosion in interest in the research and development of artificial intelligence with successful adoption and deployment in some domains. A significant force behind these advances has been an abundance of data and the evolution of simple computational models and tools with a capacity to scale up to massive learning automata. Monolithic neural networks with billions of parameters that rely on automatic differentiation are a prime example of the significant role efficient computation has had on supercharging the ability of well-established representations to extract intelligent patterns from unstructured data. Nonetheless, despite the strides taken in the digital domains of vision and natural language processing, applications of optimal control and robotics significantly trail behind and have not been able to capitalize as much on the latest trends of machine learning. This discrepancy can be explained by the limited transferability of learning concepts that rely on full differentiability to the heavily structured physical and human interaction environments, not to mention the substantial cost of data generation on real physical systems. Therefore, these factors severely limit the application scope of loosely-structured over-parameterized data-crunching machines in the mechanical realm of robot learning and control. This thesis investigates modeling paradigms of hierarchical and switching systems to tackle some of the previously highlighted issues. This research direction is motivated by insights into universal function approximation via local cooperating units and the promise of inherently regularized representations through explicit structural design. Moreover, we explore ideas from robust optimization that address model mismatch issues in statistical models and outline how related methods may be used to improve the tractability of state filtering in stochastic hybrid systems. In Chapter 2, we consider hierarchical modeling for general regression problems. The presented approach is a generative probabilistic interpretation of local regression techniques that approximate nonlinear functions through a set of local linear or polynomial units. The number of available units is crucial in such models, as it directly balances representational power with the parametric complexity. This ambiguity is addressed by using principles from Bayesian nonparametrics to formulate flexible models that adapt their complexity to the data and can potentially encompass an infinite number of components. To learn these representations, we present two efficient variational inference techniques that scale well with data and highlight the advantages of hierarchical infinite local regression models, such as dealing with non-smooth functions, mitigating catastrophic forgetting, and enabling parameter sharing and fast predictions. Finally, we validate this approach on a set of large inverse dynamics datasets and test the learned models in real-world control scenarios. Chapter 3 addresses discrete-continuous hybrid modeling and control for stochastic dynamical systems, which implies dealing with time-series data. In this scenario, we develop an automatic system identification technique that decomposes nonlinear systems into hybrid automata and leverages the resulting structure to learn switching feedback control via hierarchical reinforcement learning. In the process, we rely on an augmented closed-loop hidden Markov model architecture that captures time correlations over long horizons and provides a principled Bayesian inference framework for learning hybrid representations and filtering the hidden discrete states to apply control accordingly. Finally, we embed this structure explicitly into a novel hybrid relative entropy policy search algorithm that optimizes a set of local polynomial feedback controllers and value functions. We validate the overall switching-system perspective by benchmarking the open-loop predictive performance against popular black-box representations. We also provide qualitative empirical results for hybrid reinforcement learning on common nonlinear control tasks. In Chapter 4, we attend to a general and fundamental problem in learning for control, namely robustness in data-driven stochastic optimization. The question of sensitivity has a strong priority, given the rising popularity of embedding statistical models into stochastic control frameworks. However, data from dynamical, especially mechanical, systems is often scarce due to a high extraction cost and limited coverage of the state-action space. The result is usually poor models with narrow validity and brittle control laws, particularly in an ill-posed over-parameterized learning example. We propose to robustify stochastic control by finding the worst-case distribution over the dynamics and optimizing a corresponding robust policy that minimizes the probability of catastrophic failures. We achieve this goal by formulating a two-stage iterative minimax optimization problem that finds the most pessimistic adversary in a trust region around a nominal model and uses it to optimize a robust optimal controller. We test this approach on a set of linear and nonlinear stochastic systems and supply empirical evidence of its practicality. Finally, we provide an outlook on how similar multi-stage distributional optimization techniques can be applied in approximate filtering of stochastic switching systems in order to tackle the issue of exponential explosion in state mixture components. In summation, the individual contributions of this thesis are a collection of interconnected principles for structured and robust learning for control. Although many challenges remain ahead, this research lays a foundation for reflecting on future structured learning questions that strive to combine optimal control and statistical machine learning perspectives for the automatic decomposition and optimization of hierarchical models

    Study Of Stochastic Market Clearing Problems In Power Systems With High Renewable Integration

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    Integrating large-scale renewable energy resources into the power grid poses several operational and economic problems due to their inherently stochastic nature. The lack of predictability of renewable outputs deteriorates the power grid’s reliability. The power system operators have recognized this need to account for uncertainty in making operational decisions and forming electricity pricing. In this regard, this dissertation studies three aspects that aid large-scale renewable integration into power systems. 1. We develop a nonparametric change point-based statistical model to generate scenarios that accurately capture the renewable generation stochastic processes; 2. We design new pricing mechanisms derived from alternative stochastic programming formulations of the electricity market clearing problem under uncertainty; 3. We devise a novel approach to coordinate strategic operations of multiple noncooperative system operators. The current industry practices are based on deterministic models that do not account for the stochasticity of renewable energy. Therefore, the solutions obtained from these deterministic models will not provide accurate measurements. Stochastic programming (SP) can accommodate the stochasticity of renewable energy by considering a set of possible scenarios. However, the reliability of the SP model solution depends on the accuracy of the scenarios. We develop a nonparametric statistical simulation method to develop scenarios for wind generation using wind speed data. In this method, we address the nonstationarity issues that come with wind-speed time-series data using a nonparametric change point detection method. Using this approach, we retain the covariance structure of the original wind-speed time series in all the simulated series. With an accurate set of scenarios, we develop alternative two-stage SP models for the two-settlement electricity market clearing problem using different representations of the non-anticipativity constraints. Different forms of non-anticipativity constraints reveal different hidden dual information inside the canonical two-stage SP model, which we use to develop new pricing mechanisms. The new pricing mechanisms preserve properties of previously proposed pricing mechanisms, such as revenue adequacy in expectation and cost recovery in expectation. More importantly, our pricing mechanisms can guarantee cost recovery for every scenario. Furthermore, we develop bounds for the price distortion under every scenario instead of the expected distortion bounds. We demonstrate the differences in prices obtained from the alternative mechanisms through numerical experiments. Finally, we discuss the importance of distributed smart grid operations inside the power grid. We develop an information and electricity exchange system among multiple distribution systems. These distribution systems participate/compete in common markets cohere electricity is exchanged. We develop a standard Nash game treating each distribution system (DS) as an individual player who optimizes their strategies separately. We develop proximal best response (BR) schemes to solve this problem. We present results from numerical experiments conducted on three and six DS settings

    Benelux meeting on systems and control, 23rd, March 17-19, 2004, Helvoirt, The Netherlands

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    Book of abstract

    Fuel Optimal Control Algorithms for Connected and Automated Plug-In Hybrid Vehicles

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    Improving the fuel economy of light-duty vehicles (LDV) is a compelling solution to stabilizing Greenhouse Gas (GHG) emissions and decreasing the reliance on fossil fuels. Over the years, there has been a considerable shift in the market of LDVs toward powertrain electrification, and plug-in hybrid electric vehicles (PHEVs) are the most cost-effective in avoiding GHG emissions. Meanwhile, connected and automated vehicle (CAV) technologies permit energy-efficient driving with access to accurate trip information that integrates traffic and charging infrastructure. This thesis aims at developing optimization-based algorithms for controlling powertrain and vehicle longitudinal dynamics to fully exploit the potential for reducing fuel consumption of individual PHEVs by utilizing CAV technologies. A predictive equivalent minimization strategy (P-ECMS) is proposed for a human-driven PHEV to adjust the co-state based on the difference between the future battery state-of-charge (SOC) obtained from short-horizon prediction and a future reference SOC from SOC node planning. The SOC node planning, which generates battery SOC reference waypoints, is performed using a simplified speed profile constructed from segmented traffic information, typically available from mobile mapping applications. The PHEV powertrain, consisting of engine and electric motors, is mathematically modeled as a hybrid system as the state is defined by the values of the continuous variable, SOC, and discrete modes, hybrid vehicle (HV), and electric vehicle (EV) modes with the engine on/off. As a hybrid system, the optimal control of PHEVs necessitates a numerical approach to solving a mixed-integer optimization problem. It is of interest to have a unified numerical algorithm for solving such mixed-integer optimal control problems with many states and control inputs. Based on a discrete maximum principle (DMP), a discrete mixed-integer shooting (DMIS) algorithm is proposed. The DMIS is demonstrated in successfully addressing the cranking fuel optimization in the energy management of a PHEV. It also serves as the foundation of the co-optimization problem considered in the remaining part of the thesis. This thesis further investigates different control designs with an increased vehicle automation level combining vehicle dynamics and powertrain of PHEVs in within-a-lane traffic flow. This thesis starts with a sequential (or decentralized) optimization and then advances to direct fuel minimization by simultaneously optimizing the two subsystems in a centralized manner. When shifting toward online implementation, the unique challenge lies in the conflict between the long control horizon required for global optimality and the computational power limit. A receding horizon strategy is proposed to resolve the conflict between the horizon length and the computation complexity, with co-states approximating the future cost. In particular, the co-state is updated using a nominal trajectory and the temporal-difference (TD) error based on the co-state dynamics. The remaining work aims to develop a unified model predictive control (MPC) framework from the powertrain (PT) control of a human-driven to the combined vehicle dynamics (VD) and PT control of an automated PHEV. In the unified framework, the cost-to-go (the fuel consumption as the economic cost) is represented by the co-state associated with the battery SOC dynamics. In its application to automated PHEVs, a control barrier function (CBF) is augmented as an add-on block to modify the vehicle-level control input for guaranteed safety. This unified MPC framework allows for systematically evaluating the fuel economy and drivability performance of different levels and structures of optimization strategies.PHDMechanical EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/169876/1/dichencd_1.pd

    Approximation methodologies for explicit model predictive control of complex systems

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    This thesis concerns the development of complexity reduction methodologies for the application of multi-parametric/explicit model predictive (mp-MPC) control to complex high fidelity models. The main advantage of mp-MPC is the offline relocation of the optimization task and the associated computational expense through the use of multi-parametric programming. This allows for the application of MPC to fast sampling systems or systems for which it is not possible to perform online optimization due to cycle time requirements. The application of mp-MPC to complex nonlinear systems is of critical importance and is the subject of the thesis. The first part is concerned with the adaptation and development of model order reduction (MOR) techniques for application in combination to mp-MPC algorithms. This first part includes the mp-MPC oriented use of existing MOR techniques as well as the development of new ones. The use of MOR for multi-parametric moving horizon estimation is also investigated. The second part of the thesis introduces a framework for the ‘equation free’ surrogate-model based design of explicit controllers as a possible alternative to multi-parametric based methods. The methodology relies upon the use of advanced data-classification approaches and surrogate modelling techniques, and is illustrated with different numerical examples.Open Acces
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