Multi-valued control problems and mixture density network

We have proposed a novel robust inversion-based neurocontroller that searches for the optimal control law by sampling from the estimated Gaussian distribution of the inverse plant model. However, for problems involving the prediction of continuous variables, a Gaussian model approximation provides only a very limited description of the properties of the inverse model. This is usually the case for problems in which the mapping to be learned is multi-valued or involves hysteritic transfer characteristics. This often arises in the solution of inverse plant models. In order to obtain a complete description of the inverse model, a more general multicomponent distributions must be modeled. In this paper we test whether our proposed sampling approach can be used when considering an arbitrary conditional probability distributions. These arbitrary distributions will be modeled by a mixture density network. Importance sampling provides a structured and principled approach to constrain the complexity of the search space for the ideal control law. The effectiveness of the importance sampling from an arbitrary conditional probability distribution will be demonstrated using a simple single input single output static nonlinear system with hysteretic characteristics in the inverse plant model.

Distributed control of computer communication systems

Flow control in Computer Communication systems is generally a multi-layered structure, consisting of several mechanisms operating independently at different levels. Evaluation of the performance of networks in which different flow control mechanisms act simultaneously is an important area of research, and is examined in depth in this thesis. This thesis presents the modelling of a finite resource computer communication network equipped with three levels of flow control, based on closed queueing network theory. The flow control mechanisms considered are: end-to-end control of virtual circuits, network access control of external messages at the entry nodes and the hop level control between nodes. The model is solved by a heuristic technique, based on an equivalent reduced network and the heuristic extensions to the mean value analysis algorithm. The method has significant computational advantages, and overcomes the limitations of the exact methods. It can be used to solve large network models with finite buffers and many virtual circuits. The model and its heuristic solution are validated by simulation. The interaction between the three levels of flow control are investigated. A queueing model is developed for the admission delay on virtual circuits with end-to-end control, in which messages arrive from independent Poisson sources. The selection of optimum window limit is considered. Several advanced network access schemes are postulated to improve the network performance as well as that of selected traffic streams, and numerical results are presented. A model for the dynamic control of input traffic is developed. Based on Markov decision theory, an optimal control policy is formulated. Numerical results are given and throughput-delay performance is shown to be better with dynamic control than with static control.

Probabilistic control for uncertain systems

In this paper a new framework has been applied to the design of controllers which encompasses nonlinearity, hysteresis and arbitrary density functions of forward models and inverse controllers. Using mixture density networks, the probabilistic models of both the forward and inverse dynamics are estimated such that they are dependent on the state and the control input. The optimal control strategy is then derived which minimizes uncertainty of the closed loop system. In the absence of reliable plant models, the proposed control algorithm incorporates uncertainties in model parameters, observations, and latent processes. The local stability of the closed loop system has been established. The efficacy of the control algorithm is demonstrated on two nonlinear stochastic control examples with additive and multiplicative noise.

A probabilistic indirect adaptive control for systems with input-dependent noise

A probabilistic indirect adaptive controller is proposed for the general nonlinear multivariate class of discrete time system. The proposed probabilistic framework incorporates input–dependent noise prediction parameters in the derivation of the optimal control law. Moreover, because noise can be nonstationary in practice, the proposed adaptive control algorithm provides an elegant method for estimating and tracking the noise. For illustration purposes, the developed method is applied to the affine class of nonlinear multivariate discrete time systems and the desired result is obtained: the optimal control law is determined by solving a cubic equation and the distribution of the tracking error is shown to be Gaussian with zero mean. The efficiency of the proposed scheme is demonstrated numerically through the simulation of an affine nonlinear system.

Stochastic control strategies and adaptive critic methods

Adaptive critic methods have common roots as generalizations of dynamic programming for neural reinforcement learning approaches. Since they approximate the dynamic programming solutions, they are potentially suitable for learning in noisy, nonlinear and nonstationary environments. In this study, a novel probabilistic dual heuristic programming (DHP) based adaptive critic controller is proposed. Distinct to current approaches, the proposed probabilistic (DHP) adaptive critic method takes uncertainties of forward model and inverse controller into consideration. Therefore, it is suitable for deterministic and stochastic control problems characterized by functional uncertainty. Theoretical development of the proposed method is validated by analytically evaluating the correct value of the cost function which satisfies the Bellman equation in a linear quadratic control problem. The target value of the critic network is then calculated and shown to be equal to the analytically derived correct value.

A Bayesian approach to modeling the conditional density of the inverse controller

The inverse controller is traditionally assumed to be a deterministic function. This paper presents a pedagogical methodology for estimating the stochastic model of the inverse controller. The proposed method is based on Bayes' theorem. Using Bayes' rule to obtain the stochastic model of the inverse controller allows the use of knowledge of uncertainty from both the inverse and the forward model in estimating the optimal control signal. The paper presents the methodology for general nonlinear systems. For illustration purposes, the proposed methodology is applied to linear Gaussian systems. © 2004 IEEE.

A Stochastic Control Approach to a Parabolic Equation, Reciprocal Processes

2000 Mathematics Subject Classi cation: 49L60, 60J60, 93E20.

Exact Solution of Bayes and Minimax Change-Detection Problems

The challenge of detecting a change in the distribution of data is a sequential decision problem that is relevant to many engineering solutions, including quality control and machine and process monitoring. This dissertation develops techniques for exact solution of change-detection problems with discrete time and discrete observations. Change-detection problems are classified as Bayes or minimax based on the availability of information on the change-time distribution. A Bayes optimal solution uses prior information about the distribution of the change time to minimize the expected cost, whereas a minimax optimal solution minimizes the cost under the worst-case change-time distribution. Both types of problems are addressed. The most important result of the dissertation is the development of a polynomial-time algorithm for the solution of important classes of Markov Bayes change-detection problems. Existing techniques for epsilon-exact solution of partially observable Markov decision processes have complexity exponential in the number of observation symbols. A new algorithm, called constellation induction, exploits the concavity and Lipschitz continuity of the value function, and has complexity polynomial in the number of observation symbols. It is shown that change-detection problems with a geometric change-time distribution and identically- and independently-distributed observations before and after the change are solvable in polynomial time. Also, change-detection problems on hidden Markov models with a fixed number of recurrent states are solvable in polynomial time. A detailed implementation and analysis of the constellation-induction algorithm are provided. Exact solution methods are also established for several types of minimax change-detection problems. Finite-horizon problems with arbitrary observation distributions are modeled as extensive-form games and solved using linear programs. Infinite-horizon problems with linear penalty for detection delay and identically- and independently-distributed observations can be solved in polynomial time via epsilon-optimal parameterization of a cumulative-sum procedure. Finally, the properties of policies for change-detection problems are described and analyzed. Simple classes of formal languages are shown to be sufficient for epsilon-exact solution of change-detection problems, and methods for finding minimally sized policy representations are described.

Optimal sequence of landfills in solid waste management

Given that landfills are depletable and replaceable resources, the right approach, when dealing with landfill management, is that of designing an optimal sequence of landfills rather than designing every single landfill separately. In this paper we use Optimal Control models, with mixed elements of both continuous and discrete time problems, to determine an optimal sequence of landfills, as regarding their capacity and lifetime. The resulting optimization problems involve splitting a time horizon of planning into several subintervals, the length of which has to be decided. In each of the subintervals some costs, the amount of which depends on the value of the decision variables, have to be borne. The obtained results may be applied to other economic problems such as private and public investments, consumption decisions on durable goods, etc.

Branch and Bound algorithms in greenhouse climate control

The horticultural sector has become an increasingly important sector of food production, for which greenhouse climate control plays a vital role in improving its sustainability. One of the methods to control the greenhouse climate is Model Predictive Control, which can be optimized through a branch and bound algorithm. The application of the algorithm in literature is examined and analyzed through small examples, and later extended to greenhouse climate simulation. A comparison is made of various alternative objective functions available in literature. Subsequently, a modidified version of the B&B algorithm is presented, which reduces the number of node evaluations required for optimization. Finally, three alternative algorithms are developed and compared to consider the optimization problem from a discrete to a continuous control space.

DATA DRIVEN INTELLIGENT AGENT NETWORKS FOR ADAPTIVE MONITORING AND CONTROL

To analyze the characteristics and predict the dynamic behaviors of complex systems over time, comprehensive research to enable the development of systems that can intelligently adapt to the evolving conditions and infer new knowledge with algorithms that are not predesigned is crucially needed. This dissertation research studies the integration of the techniques and methodologies resulted from the fields of pattern recognition, intelligent agents, artificial immune systems, and distributed computing platforms, to create technologies that can more accurately describe and control the dynamics of real-world complex systems. The need for such technologies is emerging in manufacturing, transportation, hazard mitigation, weather and climate prediction, homeland security, and emergency response. Motivated by the ability of mobile agents to dynamically incorporate additional computational and control algorithms into executing applications, mobile agent technology is employed in this research for the adaptive sensing and monitoring in a wireless sensor network. Mobile agents are software components that can travel from one computing platform to another in a network and carry programs and data states that are needed for performing the assigned tasks. To support the generation, migration, communication, and management of mobile monitoring agents, an embeddable mobile agent system (Mobile-C) is integrated with sensor nodes. Mobile monitoring agents visit distributed sensor nodes, read real-time sensor data, and perform anomaly detection using the equipped pattern recognition algorithms. The optimal control of agents is achieved by mimicking the adaptive immune response and the application of multi-objective optimization algorithms. The mobile agent approach provides potential to reduce the communication load and energy consumption in monitoring networks. The major research work of this dissertation project includes: (1) studying effective feature extraction methods for time series measurement data; (2) investigating the impact of the feature extraction methods and dissimilarity measures on the performance of pattern recognition; (3) researching the effects of environmental factors on the performance of pattern recognition; (4) integrating an embeddable mobile agent system with wireless sensor nodes; (5) optimizing agent generation and distribution using artificial immune system concept and multi-objective algorithms; (6) applying mobile agent technology and pattern recognition algorithms for adaptive structural health monitoring and driving cycle pattern recognition; (7) developing a web-based monitoring network to enable the visualization and analysis of real-time sensor data remotely. Techniques and algorithms developed in this dissertation project will contribute to research advances in networked distributed systems operating under changing environments.

Distributed Large-scale Mixed-Integer Optimization with Application to Energy and Multi-robot Networks

Several decision and control tasks in cyber-physical networks can be formulated as large- scale optimization problems with coupling constraints. In these "constraint-coupled" problems, each agent is associated to a local decision variable, subject to individual constraints. This thesis explores the use of primal decomposition techniques to develop tailored distributed algorithms for this challenging set-up over graphs. We first develop a distributed scheme for convex problems over random time-varying graphs with non-uniform edge probabilities. The approach is then extended to unknown cost functions estimated online. Subsequently, we consider Mixed-Integer Linear Programs (MILPs), which are of great interest in smart grid control and cooperative robotics. We propose a distributed methodological framework to compute a feasible solution to the original MILP, with guaranteed suboptimality bounds, and extend it to general nonconvex problems. Monte Carlo simulations highlight that the approach represents a substantial breakthrough with respect to the state of the art, thus representing a valuable solution for new toolboxes addressing large-scale MILPs. We then propose a distributed Benders decomposition algorithm for asynchronous unreliable networks. The framework has been then used as starting point to develop distributed methodologies for a microgrid optimal control scenario. We develop an ad-hoc distributed strategy for a stochastic set-up with renewable energy sources, and show a case study with samples generated using Generative Adversarial Networks (GANs). We then introduce a software toolbox named ChoiRbot, based on the novel Robot Operating System 2, and show how it facilitates simulations and experiments in distributed multi-robot scenarios. Finally, we consider a Pickup-and-Delivery Vehicle Routing Problem for which we design a distributed method inspired to the approach of general MILPs, and show the efficacy through simulations and experiments in ChoiRbot with ground and aerial robots.

Development of Optimal Energy Management Strategies for a Hybrid Boat

The present work proposes different approaches to extend the mathematical methods of supervisory energy management used in terrestrial environments to the maritime sector, that diverges in constraints, variables and disturbances. The aim is to find the optimal real-time solution that includes the minimization of a defined track time, while maintaining the classical energetic approach. Starting from analyzing and modelling the powertrain and boat dynamics, the energy economy problem formulation is done, following the mathematical principles behind the optimal control theory. Then, an adaptation aimed in finding a winning strategy for the Monaco Energy Boat Challenge endurance trial is performed via ECMS and A-ECMS control strategies, which lead to a more accurate knowledge of energy sources and boat’s behaviour. The simulations show that the algorithm accomplishes fuel economy and time optimization targets, but the latter adds huge tuning and calculation complexity. In order to assess a practical implementation on real hardware, the knowledge of the previous approaches has been translated into a rule-based algorithm, that let it be run on an embedded CPU. Finally, the algorithm has been tuned and tested in a real-world race scenario, showing promising results.

Trajectory planning of single and dual-arm robots for time-optimal handling of liquids and objects

This Thesis studies the optimal control problem of single-arm and dual-arm serial robots to achieve the time-optimal handling of liquids and objects. The first topic deals with the planning of time-optimal anti-sloshing trajectories of an industrial robot carrying a cylindrical container filled with a liquid, considering 1-dimensional and 2-dimensional planar motions. A technique for the estimation of the sloshing height is presented, together with its extension to 3-dimensional motions. An experimental validation campaign is provided and discussed to assess the thoroughness of such a technique. As far as anti-sloshing trajectories are concerned, 2-dimensional paths are considered and, for each one of them, three constrained optimizations with different values of the sloshing-height thresholds are solved. Experimental results are presented to compare optimized and non-optimized motions. The second part focuses on the time-optimal trajectory planning for dual-arm object handling, employing two collaborative robots (cobots) and adopting an admittance-control strategy. The chosen manipulation approach, known as cooperative grasping, is based on unilateral contact between the cobots and the object, and it may lead to slipping during motion if an internal prestress along the contact-normal direction is not prescribed. Thus, a virtual penetration is considered, aimed at generating the necessary internal prestress. The stability of cooperative grasping is ensured as long as the exerted forces on the object remain inside the static-friction cone. Constrained-optimization problems are solved for 3-dimensional paths: the virtual penetration is chosen among the control inputs of the problem and friction-cone conditions are treated as inequality constraints. Also in this case experiments are presented in order to prove evidence of the firm handling of the object, even for fast motions.

Design and implementation of an optimal motion cueing algorithm for the Stuttgart Driving Simulator

Driving simulators emulate a real vehicle drive in a virtual environment. One of the most challenging problems in this field is to create a simulated drive as real as possible to deceive the driver's senses and cause the believing to be in a real vehicle. This thesis first provides an overview of the Stuttgart driving simulator with a description of the overall system, followed by a theoretical presentation of the commonly used motion cueing algorithms. The second and predominant part of the work presents the implementation of the classical and optimal washout algorithms in a Simulink environment. The project aims to create a new optimal washout algorithm and compare the obtained results with the results of the classical washout. The classical washout algorithm, already implemented in the Stuttgart driving simulator, is the most used in the motion control of the simulator. This classical algorithm is based on a sequence of filters in which each parameter has a clear physical meaning and a unique assignment to a single degree of freedom. However, the effects on human perception are not exploited, and each parameter must be tuned online by an engineer in the control room, depending on the driver's feeling. To overcome this problem and also consider the driver's sensations, the optimal washout motion cueing algorithm was implemented. This optimal control-base algorithm treats motion cueing as a tracking problem, forcing the accelerations perceived in the simulator to track the accelerations that would have been perceived in a real vehicle, by minimizing the perception error within the constraints of the motion platform. The last chapter presents a comparison between the two algorithms, based on the driver's feelings after the test drive. Firstly it was implemented an off-line test with a step signal as an input acceleration to verify the behaviour of the simulator. Secondly, the algorithms were executed in the simulator during a test drive on several tracks.