Structural vibration control with spatially varied disturbance input using a spatial [formula omitted] method

A novel distributed-decentralized fixed-time optimal frequency and excitation (Di-De-FTOFE) control framework in a network-preserving power system with nonlinear power flow is proposed in this paper. Firstly, to obtain the solution of the economic dispatch (ED) problem, the proposed control framework contains the distributed fixed-time consensus-based optimal frequency (Di-FTCOF) control to make the Lagrange multiplier of each generation reach consensus in a fixed time and the decentralized fixed-time excitation (De-FTE) control to ensure the power system frequency back to the rated value in a fixed time for satisfying the load-generation balance constraints of ED problem. Secondly, the voltage dynamic also can be maintained around the rated value by the designed De-FTE control which owns good universality to coordinate other optimal frequency control methods. Thirdly, the Di-De-FTOFE control framework is robust to communication failure through the self-adaptive adjustment, which is both analyzed in the theoretical verification and simulation. Finally, the performance of the Di-De-FTOFE control framework is evaluated in simulation with several adverse situations, such as load decrease/increase and communication failure.

The synthesis of structural health monitoring and vibration control is important in order to provide facilities for constructing smart structures. In recent years, some techniques have been developed to integrate structural identification and optimal vibration control. However, it is still challenging to integrate the identification and vibration control of time-varying structures subject to unknown earthquake excitation. The main difficulties are that structural dynamic responses collected by a simple harmonic motion system are absolute responses under unknown earthquake ground motion while previous identification approaches for unknown external excitation are not applicable for this situation and the need of an efficient algorithm to accurately track the various scenarios of time-varying structures with inexpensive computation to ensure the real-time performance requested by structural vibration control. In this paper, a novel algorithm is presented, in which structural time-varying parameters are treated as ‘virtual unknown inputs’ to the underlying time-invariant structure, a generalized Kalman filter with unknown inputs is proposed for joint identification of joint structural state, unknown earthquake excitation and ‘virtual unknown inputs’ with only partially measured structural absolute responses, and the identification results are integrated in real-time with the instantaneous optimal control scheme to reach the goal of optimal semi-active control provided by magneto-rheological dampers. Some numerical examples of integrated identification and vibration control of various time-varying structures subject to unknown earthquake excitation are used to demonstrate the performances of the proposed algorithm.

In this paper, we propose to solve the classical backward parabolic equation under the optimal control framework associated with the Tikhonov regularization formulation, where the initial condition is set to be the control variable while the misfit of the final condition is formulated as the Tikhonov objective functional to be minimized. The corresponding first-order necessary optimality system is discretized in a one-shot manner by a second-order finite difference scheme in space and time. The proposed optimal control setting, as discussed in the paper, provides more general framework in terms of solving this type of ill-posed inverse problem. In particular, several existing nonlocal quasi-boundary value methods appear to be the special cases of our proposed optimal control framework with appropriately chosen generalized regularization setting respectively. The relationship between our Tikhonov regularization approach and the quasi-boundary value methods is discussed in detail. The optimal control approach based on Tikhonov regularization is shown to deliver the known optimal order convergence rate. Numerical examples are provided to demonstrate both effective accuracy of approximation as well as excellent stability under the optimal control realization, comparing with three recent quasi-boundary value methods in literature.

The synthesis of structural identification with vibration control is cost-effective and beneficial for developing smart building structures. In the past several decades, techniques have been put forward for the combination of structural identification and vibration control. However, it is still a challenging task to synthesize identification and vibration control of time-varying structures under unknown earthquake excitation. First, structural dynamic responses collected by a structural health monitoring (SHM) system are absolute responses under unknown earthquake excitation, so existing identification approaches for unknown external excitations are not applicable for this situation. Moreover, it is essential to have an efficient algorithm for accurately tracking the various scenarios of time-varying structural physical parameters with inexpensive computation to ensure the real-time performance requested by structural vibration control. In this paper, an algorithm is put forward to tackle this challenging problem. It is proposed to treat structural time-varying effect as “virtual unknown inputs” to the corresponding time-invariant structure. A generalized extended Kalman filtering with unknown input (GEKF-UI) is proposed to circumvent the limitations of the existing EKF-UI approaches. The proposed GEKF-UI can simultaneously identify structural system, unknown earthquake excitation, and the “virtual unknown inputs” using only partially measured structural absolute responses. Then, the identified structural state is synthesized in real time with the instantaneous optimal control strategy for optimal semiactive control provided by magnetorheological dampers. Therefore, the proposed algorithm can track various structural time-varying with much less computation, which is more suitable for synthesis with structural control compared with other existing approaches. Some numerical cases of synthesizing identification and vibration control of various type time-varying structures under unknown earthquake motion are adopted to investigate the feasibilities of the proposed algorithm.

1 A Survey on Computational Optimal Control.- Issues in the Direct Transcription of Optimal Control Problems to Sparse Nonlinear Programs.- Optimization in Control of Robots.- Large-scale SQP Methods and their Application in Trajectory Optimization.- Solving Optimal Control and Pursuit-Evasion Game Problems of High Complexity.- 2 Theoretical Aspects of Optimal Control and Nonlinear Programming.- Continuation Methods In Boundary Value Problems.- Second Order Optimality Conditions for Singular Extremals.- Synthesis of Adaptive Optimal Controls for Linear Dynamic Systems.- Control Applications of Reduced SQP Methods.- Time Optimal Control of Mechanical Systems.- 3 Algorithms for Optimal Control Calculations.- Second Order Algorithm for Time Optimal Control of a Linear System.- An SQP-type Solution Method for Constrained Discrete-Time Optimal Control Problems.- Numerical Methods for Solving Differential Games, Prospective Applications to Technical Problems.- Construction of the Optimal Feedback Controller for Constrained Optimal Control Problems with Unknown Disturbances.- Repetitive Optimization for Predictive Control of Dynamic Systems under Uncertainty.- Optimal Control of Multistage Systems Described by High-Index Differential-Algebraic Equations.- A New Class of a High Order Interior Point Method for the Solution of Convex Semiinfinite Optimization Problems.- A Structured Interior Point SQP Method for Nonlinear Optimal Control Problems.- 4 Software for Optimal Control Calculations.- Automated Approach for Optimizing Dynamic Systems.- ANDECS: A Computation Environment for Control Applications of Optimization.- Application of Automatic Differentiation to Optimal Control Problems.- OCCAL: A mixed symbolic-numeric Optimal Control CALculator.- 5 Applications of Optimal Control.- A Robotic Satellite with Simplified Design.- Nonlinear Control under Constraints of a Biological System.- An Object-Oriented Approach to Optimally Describe and Specify a SCADA System Applied to a Power Network.- Near-Optimal Flight Trajectories Generated by Neural Networks.- Performance of a Feedback Method with Respect to Changes in the Air-Density during the Ascent of a Two-Stage-To-Orbit Vehicle.- Linear Optimal Control for Reentry Flight.- Steady-State Modelling of Turbine Engine with Controllers.- Shortest Paths for Satellite Mounted Robot Manipulators.- Optimal Control of the Industrial Robot Manutec r3.

We develop an optimality-based disturbance rejection control framework for nonlinear cascade systems with bounded energy (square-integrable) L/sub 2/ disturbances. Specifically, using a nonlinear-nonquadratic disturbance rejection optimal control framework we develop a family of globally stabilizing generalized backstepping controllers parametrized by the cost functional that is minimized. Furthermore, it is shown that the control Lyapunov function guaranteeing closed-loop stability is a solution to the steady-state Hamilton-Jacobi-Bellman equation for the controlled system and thus guarantees both optimality and stability. In addition, the resulting optimal controller guarantees that the closed-loop system is non-expansive (gain bounded). The results are then used to design disturbance rejection controllers for jet engine compression systems with bounded energy L/sub 2/ disturbances.

In the present work, the modal characteristics and vibration control performance of a cylindrical structure in air and water are experimentally investigated, and the results are presented in time and frequency domains. In order to achieve this goal, an end-capped cylindrical shell structure is considered as a host structure, and MFC (macro fiber composite) actuators, which are flexible, are bonded on the surface of the structure. After manufacturing a cylindrical shell structure with aluminum, a modal test is carried out, and the natural frequencies of the proposed structure are obtained and analyzed. To verify the modal test results, a finite element analysis is also performed, and the results are compared with the modal test results. By using the experimentally obtained modal characteristics, a state space control model is established. An optimal controller is then designed in order to control the unwanted vibration and is experimentally realized. It has been shown that the structural vibration can be effectively decreased with the optimal control methodology in both air and water environmental conditions.

Adaptive optimal backstepping control for strict-feedback nonlinear systems with time-varying partial output constraints

The centralized paradigm of a single controller and a single plant upon which modern control theory is built is no longer applicable to modern cyber-physical systems of interest, such as the power-grid, software defined networks or automated highways systems, as these are all large-scale and spatially distributed. Both the scale and the distributed nature of these systems has motivated the decentralization of control schemes into local sub-controllers that measure, exchange and act on locally available subsets of the globally available system information. This decentralization of control logic leads to different decision makers acting on asymmetric information sets, introduces the need for coordination between them, and perhaps not surprisingly makes the resulting optimal control problem much harder to solve. In fact, shortly after such questions were posed, it was realized that seemingly simple decentralized optimal control problems are computationally intractable to solve, with the Wistenhausen counterexample being a famous instance of this phenomenon. Spurred on by this perhaps discouraging result, a concerted 40 year effort to identify tractable classes of distributed optimal control problems culminated in the notion of quadratic invariance, which loosely states that if sub-controllers can exchange information with each other at least as quickly as the effect of their control actions propagates through the plant, then the resulting distributed optimal control problem admits a convex formulation. The identification of quadratic invariance as an appropriate means of convexifying distributed optimal control problems led to a renewed enthusiasm in the controller synthesis community, resulting in a rich set of results over the past decade. The contributions of this thesis can be seen as being a part of this broader family of results, with a particular focus on closing the gap between theory and practice by relaxing or removing assumptions made in the traditional distributed optimal control framework. Our contributions are to the foundational theory of distributed optimal control, and fall under three broad categories, namely controller synthesis, architecture design and system identification. We begin by providing two novel controller synthesis algorithms. The first is a solution to the distributed H∞ optimal control problem subject to delay constraints, and provides the only known exact characterization of delay-constrained distributed controllers satisfying an H∞ norm bound. The second is an explicit dynamic programming solution to a two player LQR state-feedback problem with varying delays. Accommodating varying delays represents an important first step in combining distributed optimal control theory with the area of Networked Control Systems that considers lossy channels in the feedback loop. Our next set of results are concerned with controller architecture design. When designing controllers for large-scale systems, the architectural aspects of the controller such as the placement of actuators, sensors, and the communication links between them can no longer be taken as given -- indeed the task of designing this architecture is now as important as the design of the control laws themselves. To address this task, we formulate the Regularization for Design (RFD) framework, which is a unifying computationally tractable approach, based on the model matching framework and atomic norm regularization, for the simultaneous co-design of a structured optimal controller and the architecture needed to implement it. Our final result is a contribution to distributed system identification. Traditional system identification techniques such as subspace identification are not computationally scalable, and destroy rather than leverage any a priori information about the system's interconnection structure. We argue that in the context of system identification, an essential building block of any scalable algorithm is the ability to estimate local dynamics within a large interconnected system. To that end we propose a promising heuristic for identifying the dynamics of a subsystem that is still connected to a large system. We exploit the fact that the transfer function of the local dynamics is low-order, but full-rank, while the transfer function of the global dynamics is high-order, but low-rank, to formulate this separation task as a nuclear norm minimization problem. Finally, we conclude with a brief discussion of future research directions, with a particular emphasis on how to incorporate the results of this thesis, and those of optimal control theory in general, into a broader theory of dynamics, control and optimization in layered architectures.

Water Distribution Networks (WDNs) are crucial for meeting current and future urban water demands. Knowledge of future water demand at different time scales is fundamental for optimal WDN design and operations. Various predictive models of water demand have been proposed in the literature, ranging from traditional time series analysis to cutting-edge machine learning and deep learning techniques. However, the task of forecasting urban water demand remains mostly decoupled from the design of the optimal control of the related WDN. Current performance assessment of demand predictive models focuses predominantly on forecast accuracy, overlooking their practical implications on WDN operations. Meanwhile, the existing research on WDN management often assumes either perfect knowledge of future water demands or employs empirical approximations and aggregate statistics to estimate future water needs. This study bridges this gap by scrutinizing the actual operational value of water demand forecasts in designing optimal operations of WDNs.Here, we develop a forecast-informed optimal WDN control framework to evaluate the operational value of water demand forecasts for WDN operations. Our framework comprises two main modules. The first module computes water demand forecasts. We comparatively evaluate a suite of different forecasting models —including Seasonal Auto-Regressive Integrated Moving Average with eXogenous factors, Multilayer Perceptron, Convolutional Neural Network, and Long Short-Term Memory (a network augmented with an attention mechanism) —across various forecast horizons (1/6/12 hours and 1/3/7/14 days ahead). The most accurate forecasts are integrated into the second module, an economic nonlinear Model Predictive Control (MPC) algorithm designed to optimize WDN operations. Within this module, an Artificial Neural Network (ANN) – based surrogate model encapsulates the hydraulics of the physical WDN, enhancing the optimization process while reducing complexity.We demonstrate our forecast-informed optimal WDN control framework on a real WDN of a rural town with approximately 10,000 inhabitants. Water demand data collected in the Netherlands for a period of 10 years (2007-2017) at 5-minute resolution and corresponding meteorological data are used to train the water demand forecasting models. The MPC module computes the optimal control sequence for 7 pumps and 1 valve in the WDN to minimize pump energy costs while meeting water demands and ensuring safety storage in 5 tanks. Initial findings reveal that the ANN-based surrogate model can accurately incorporate the WDN characteristics (R2 > 0.85), facilitating its integration into the MPC for an efficient and simplified representation of a real-world WDN. Further, MPC fed by 24-hour ahead water demand forecasts achieves potential energy savings of approximately 18% compared to a benchmark rule-based control strategy. Our framework yields a versatile simulation-based optimization tool for evaluating the impact of demand forecasts on WDN management. Future research efforts will aim at refining and comparing deterministic and stochastic water demand forecasts within the MPC framework, under diverse operational objectives.

In this paper, we present an optimal control approach using Linear Matrix Inequalities (LMIs) for trajectory tracking control of a three-wheeled omnidirectional mobile robot in the presence of external disturbances on the robot's actuators and noise in the robot's sensor measurements. First, a state-space representation of the omnidirectional robot dynamics is derived using a point-mass dynamic model. Then, we propose an LMI-based full-state feedback H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> -optimal controller for the tracking problem. The robot's tracking performance with the H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> -optimal controller is compared to its performance with a classical full-state feedback tracking controller in simulations with circular and bowtie-shaped reference trajectories. In order to evaluate our proposed controller in practice, we also implement the H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> -optimal and classical controllers for these reference trajectories on a three-wheeled omnidirectional robot. The H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> -optimal controller guarantees stabilization of the robot motion and attenuates the effects of frictional disturbances and measurement noise on the robot's tracking performance. Using the H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> -optimal controller, the robot is able to track the reference trajectories with up to a 47.8% and 45.8% decrease in the maximum pose and twist errors, respectively, over a full cycle of the trajectory compared to the classical controller. The simulation and experimental results show that our LMI-based H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> -optimal controller is robust to undesired effects of disturbances and noise on the dynamic behavior of the robot during trajectory tracking and can outperform the classical controller in attenuating their effects.

Buildings account for about 41% of primary energy consumption and 75% of the electricity. Space heating, space cooling, and ventilation are the dominant end uses, accounting for 41% of all energy consumed in the buildings sector. Growing interest in sustainability has resulted in research efforts to reduce energy consumption while providing adequate comfort to users. In this work, we present a Model Predictive Control (MPC) framework for optimal HVAC control that minimizes energy consumption while staying within the comfort bounds of the occupants. The novelty of our approach lies in the use of prediction occupancy models derived from data traces and incorporating those models within the MPC framework. We use a Blended Markov Chain (BMC) occupancy prediction model in order to predict thermal load and occupancy of each zone in the building. We test our approach in simulation and compare it with occupancy schedules and control rules currently use in our university buildings. Our preliminary results show that 15.5% savings in cooling in the summer, and 9.4% savings in heating in the winter are achievable when conditioning the building using our MPC/BMC control framework.

Proportional-Integral-Derivative (PID) scheme is the most commonly used algorithm for designing the controllers for unmanned aerial vehicles (UAVs). However, tuning PID gains is a non trivial task. A number of methods have been developed for tuning the PID gains for UAV systems. However, these methods do not handle wind disturbances, which is a major concern for small UAVs. In this paper, we propose a new method for determining optimized PID gains in the ℋ 2 optimal control framework, which achieves improved wind disturbance rejection. The proposed method compares the classical PID control law with the ℋ 2 optimal controller to determine the ℋ 2 optimal PID gains, and involves solving a convex optimization problem. The proposed controller is tested in two scenarios, namely, vertical velocity control, and vertical position control. The results are compared with the existing LQR based PID tuning method.

This paper describes a whole new framework to quickly develop dynamic visual servoing systems embedded in an FPGA. Parallel design of the algorithms increases the precision of this kind of controllers, whereas minimizes the response time. Embedding dynamic visual servoing algorithms converts these systems into real-time systems. Additionally, an optimal control framework to dynamically visual control robot arms is proposed. The architecture re-configurability is tested with the implementation of two dynamic visual servoing controllers. One of the implemented controllers is derived from the proposed control framework and the other is the well-known image transpose Jacobian controller. From these experiments, FPGA resources utilization and timeline of the pipeline show the optimization of the proposed framework.

The authors consider infinite-horizon nonlinear optimal control problems with unbounded performance indexes using notions of overtaking optimality. In the framework of optimal control, new sufficient conditions of Caratheodory-Hamilton-Jacobi type for both weak overtaking and overtaking optimality are presented and compared with known results from the calculus of variations setting. Using local structural properties of a related control Hamiltonian, conclusions are drawn on aspects of existence of overtaking and weak overtaking optimal controls, stability of optimal trajectories, and approximation of weak overtaking optimal controls. Both similarities and differences among alternative approaches to overtaking, weak overtaking, and strong optimal control problems are discussed. The formulation and results are illustrated in the classical linear-quadratic tracking problem and in an optimization approach to gain scheduling.