Optimal Control Methodology Research Articles

Coot Bird Algorithms-Based Tuning PI Controller for Optimal Microgrid Autonomous Operation

This paper develops a novel methodology for optimal control of islanded microgrids (MGs) based on the coot bird metaheuristic optimizer (CBMO). To this end, the optimum gains for the PI controller are found using the CBMO under a multi-objective optimization framework. The Response Surface Methodology (RSM) is incorporated into the developed procedure to achieve a compromise solution among the different objectives. To prove the effectiveness of the new proposal, a benchmark MG is tested under various scenarios, 1) isolate the system from the grid (autonomous mode), 2) islanded system exposure to load changes, and 3) islanded system exposure to a 3 phase fault. Extensive simulations are performed to validate the new method taking conventional data from PSCAD/EMTDC software. The validity of the suggested optimizer is proved by comparing its results with that achieved using the LMSRE-based adaptive control, sunflower optimization algorithm (SFO), Ziegler-Nichols method and the particle swarm optimization (PSO) techniques. The article shows the superiority of the suggested CBMO over the LMSRE-based adaptive control, SFO, Ziegler-Nichols and the PSO techniques in the transient responses of the system.

Multilevel Selective Harmonic Modulation by Duality*

We address the Selective Harmonic Modulation (SHM) problem in power electronic engineering, consisting in designing a multilevel staircase control signal with some prescribed frequencies to improve the performances of a converter. In this work, SHM is addressed through an optimal control methodology based on duality, in which the admissible controls are piece-wise constant functions, taking values only in a given finite set. To fulfill this constraint, the cornerstone of our approach is the introduction of a special penalization in the cost functional, in the form of a piece-wise affine approximation of a parabola. In this manner, we build optimal multilevel controls having the desired staircase structure.

Methodology for optimal design and control of wind energy system based on simplifying assumptions

The study presented in this paper concerns the development of a new methodology for design and controlling a wind energy generation chain. This methodology is based on combined Analytical-Finite Element-Experimental method. This type of converter chosen is an AC-DC inverter with IGBTs to improve the robustness of the power chain structure. It offers a reduction of the cost of the power chain and the improvement of the performances of the global studied system, as the control at power factor equal to unity and providing an electromagnetic torque which is added to the useful torque in order to extract the maximal energy. The control algorithms permit to regulate Le charging voltage and current in their rated values considered as optimal battery charging voltage and current. The global model of the power chain is implemented under the Matlab-Sumilink simulation environment for performance and efficiency analysis.

Achieving fast high-fidelity optimal control of many-body quantum dynamics

We demonstrate the efficiency of a recent exact-gradient optimal control methodology by applying it to a challenging many-body problem, crossing the superfluid to Mott-insulator phase transition in the Bose-Hubbard model. The system size necessitates a matrix product state representation and this seamlessly integrates with the requirements of the algorithm. We observe fidelities in the range 0.99--0.9999 with associated minimal process duration estimates displaying an exponential fidelity-duration trade-off across several orders of magnitude. The corresponding optimal solutions are characterized in terms of a predominantly linear sweep across the critical point followed by bang-bang-like structure. This is quite different from the smooth and monotonic solutions identified by earlier gradient-free optimizations which are hampered in locating the higher complexity protocols in the regime of high fidelities at low process durations. Overall, the comparison suggests significant methodological improvements also for many-body systems in the ideal open-loop setting. Acknowledging that idealized open-loop control may deteriorate in actual experiments, we discuss the merits of using such an approach in combination with closed-loop control---in particular, high-fidelity physical insights extracted with the former can be used to formulate practical, low-dimensional search spaces for the latter.

Optimal inspection and maintenance planning for deteriorating structural components through dynamic Bayesian networks and Markov decision processes

Civil and maritime engineering systems, among others, from bridges to offshore platforms and wind turbines, must be efficiently managed, as they are exposed to deterioration mechanisms throughout their operational life, such as fatigue and/or corrosion. Identifying optimal inspection and maintenance policies demands the solution of a complex sequential decision-making problem under uncertainty, with the main objective of efficiently controlling the risk associated with structural failures. Addressing this complexity, risk-based inspection planning methodologies, supported often by dynamic Bayesian networks, evaluate a set of pre-defined heuristic decision rules to reasonably simplify the decision problem. However, the resulting policies may be compromised by the limited space considered in the definition of the decision rules. Avoiding this limitation, Partially Observable Markov Decision Processes (POMDPs) provide a principled mathematical methodology for stochastic optimal control under uncertain action outcomes and observations, in which the optimal actions are prescribed as a function of the entire, dynamically updated, state probability distribution. In this paper, we combine dynamic Bayesian networks with POMDPs in a joint framework for optimal inspection and maintenance planning, and we provide the relevant formulation for developing both infinite and finite horizon POMDPs in a structural reliability context. The proposed methodology is implemented and tested for the case of a structural component subject to fatigue deterioration, demonstrating the capability of state-of-the-art point-based POMDP solvers of solving the underlying planning stochastic optimization problem. Within the numerical experiments, POMDP and heuristic-based policies are thoroughly compared, and results showcase that POMDPs achieve substantially lower costs as compared to their counterparts, even for traditional problem settings.

A novel domain of attraction based synthesis of inverse optimal control

AbstractThis article proposes a novel and systematic methodology for the inverse optimal control (IOC) of a class of input affine nonlinear systems. First, the system is represented in the pseudo‐linear state‐dependent coefficient (SDC) form so as to facilitate the use of matrix algebraic concepts in the design, while preserving the nonlinear system dynamics. Second, the IOC problem which seeks the solution to the Hamilton–Jacobi–Bellman equation is translated to a diagonal stability (D‐stability) problem. Therefore, the general notion of D‐stability, which deals with the characterization of a matrix for the existence of a diagonal matrix such that , is redefined with respect to SDC factored matrices in this work. Consequently, the criteria for the existence (necessary condition) and determination of a diagonal solution (sufficient condition) are formulated in terms of the SDC matrices. It is shown in this work that these criteria can be readily met by the closed‐loop system matrix , for any arbitrary domain in state‐space, by manipulating only the diagonal elements using the diagonal matrix constituted by the IOC feedback. In short, the IOC feedback is designed such that the criteria for D‐stability by the closed‐loop system matrix is fulfilled. Hence this novel design methodology is meaningfully named as “Inverse optimal control via diagonal stabilization” (IOC‐D). The main advantages of IOC‐D include: (i) guaranteed estimate of the domain of attraction (DOA), (ii) Immense flexibility of design, and (iii) guaranteed closed form solution which makes the design procedure analytic and computationally efficient. Numerical simulations validate the theoretical developments and the overall efficiency of the proposed approach.

Piezo-based flexural vibration suppression for an annular rotor via rotating-frame H2 control optimization

Elastic vibration can arise in annular and thin-walled rotor structures, impacting on operating performance and the risk of failure. Feedback control to reduce flexural vibration can be realized using lightweight actuators and sensors embedded in the rotor structure. To design optimal controllers, rotating-frame models of both the structural dynamics and sources of excitation are required. This paper describes a solution to this problem for the case of an annular rotor equipped with piezo patch actuators and sensors. To account for space-fixed external excitation sources, a forcing function is considered involving specified spatial and frequency domain distributions. A model-based [Formula: see text] synthesis is used to compute optimal control solutions. These are tested experimentally on a thin-walled cylindrical steel rotor for cases with narrowband and broadband excitation sources, applied from the fixed frame. The results show that frequency-splitting within the rotating-frame dynamics plays a key role in predicting and controlling resonance. The effectiveness of the optimal control methodology in reducing circumferential vibration of the annular rotor is also confirmed.

Development of methods to increase the efficiency of railway maintenance

Object of research: technology of track maintenance optimization
 Solved problem: In the development of decisions to optimize the decision-making system in the content of the upper structure of the track used methods of control theory, systems analysis, methodology of optimal control.
 Main scientific results: An analysis of the degrees of research on improving the efficiency of the technical management of railways showed that there was no systematic approach and that existing developments in the organization, in particular the relative optimization, Separate track repair standards or take into account parameter models, process requirements and conditions.
 Area of practical use of research results: industrial enterprises, railway stations.
 Providing the stable support of the railway, sustainable and rhythmic operation of railway traffic is ensured. About 7.3 thousand km are exploited in the ferrous metallurgy of Ukraine. More than 70 % of routes are up to 500 km long and belong to a large company. Consequently, an important task is to maintain the technical state of railways at the production demands level.
 Innovative technological product: combined transportations that can interact with similar networks of foreign countries.
 Scope of application of innovative technological product: formation and effective functioning of railway-transport complex, improvement of tariff policy, substantiation of perspective parameters of transportation process and its technical means, creation of advanced technologies, choice of rational structure of transport network, formation of transport corridors, development of fundamentally new management systems.

Minimum-lap-time optimisation and simulation

The paper begins with a survey of advances in state-of-the-art minimum-time simulation for road vehicles. The techniques covered include both quasi-steady-state and transient vehicle models, which are combined with trajectories that are either pre-assigned or free to be optimised. The fundamentals of nonlinear optimal control are summarised. These fundamentals are the basis of most of the vehicular optimal control methodologies and solution procedures reported in the literature. The key features of three-dimensional road modelling, vehicle positioning and vehicle modelling are also summarised with a focus on recent developments. Both cars and motorcycles are considered.

Robust flight planning impact assessment considering convective phenomena

Thunderstorms are one of the leading causes of Air Traffic Management delays. In this paper, we assess how incorporating convective information into flight planning algorithms can lead to reductions in reroutings due to storm encounters during the execution of the flight. We use robust open-loop optimal control methodology at the flight planning level and incorporate meteorological uncertainties based on Ensemble Prediction System forecasts. Convective risk areas can be derived from the latter to be included in the objective function. At the execution level, the planned trajectories are included in an air traffic simulator (NAVSIM) under observed weather (wind and storms). In this simulation process, track modifications might be triggered in case of encountering an observed thunderstorm. A tool termed DIVMET based on pathfinding algorithms has been integrated into NAVSIM is considered to that end. Results show that planning robust trajectories (avoiding thus convective areas) reduces the number of storms encounters and increases predictability. This increase in predictability is at a cost in terms of fuel and time, also quantified.

A novel looped space tether transportation system with multiple climbers for high efficiency

This paper proposes a novel concept of looped tether transportation system with multiple climbers for highly efficient transportation of payloads. It is formed by connecting two parallel tether transportation systems or partial space elevators with multiple climbers per tether at upper and lower ends. A high-fidelity and accurate model for the system is built up to capture the high order flexural modes of tethers based on the nodal position finite element method in the arbitrary Lagrangian-Eulerian description. Numerical analysis is conducted to understand the dynamic characteristics of the looped tether transportation system compared to the tether transportation system with a single tether. The results show that the high-order flexural modes of tethers must be considered in the system's engineering analysis. The analysis also shows the interaction between two tethers caused by climbers on different tethers moving in different directions could be beneficial. It will reduce the overall libration of the system while keeping the magnitude of tether tension comparable to the tether transportation system with a single tether. In addition, the analysis of high order flexural modes of tether indicates that there exists a risk of tether collision in the payload transportation, which indicates again the necessity to include the high order flexural modes of tether in the analysis. Finally, the study shows the risk of tether collision could be avoided by optimizing the number of climbers per tether, the climber's moving profiles, and the distance between climbers using the optimal control methodology.

Influence of atmospheric uncertainty, convective indicators, and cost-index on the leveled aircraft trajectory optimization problem

The existence of significant uncertainties in the models and systems required for trajectory prediction represents a major challenge for the Air traffic Management (ATM) system. Weather can be considered as one of the most relevant sources of uncertainty. Understanding and managing the impact of these uncertainties is necessary to increase the predictability of the ATM system. State-of-the-art probabilistic forecasts from Ensemble Prediction Systems are employed to characterize uncertainty in the wind and potential convective areas. A robust optimal control methodology to produce efficient and predictable aircraft trajectories in the presence of these uncertainties is presented. Aircraft motion is assumed to be at a constant altitude and variable speed, considering BADA4 as the aircraft performance model. A set of Pareto-optimal trajectories is obtained for different preferences among predictability, convective risk, and average cost index running a thorough parametric study on a North Atlantic crossing use case. Results show that the cost of reducing the arrival time window by 10 s. is between 100 and 200 kg or 3 and 6 min., depending on the cost-index. They also show that reducing the exposure to convection by 50 km is on the order of 5 and 10 min. or 100 and 200 kg. of average fuel consumption.

Time-optimal bang-bang control for the driven spin-boson system

In this paper we investigate the application of optimal control of a single qubit coupled to an ohmic heat bath. For the weak bath coupling regime, we derive a Bloch-Redfield master equation describing the evolution of the qubit state parametrized by vectors in the Bloch sphere. By use of the optimal control methodology we determine the field that generates an arbitrary single qubit rotation in minimum time. In particular we develop an efficient method for solving the time-optimal control problem, namely the implementation of $X$ gate, which consists of a rotation about the $\stackrel{P\vec}{ox}$ axis through angle $\ensuremath{\pi}$. The time-optimal control problem requires a bounded control. If upper and lower bounds are imposed for the external control, the optimal solution is of bang-bang type and switches from the upper to the lower values of the control bounds. We compare our results using the techniques of automatic differentiation to compute the gradient for the cost functional with some known results using Pontryagin's minimum principle. We use an alternative numerical approach for the optimization strategy.

Joint Propulsion and Cooling Energy Management of Hybrid Electric Vehicles by Optimal Control

This paper develops an optimal control methodology for the energy management (EM) of a series hybrid electric vehicle (HEV) with consideration of ancillary cooling losses, to minimize fuel consumption. Both engine and battery thermal management (TM) models are integrated into the HEV powertrain model as they interact with each other during operation. By collecting all components for propulsion and cooling, a control-oriented model is established, which enables the joint EM and TM optimization problem to be solved simultaneously. Experimental driving cycles are utilized to reveal the impact of the cooling losses on the fuel economy under different driving circumstances. The case study shows the effectiveness of the proposed strategy in finding the optimal power sharing of the hybrid powertrain with consideration of both propulsion and overall cooling requirements. Moreover, a benchmark method based on separately optimized EM and conventional thermostat and PI controlled cooling systems is introduced to verify the solution quality of the proposed approach. It is demonstrated that the proposed method outperforms the benchmark by 0.7%–2.49% in terms of fuel economy, depending on the driving scenarios.

Active vibration suppression in robotic milling using optimal control

Six degree-of-freedom (6-dof) industrial robots are attractive alternatives to Computer Numerical Control (CNC) machine tools for milling of large parts because of their low-cost, greater versatility, and larger work volume. However, 6-dof industrial robots are significantly more compliant than CNC machine tools, which makes them prone to vibrations during milling. An additional complexity of industrial robots is their pose-dependent vibration characteristics. This paper presents a pose-dependent optimal control methodology to actively suppress tool tip vibrations generated by the periodic milling forces in robotic milling. Discretely sampled robot structural modal parameters as a function of robot configuration (pose) are used to develop a data-driven Gaussian Process Regression (GPR) model. The model is then utilized to solve the Linear Quadratic Regulator (LQR) optimal control problem to obtain pose-dependent controller gains necessary for vibration suppression. The pose-dependent controller is implemented on a 6-dof industrial robot and its performance evaluated through process-independent offset mass experiments and through milling experiments. The methodology is shown to be effective in decreasing the tool tip vibrations and improving the machining accuracy in robotic milling.

Adaptive dynamic programming based robust control of nonlinear systems with unmatched uncertainties

This paper proposes a new approach to address robust control design for nonlinear continuous-time systems with unmatched uncertainties. First, we transform the robust control problem into an equivalent optimal control problem, which allows to simplify the control design. A critic neural network (NN) is then adopted to reformulate the derived Hamilton–Jacobi–Bellman (HJB) equation based on the optimal control methodology. Then, a novel adaptation algorithm is used to online directly estimate the unknown NN weights, so as to achieve the guaranteed convergence. The control system stability and the convergence of the derived control action to the optimal solution can be rigorously proved. Finally, two simulation examples are provided to illustrate the validity and efficacy of the proposed method.

Stochastic optimal control methodologies in risk-informed community resilience planning

The absorptive and restorative abilities of a community are two key elements of community resilience following disasters. The recovery of communities relies on an efficient restoration planning of damaged critical infrastructure systems, household units, and impaired supporting social and economic functions. These interdependent systems form a dynamic system of systems that changes continuously during restoration. Therefore, an effective and practical recovery planning process for a community can be modeled as a sequential dynamic optimization problem under uncertainty. This paper seeks to enhance our understanding of dynamic optimization concepts and their role in formulating post-disaster, community-level recovery strategies. Various methods of classic dynamic programming and reinforcement learning are examined and applied. Simulation-based approximate dynamic programming techniques are introduced to overcome the curse of dimensionality, which is characteristic of large-scale and multi-state systems of systems. The paper aims not only to study the unexplored topic of dynamic optimization in community resilience, but also to be a practical reference for policymakers, practitioners, engineers, and operations analysts to harness the power of dynamic optimization toward assessing and achieving community resilience.

Stochastic Optimization Models of Actuarial Mathematics

The paper overviews stochastic optimization models of actuarial mathematics and methods for their solution from the point of view of the methodology of multicriteria stochastic programming and optimal control. The evolution of the capital of an insurance company is considered in discrete time. The main random parameters of the models are insurance payouts, i.e., the ratios of paid insurance claims to the corresponding premiums per unit time. Optimization variables are the structure of the insurance portfolio (gross premium structure) and amount of dividends. As efficiency criteria, indicators of the profitability of the insurance business are used, and, as risk indicators the ruin probability and the recourse capital necessary to prevent the ruin are taken. The goal of the optimization is to find Pareto-optimal solutions. Methods for finding these solutions are proposed.

Tuning heuristics and convergence analysis of reinforcement learning algorithm for online data-based optimal control design

A heuristic for tuning and convergence analysis of the reinforcement learning algorithm for control with output feedback with only input / output data generated by a model is presented. To promote convergence analysis, it is necessary to perform the parameter adjustment in the algorithms used for data generation, and iteratively solve the control problem. A heuristic is proposed to adjust the data generator parameters creating surfaces to assist in the convergence and robustness analysis process of the optimal online control methodology. The algorithm tested is the discrete linear quadratic regulator (DLQR) with output feedback, based on reinforcement learning algorithms through temporal difference learning in the policy iteration scheme to determine the optimal policy using input / output data only. In the policy iteration algorithm, recursive least squares (RLS) is used to estimate online parameters associated with output feedback DLQR. After applying the proposed tuning heuristics, the influence of the parameters could be clearly seen, and the convergence analysis facilitated.

Optimal Regulators for Nonlinear Systems with Incompatible State and Input Cost Functions

When a desired state is different from the state at which input cost becomes zero, a naive application of the optimal control methodology may lead an ill-posed problem. In this study, we propose a new method where the input cost is slightly changed so that the optimal control problem is well defined. The method can realize an energy-efficient control, which considers the actual energy consumption. We also confirm the effectiveness of the proposed method via a case study of an example.