Optimal Control Approach Research Articles

A new model of the spread of COVID-19 among diabetes population: a mathematical analysis and optimal control approach for intervention strategies

A new model of the spread of COVID-19 among diabetes population: a mathematical analysis and optimal control approach for intervention strategies

Data-driven optimal control of a seir model for COVID-19

We present a data-driven optimal control approach which integrates the reported partial data with the epidemic dynamics for COVID-19. We use a basic Susceptible-Exposed-Infectious-Recovered (SEIR) model, the model parameters are time-varying and learned from the data. This approach serves to forecast the evolution of the outbreak over a relatively short time period and provide scheduled controls of the epidemic. We provide efficient numerical algorithms based on a generalized Pontryagin's Maximum Principle associated with the optimal control theory. Numerical experiments demonstrate the effective performance of the proposed model and its numerical approximations.

Optimal Control of Pendubot System Using SIMATIC S7-1200

In optimal control, a common problem is developing a control law that can drive a dynamical system from one state to another as quickly as possible. The objective of paper is to design optimal control approach based SIMATIC S7-1200 for under-actuated Pendubot system. The main contribution of this paper is to introduce and validate control method for laboratory model of Pendubot system by using industrial device, namely, Programmable logic controller (PLC). Besides, Lyapunov Analysis is used to analyze the stability of optimal control. The simulation is performed in MATLAB/Simulink environment and experiment is carried out in TIA PORTAL environment. The simulation results and experimental results illustrate that the proposed control method is effective and robust by using PLC.

SPOCK: A proximal method for multistage risk-averse optimal control problems

Risk-averse optimal control problems have gained a lot of attention in the last decade, mostly due to their attractive mathematical properties and practical importance. They can be seen as an interpolation between stochastic and robust optimal control approaches, allowing the designer to trade-off performance for robustness and vice-versa. Due to their stochastic nature, risk-averse problems are of a very large scale, involving millions of decision variables, which poses a challenge in terms of efficient computation. In this work, we propose a splitting for general risk-averse problems involving linear dynamical systems and show how to efficiently compute iterates on a GPU-enabled hardware. Moreover, we propose Spock — a new algorithm that utilizes the proposed splitting and takes advantage of the SuperMann scheme combined with fast directions from Anderson's acceleration method for enhanced convergence speed. We implement Spock in Julia as an open-source solver, which is amenable to warm-starting and massive parallelization.

Event-Triggered Robust Optimal Control for Robotic Manipulators with Input Constraints via Adaptive Dynamic Programming

This paper proposes an event-triggered robust tracking control method for robotic manipulators with asymmetrical input constraints based on adaptive dynamic programming (ADP). First, the original robust tracking control problem is transformed into an optimal control problem for a nominal system with the help of a novel cost function design. Next, an event-triggered optimal control approach is proposed to solve this optimization problem and obtain the optimal solution to the Hamilton-Jacobi-Bellman (HJB) equation. The classical ADP framework is then used to approximate the optimal cost function and controller. Unlike existing weight adaptive laws, an additional term is introduced for removing the requirement of initial stabilization. Based on the Lyapunov theory, the stability of the original robotic system and the convergence of weight estimation are both guaranteed. Finally, simulation results are presented to demonstrate the effectiveness of the proposed event-triggered optimal control method.

Developing the optimization control of pollution constrained by the convection diffusion equations

In this paper, an optimization control of pollution subject to the convection diffusion equations is developed and analyzed. The optimization objective function is to consider the pollution effects for minimizing the weighted derivation between simulated concentrations and allowable concentrations at observation sites and the costs of emission reductions, pollution taxes, and the cost related to layout of pipelines. The proposed optimal control problem is defined on the multiple observation and polluting points and is constrained by the convection diffusion equations. We analyze this optimization problem from a rigorous mathematical viewpoint and prove the existence of a solution of the pollution optimal control. We build the numerical optimal control approach by a second-order improved splitting upwind finite volume method to solve the convection diffusion equations and by the constrained difference evolution (DE) algorithm to compute the optimization procedure. Three numerical experiments are investigated, where the first one aims at searching the optimal disposal fluxes while minimizing concentration deviation and reduction cost, the other two are to minimize the whole economical costs that contain waste water treatment cost, pipeline layout cost and pollution taxation by finding the optimal effluent concentration of waste water. The developed optimal control is efficient and it can be applied in applications.

Macroscopic hyperpolarization enhanced with quantum optimal control

Hyperpolarization of nuclear spins enhances nuclear magnetic resonance signals, which play a key role for imaging and spectroscopy in the natural and life sciences. This signal amplification unlocks previously inaccessible techniques, such as metabolic imaging of cancer cells. In this work, electron spins from the photoexcited triplet state of pentacene-doped naphthalene crystals are used to polarize surrounding protons. As existing strategies are rendered less effective by experimental constraints, they are replaced with optimal control pulses designed with RedCRAB. In contrast to previous optimal control approaches, which consider an average single nucleus, this closed-loop optimization is macroscopic. A 28% improvement in signal and 15% faster polarization rate is observed. Additionally, a strategy called Autonomously-optimized Repeated Linear Sweep (ARISE) is introduced to efficiently tailor existing hyperpolarization sequences in the presence of experimental uncertainty to enhance their performance. ARISE is expected to be broadly applicable in many experimental settings.

Cost-effectiveness of a mathematical modeling with optimal control approach of spread of COVID-19 pandemic: A case study in Peru

COVID-19 pandemic affects 213 countries and regions around the world. Which the number of people infected with the virus exceeded 26 millions infected and more than 870 thousand deaths until september 04, 2020, in the world, and Peru among the countries most affected by this pandemic. So we proposed a mathematical model describes the dynamics of spread of the COVID-19 pandemic in Peru. The optimal control strategy based on the model is proposed, and several reasonable and suitable control strategies are suggested to the prevention and reduce the spread COVID-19 virus, by conducting awareness campaigns and quarantine with treatment. coronavirus 2019 (COVID-19). Pontryagin’s maximum principle is used to characterize the optimal controls and the optimality system is solved by an iterative method. Finally, some numerical simulations are performed to verify the theoretical analysis using Matlab.

Stick-slip stabilization in oil well drill-strings via optimal hybrid fractional order fuzzy logic control scheme

Stick-slip vibration is regarded as one of the major factors that negatively influence the efficiency of the drilling processes. Therefore, it would be highly preferable to overcome the stick-slip vibration challenge through an effective control scheme. This study aims to address the stick-slip vibration problem in oil well drill-strings through a novel concept of an optimal hybrid fractional order fuzzy logic control (OH-FOFLC) scheme. By combining the robustness of fuzzy logic with the convergence speed of the fractional order method, the proposed scheme may enhance tracking performance in drill-strings under various operating conditions. In addition, the fuzzy logic controller for the OH-FOFLC scheme was designed by considering the minimum rules to decrease the computational burden as well as to reduce the controller’s cost. Furthermore, a particle swarm optimization algorithm was implemented for optimizing the coefficients of the OH-FOFLC scheme. To illustrate the overall performance and effectiveness of the OH-FOFLC, four different controllers, including proportional–integral–derivative (PID), fractional order PID, sliding mode control, and optimal hybrid fuzzy logic control approaches, are considered. The validity of the suggested OH-FOFLC was demonstrated through numerical simulations and comprehensive comparative studies which demonstrated that the OH-FOFLC scheme performs better than the four other controllers under various operating conditions.

A nonlinear optimal control approach for underactuated offshore cranes

ABSTRACT The article proposes a nonlinear optimal control approach for the model of boom cranes being mounted on vessels. The dynamic model of the boom cranes undergoes approximate linearisation with the use of Taylor series expansion around a temporary operating point which is recomputed at each iteration of the control method. For the approximately linearised model, an H-infinity feedback controller is designed. The linearisation procedure relies on the computation of the Jacobian matrices of the state-space model of the system. For the computation of the controller's feedback gains, an algebraic Riccati equation is solved at each time step of the control method. The new nonlinear optimal control approach achieves fast and accurate tracking for all state variables of the boom cranes, under moderate variations of the control inputs. The stability properties of the control scheme are proven through Lyapunov analysis.

Improving Stability and Power Sharing of Bidirectional Power Converters by Relaxing DC Capacitor Voltage

This article presents a new control structure for bidirectional power electronic converters. Commonly, a proportional-integrating (PI) controller is used in the dc capacitor voltage loop, to generate the set point for the current controller, which tightly regulates this voltage to a given value. This article shows that such an approach causes stability issues that are aggravated during reverse power flow operation and intensify during weak grid conditions and uncertainties. The proposed controller allows small variations of dc capacitor voltage in proportion to the power flowing through the converter. This improves the stability of the converter irrespective of the power direction and in the presence of uncertainties and weak grid conditions. The proposed control structure also simplifies the design process, and it can be applied to dc/dc and dc/ac (single-phase and three-phase) converters. Moreover, the proposed method grants an inherent power-sharing capability when multiple converters share the same dc bus. The article also adopts full state feedback and an optimal control approach, i.e., the linear-quadratic tracker (LQT), for systematic design of the current control loop and enhanced robustness. Detailed analyses, simulations, comparisons, and experimental results are included to demonstrate the effectiveness of the proposed approach.

Optimal Control Approach to Scheduling Power Supply Facilities: Theory and Heuristics

In this article, we consider a scheduling problem for a power charging facility under hard bounds on the deliverable power. Appliances require an amount of energy for a certain time interval at specific times. Under congestion, power supply to the appliances may be possibly delayed and the goal of the scheduler is to minimize the average waiting time. We formulate the problem as an optimal control problem. We study three versions of the problem: the case when no interruption of an appliance is possible after admission, the case in which it is possible, and the case in which the overall energy can be delivered at an arbitrary rate over time. We show that these three versions of the problem can be faced in the proposed framework by suitably choosing the cost function. We then propose some relaxations to derive lower bounds for the cost. These lower bounds will be used to test some heuristics with real data available from the literature.

Abatement of Sewer Overflow Pollution Based on Distributed Optimal Control Approach

Abatement of Sewer Overflow Pollution Based on Distributed Optimal Control Approach

Learning quantum-state feedback control with backpropagation-free stochastic optimization

High-fidelity state preparation represents a fundamental challenge in the application of quantum technology. While the majority of optimal control approaches use feedback to improve the controller, the controller itself often does not incorporate explicit state dependence. Here, we present a general framework for training deep feedback networks for open quantum systems with continuous weak measurement that allows a variety of system and control structures that are prohibitive by many other techniques and can in effect react to unmodeled effects through nonlinear filtering. Our approach benefits from characteristics of both stochastic sampling and gradient-based optimization methods yet does not require differentiability as in backpropagation approaches. We demonstrate that this method is efficient due to inherent parallelizability, robust to open system interactions, and outperforms landmark state-dependent feedback control results in simulation.

Optimal control approach for nonlinear chemical processes with uncertainty and application to a continuous stirred-tank reactor problem

Practical chemical process is usually a dynamic process including uncertainty. Stochastic constraints can be used to chemical process modeling, where constraints cannot be strictly satisfied or need not be fully satisfied. Thus, optimal control of nonlinear systems with stochastic constraints can be available to address practical nonlinear chemical process problems. This problem is hard to cope with due to the stochastic constraints. By introducing a novel smooth and differentiable approximation function, an approximation-based approach is proposed to address this issue, where the stochastic constraints are replaced by some deterministic ones. Following that, the stochastic constrained optimal control problem is converted into a deterministic parametric optimization problem. Convergence results show that the approximation function and the corresponding feasible set converge uniformly to that of the original problem. Then, the optimal solution of the deterministic parametric optimization problem is guaranteed to converge uniformly to the optimal solution of the original problem. Following that, a computation approach is proposed for solving the original problem. Numerical results, obtained from a nonlinear continuous stirred-tank reactor problem including stochastic constraints, show that the proposed approach is less conservative compared with the existing typical methods and can obtain a stable and robust performance when considering the small perturbations in initial system state.

Online Optimization Method for Nonlinear Model-Predictive Control in Angular Tracking for MEMS Micromirror.

In this brief, a precise angular tracking control strategy using nonlinear predictive optimization control (POC) approach is address. In order to deal with the model uncertainty and noise interference, a online Hammerstein-model-based POC is designed using online estimated parameters and model residual. Above all, a rate-dependent Duhem model is used to describe the nonlinear sub-model of the whole Hammerstein architecture for depicting multi-valued mapping nonlinear characteristic. Then, predictive output of angular deflection is obtained by Diophantine function based on linear submodel. Subsequently, the iterative control value depends on estimated parameters through data-driven is acquired. Later, based on the cost function, the iteratively optimization control quantity is fed back to the electromagnetic driven deflection micromirror (EDDM) system on the basis of Hammerstein architecture. It should be stressed that the control value is determined by real-time update model residual and defined cost function. Moreover, the stability of POC strategy is proposed. In addition, experimental result is proposed to validate the effectiveness of the control technique adopted in this paper.

Control Approach to Fault Disambiguation

To ensure resilience, systems must be endowed with capabilities for rapid detection, response, and recovery to disruptiveevents. In this paper we focus on faults as disruptive events and use a diagnosis engine for their detection and isolation. In particular we use model-based diagnosis, where the diagnosis engine is provided with a model of the system, nominal values of the parameters of the model and values of some of its inputs and outputs. However, there is no guarantee that the information measured by sensors is sufficient to distinguish between multiple root-causes. We address this challenge using an optimal control approach: we design control inputs such that the similarity between outputs in ambiguous fault modes is reduced. We show that under certain assumptions on the system model, minimizing a similarity metric in terms of outputs is equivalent to increasing the diagnosis certainty. We use an optimization-based approach to input design, where the system model acts as a constraint. We show that by using a surrogate model expressed with constructs endowed with differential operators, we improve the time efficiency of the optimal control problem. We demonstrate our approach on a fuel line system, where feedback control is used to ensure the mass flow rate at the engine follows a prescribed reference. We consider leak faults that affect the fuel lines. We show that under the control inputs generated by the nominal controller, mass flow rate measurements are not enough to accurately isolate leaks. We demonstrate that by using custom inputs that minimize the similarity between the outputs in the ambiguous faults modes, the diagnosis uncertainty is eliminated.

Dynamic Stability Control of Sudan National Grid Using Power System Stabilizer

Application of power system stabilizers (PSS), as supplementary control signals for the excitation system in order to damp the low frequency, generator angle, speed variation, generator power, voltage magnitude and power flow oscillations. This paper presents the application of robust decentralized power system stabilizer (PSS) design approaches, for Sudan power system which consists of 41 machines with 167 buses. The paper mainly focus on operator testing of robust decentralized control techniques for power systems, and the optimal control approach to robust control design. Results of robust decentralized control design approaches are defined by using state space model equations. Also for testing dynamic stability Lyapunov theorem is used. The simulations were carried out using symmetrical fault and results presented by Power System Analysis Toolbox, MATLAB.

Numerical gate synthesis for quantum heuristics on bosonic quantum processors

There is a recent surge of interest and insights regarding the interplay of quantum optimal control and variational quantum algorithms. We study the framework in the context of qudits which are, for instance, definable as controllable electromagnetic modes of a superconducting cavity system coupled to a transmon. By employing recent quantum optimal control approaches described in (Petersson and Garcia, 2021), we showcase control of single-qudit operations up to eight states, and two-qutrit operations, mapped respectively onto a single mode and two modes of the resonator. We discuss the results of numerical pulse engineering on the closed system for parametrized gates useful to implement Quantum Approximate Optimization Algorithm (QAOA) for qudits. The results show that high fidelity (>0.99) is achievable with sufficient computational effort for most cases under study, and extensions to multiple modes and open, noisy systems are possible. The tailored pulses can be stored and used as calibrated primitives for a future compiler in circuit quantum electrodynamics (cQED) systems.

Trajectory Tracking Design for a Swarm of Autonomous Mobile Robots: A Nonlinear Adaptive Optimal Approach

This research presents a nonlinear adaptive optimal control approach to the trajectory tracking problem of a swarm of autonomous mobile robots. Mathematically, finding an analytical adaptive control solution that meets the H2 performance index for the trajectory tracking problem when controlling a swarm of autonomous mobile robots is an almost impossible task, due to the great complexity and high dimensions of the dynamics. For deriving an analytical adaptive control law for this tracking problem, a particular formulation for the trajectory tracking error dynamics between a swarm of autonomous mobile robots and the desired trajectory is made via a filter link. Based on this prior analysis of the trajectory tracking error dynamics, a closed-form adaptive control law is analytically derived from a high-dimensional nonlinear partial differential equation, which is equivalent to solving the trajectory tracking problem of a swarm of autonomous mobile robots with respect to an H2 performance index. This delivered adaptive nonlinear control solution offers the advantages of a simple control structure and good energy-saving performance. From the trajectory tracking verification, this proposed control approach possesses satisfactory trajectory tracking performance for a swarm of autonomous mobile robots, even under the effects of huge modeling uncertainties.