Dynamic Optimal Control Research Articles

Optimal Determination and Dynamic Control Analysis of the Graded and Staged Drought Limit Water Level of Typical Plateau Lakes

The technical research on determining the drought limit water level can be used as an important basis for starting the emergency response of drought resistance in the basin and guiding the drought resistance scheduling of water conservancy projects. When the concept of drought limit water level was first proposed, the main research object was reservoirs, and the method for determining the lake drought limit water level was not established. Referring to the calculation method of reservoir drought limit water level, the drought limit water level is used as a single warning indicator throughout the year, which lacks graded and staged standards, and also lacks rationality and effectiveness in practical application. Therefore, this article has improved the concept of lake drought limit water level (flow). Under different degrees of drought and water use patterns during the drought period, combined with the characteristics of lake water inflow, considering the factors such as ecology, water supply, and demand, lake inflow, evapotranspiration loss, a graded and staged standard of lake drought limit water level has been developed. For different types of lakes, a general method for determining the lake’s graded and staged drought limit water level has been established. The SCSSA-Elman neural network is used to construct the medium and long-term water inflow prediction model for lakes, and the calculation results of this model are used for the warning and dynamic control analysis of the lake drought limit water level. The application of this method has the characteristics of strong applicability and high reliability. Finally, the determination method and dynamic control method of the lake’s graded and staged drought limit water level have been successfully applied at Dianchi Lake in Yunnan.

Dynamic Analysis and Optimal Control of Fractional Order African Swine Fever Models with Media Coverage.

African swine fever is a highly contagious virus that causes pig disease. Its onset process is short, but the mortality rate is as high as 100%. There are still no effective drugs that have been developed to treat African swine fever, and prevention and control measures are currently the best means to avoid infection in pig herds. In this paper, two fractional order mathematical models with media coverage are constructed to describe the transmission of African swine fever. The first model is a basic model with media coverage, and no control measures are considered. For this model, the reproduction number is obtained by using the next generation matrix method. Then, the sufficient conditions for the existence and stability of two equilibriums are obtained. Based on the first model, the second model is established incorporating two control measures. By using Pontryagin's maximal principle, the optimal control solution is derived. After that, some numerical simulations are performed for the two models to verify the theoretical results. Both the qualitative analysis and numerical results indicate that timely media coverage combined with disinfection control measures is crucial to preventing the spread of disease.

Dynamic Optimal Control for Wastewater Treatment Process Under Multiple Operating Conditions

Wastewater treatment process (WWTP) is operated with multiple conditions. Accurately identify these conditions and satisfy the different requirements are the keys to guarantee the optimal operation of WWTP. To solve this problem, a dynamic optimal control (DOC) strategy is designed in this paper. First, with the aid of the predicting models by adaptive fuzzy neural network for effluent nitrate and total nitrogen, different operating conditions can be identified. Corresponding to each condition, changing number of operating objectives are formulated to match the different requirements. Second, due to the changeable operating objectives can cause the expanded/contracted dimension of Pareto-optimal set, a dynamic multi-objective particle swarm optimization algorithm is developed. In this algorithm, self-adjusting mechanism of population size and global optimal solution are designed to derive the optimal solutions of control variables. Third, fuzzy controllers, matched with the different conditions, are designed to trace these optimal solutions. Finally, the effectiveness of DOC strategy is tested on a real WWTP. The results demonstrate that this proposed DOC strategy enables to achieve promising operating performance. <i>Note to Practitioners</i>&#x2014;This article aims to develop an optimal control strategy to match the multiple conditions and improve the operating performance. To achieve this goal, a dynamic optimal control (DOC) strategy, with the consideration of different operating conditions, is designed. Two key points are contained, the identification of multiple operating conditions and the satisfaction of different requirements. Due to each condition confronts with different requirements, it is important to accurately identify the conditions and construct the corresponding operating objectives. Based on the obtained operating data, changeable operating objectives are established to describe the different conditions. In addition, to satisfy the operating requirements, it is necessary to optimize the changeable objectives, but the changes in the number of objectives can cause the expanded/ contracted of Pareto-optimal set. A dynamic multi-objective particle swarm optimization algorithm, with self-adjusting mechanism of population size and global optimal solution, is designed to deal with this kind of optimization problem. The effectiveness and applicability of the proposed DOC strategy are evaluated on a pilot platform of a real WWTP, showing the improvement on the operating performance. These advantages can be valuable for transplanting this strategy to other real wastewater treatment plants to realize the optimal operation.

Mixed H 2/H ∞ Control With Dynamic Event-Triggered Mechanism for Partially Unknown Nonlinear Stochastic Systems

This technical note discusses the design process of dynamic event-triggered control (DETC) with the mixed <inline-formula> <tex-math notation="LaTeX">$H_2/H_\infty$</tex-math> </inline-formula> for partially unknown nonlinear stochastic systems. The purpose of this problem is to design a controller to make the closed-loop system achieve the expected <inline-formula> <tex-math notation="LaTeX">$H_2$</tex-math> </inline-formula> performance under the condition that the <inline-formula> <tex-math notation="LaTeX">$H_\infty$</tex-math> </inline-formula> continuous attenuation level is protected. Firstly, a two-player non-zero-sum game for stochastic system is given. Then we prove the optimal control strategy and the worst interference, which constitute the Nash equilibrium solution and can be derived from the corresponding Hamiltonian functions. Furthermore, two neural networks (NNs) are used to realize Nash equilibrium. Under the condition of dynamic event-triggered mechanism (DETM), the control strategy only is updated at the trigger moment. In addition, the stability and weights convergence of the system are proved mathematically. Finally, two numerical example are given to prove it. <i>Note to Practitioners</i>&#x2014;In the practice of control engineering, mixed <inline-formula> <tex-math notation="LaTeX">$H_2/H_\infty$</tex-math> </inline-formula> control can not only evaluate the <inline-formula> <tex-math notation="LaTeX">$H_2$</tex-math> </inline-formula> performance index of the transient behavior of the system, but also measure the <inline-formula> <tex-math notation="LaTeX">$H_\infty$</tex-math> </inline-formula> performance index of the system&#x2019;s robustness to external disturbances and parameter uncertainty. And many useful signals and interference vary randomly. Therefore, the optimal control of stochastic systems and dynamics play an important role in the modern industry. Saving control resources is very important for actual production. Therefore DETC is considered in this paper. On the other hand, in practice, accurate system models are difficult to obtain. In order to tackle this difficulty, by designing a novel scheme via integral reinforcement learning technique, the system relaxes the requirement of drift dynamic and Zeno behavior is avoided.

Dynamic analysis and optimal control of a novel fractional-order 2I2SR rumor spreading model

In this paper, a novel fractional-order 2I2SR rumor spreading model is investigated. Firstly, the boundedness and uniqueness of solutions are proved. Then the next-generation matrix method is used to calculate the threshold. Furthermore, the stability of rumor-free/spreading equilibrium is discussed based on fractional-order Routh–Hurwitz stability criterion, Lyapunov function method, and invariance principle. Next, the necessary conditions for fractional optimal control are obtained. Finally, some numerical simulations are given to verify the results.

Dynamic modeling and optimal control of reactive batch distillation: An experimental case study

In the present study, dynamic modeling, optimal operation and control of a reactive batch distillation process is illustrated based on experimental and simulation studies using methyl acetate production case study. An equilibrium stage model, incorporating non-ideal VLE and start-up region of heating, is developed based on data generated on an experimental unit by identifying five input parameters representing uncertainties. The optimal control problem is solved using genetic algorithm, considering the objective function identified on the basis of trend analysis using the developed dynamic model, to find the optimal reflux ratio, heat input to the reboiler, and mole ratio of methanol to acetic acid in the initial reaction mixture. Open-loop and closed-loop implementations clearly illustrate the improved performance with respect to the quantity of methyl acetate in the distillate product with a reasonably high conversion and product purity within reasonably short batch duration, illustrating the successful optimal control implementation experimentally.

Weighting Factor Design Techniques for Predictive Control of Power Electronics and Motor Drives

The rapid growth of energy demand requires progressive energy generation. This, together with the demand for higher efficiency and flexibility, has promoted the application of power electronics in energy systems. During the past decade, model predictive control (MPC) of power electronics has witnessed significant advancements in both dynamic performance and optimal control of the multi-objective terms. Several of these terms can have equal control priorities, resulting in a symmetrical cost function; however, most objectives have different priorities and require weighting factors to resolve the asymmetry in the cost function. Currently, researchers continue to encounter challenges in the optimal design of weighting factors. Moreover, the relative performance of different techniques that either utilize or avoid the weighting factor are uncertain. Therefore, this study focuses on weighting factor design techniques in the literature as applied to wind/solar energy conversion, microgrids, grid-connected converters, and other high-performance converter-based systems. These are grouped under the heuristic, offline tuning, sequential, and online optimization methods. This study demonstrates that optimal online tuning of weighting factors and sequential MPC methods can both offer improved robustness against parameter uncertainties. In addition, the advantages and limitations of different techniques are highlighted.

An Improved Dynamic Optimization Control System for the Drilling Rate of Penetration (ROP) and Its Industrial Application

Optimization control of the rate of penetration (ROP) is crucial in the drilling process due to its vital role in improving the drilling efficiency and safety. In this paper, an improved dynamic optimization control system for ROP is proposed and successfully applied to a drilling site. First, a three layers (intelligent optimization layer, basic automation layer, and process monitoring layer) system framework is proposed according to the drilling characteristics. After that, &#x201C;If-Then&#x201D; strategy is used as the method to identify the rotary drilling condition from four different working conditions. Moving-window strategy is selected to establish the dynamic ROP model that can better adapt to environmental changes. Moreover, Jaya algorithm, a new meta-heuristic optimization method is introduced to solve the dynamic ROP optimization issue. In the simulations, the optimization performance of the proposed system is better than moving window-extreme learning machine-hybrid bat algorithm with more stable (fewer switch times) drilling operational parameters. Finally, in an industrial application to a drilling process in Dandong area, Northeast China, the ROP was improved by 20.79&#x0025; compared with manual operation. Both simulation and industrial application results indicated that the proposed system has significantly improved the drilling efficiency and safety.

Adaptive dynamic programming discrete-time LQR optimal control on electromagnetic levitation system with a $$H_\infty $$ Kalman filter

Adaptive dynamic programming discrete-time LQR optimal control on electromagnetic levitation system with a $$H_\infty $$ Kalman filter

Optimal Statistical Estimation and Dynamic Adaptive Control of Airline Seat Protection Levels for Several Nested Fare Classes under Parametric Uncertainty of Customer Demand Models

Assigning seats in the same compartment to different fare classes of passengers is a major problem of airline seat allocation. Airlines sell the same seat at different prices according to the time at which the reservation is made and other conditions. Thus the same seat can be sold at different prices. The problem is to find an optimal policy that maximizes total expected revenue. To solve the above problem, this paper presents the novel computational approach to optimization and dynamic adaptive prediction of airline seat protection levels for multiple nested fare classes of single-leg flights under parametric uncertainty. It is assumed that time T (before the flight is scheduled to depart) is divided into h periods, namely a full fare period and h-1 discounted fare periods. The fare structure is given. An airplane has a seat capacity of N. For the sake of simplicity, but without loss of generality, we consider (for illustration) the case of nonstop flight with two fare classes (business and economy). The proposed airline's inventory management policy is based on the use of the proposed computational models. These models emphasize pivotal quantities and ancillary statistics relevant for obtaining statistical predictive limits for anticipated quantities under parametric uncertainty and are applicable whenever the statistical problem is invariant under a group of transformations that acts transitively on the parameter space. The proposed technique is based on a probability transformation and pivotal quantity averaging. It is conceptually simple and easy to use. Finally, we give illustrative examples, where the proposed analytical methodology is illustrated in terms of the two-parameter exponential distribution. Applications to other log-location-scale distributions could follow directly.

Dynamic analysis and optimal control of a stochastic information spreading model considering super-spreader and implicit exposer with random parametric perturbations

Environmental factors in social systems affect information spreading at all times. This paper proposes a stochastic S2EIR model that considers the presence of super-spreaders and implicit exposers in information spreading, as well as the stochastic perturbation of model parameters. The existence of a global positive solution using the Itô′s formula is then demonstrated. Sufficient conditions for information disappearance and smooth distribution of information are calculated by using the Borel–Cantelli lemma and the strong law of large numbers. Furthermore, the optimal control strategy for the stochastic model is proposed using the Hamiltonian function. The results of the theoretical analysis are supported by numerical simulations and compared to the parameter variations of the deterministic model. The results of this study indicate that white noise facilitates the spread of information. The intensity of perturbation is proportional to the fluctuation of information spreading. Controlling random parameters can effectively facilitate the spread of information. For positive information, the randomness and complexity of the social system should be utilized to increase the spread of information. In contrast, for negative information, randomness in the social system should be suppressed to the greatest extent possible to limit information dissemination.

Dynamic optimization of a wastewater treatment process for sustainable operation using multi-objective genetic algorithm and non-dominated sorting cuckoo search algorithm

Wastewater treatment plants (WWTP) face challenges due to nonlinearity and influent oscillations. An efficient optimal control system is necessary to improve effluent water quality without increasing operating costs. This research proposes a novel dynamic optimization control system using a non-dominated sorting-based multi-objective cuckoo search optimization algorithm (NSMOCS). Benchmark Simulation Model 1 (BSM1) was used as the WWTP model. Two sets of objectives were analyzed: the first set consists of the effluent quality index (EQI) and operating cost index (OCI), and the second comprises the reduction in nitrogen and ammonia concentrations at the WWTP. A Pareto front was obtained by evaluating these objectives using a multi-objective genetic algorithm (MOGA). Contribution analysis was used to find the individual weight values of these objectives. Furthermore, two sets of multi-objective cost functions were devised using weighted sum analysis. By minimizing the above-mentioned cost functions with NSMOCS algorithm, the best tuning parameters for the proportional integral (PI) controller were found. The simulation results with this proposed control strategy showed that the pollution units per day and the operating cost index were reduced during dry, rain, and storm weather conditions, with reductions of 1.3 %, 0.77 %, 0.91 %, and 0.9 %, 0.85 %, and 0.63 %, respectively.

Droop control strategy for microgrid inverters: A deep reinforcement learning enhanced approach

To better tap into the potential of distributed renewable energy generation, microgrid system has become an emerging technology. As the bridge of microgrids, the inverters can flexibly convert distributed DC power input into AC power output. It is verified that the traditional droop control strategy for microgrid inverters has inherent defects of uneven reactive power distribution. To this end, this paper proposes a droop control strategy as a multi-objective optimization problem while considering the deviations of bus voltage and reactive power distributions of microgrids. Then, the optimization problem is further formulated as a Markov decision process and solved by a deep reinforcement learning (DRL) algorithm called deep deterministic policy gradient to obtain a dynamic optimal droop coefficient control strategy. Simulation results demonstrated that our DRL-based strategy eliminates the uneven reactive power distribution without voltage drop.

Operational Absolutely Optimal Dynamic Control of the Stochastic Differential Plant’s State by Its Output

Operational Absolutely Optimal Dynamic Control of the Stochastic Differential Plant’s State by Its Output

Variational problem of adaptive optimal control. Theoretical and applied computer analysis

The problem of adaptive optimal control of a dynamical system, which belongs to the class of conditional variational problems with moving boundaries, is considered. A variational and computer study of the controlled adaptive motion of a material point is carried out for the problem of the energy quality functional minimizing with a moving, not predetermined right transboundary and in the case when the mass of the point changes depending on the unfixed final time. The problem is solved using the schemes and procedures of the classical calculus of variations, as well as adaptive estimation techniques, including the derivation of the variation of the auxiliary quality functional, the corresponding Euler equations, and the adaptive estimation algorithm. When solving a general conditional variational problem, the obtained closed system of differential equations was studied for the formation of an adaptive optimal control system for a dynamic plant with a given performance functional. The results of the unconditional formulation of the problem are generalized to the case of additional differential (nonholonomic) and holonomic constraints. In a variational adaptive optimal control problem, the transversality condition is formulated in terms of the local programming condition. The developed variational scheme of adaptive optimal synthesis can be used in the calculation and design of controlled dynamic systems. This optimization scheme is also promising for use in systems where operating time is non-fixed in advance. The results achieved in this paper concern obtaining specific equations, expressions, and formulas relative to the model example under study and finding graphs of the main time functions that determine the nature of the movement of the control object and the quality of the corresponding transients. The proposed adaptive optimal control algorithms for purposeful movement of the studied material point were tested in digital mode and showed their effectiveness which makes them promising for further use in more complex nonlinear adaptive systems of dynamic optimal control.

Formation Control for Mixed-Order UAVs–USVs–UUVs Systems under Cooperative and Optimal Control

In this paper, cooperative control and optimal control methods are used for the formation control of mixed-order heterogeneous multi-agent systems. The system consists of unmanned aerial vehicles (UAVs), unmanned surface vehicles (USVs), and unmanned underwater vehicles (UUVs). The system is represented in a state space using a block Kronecker product. The static and dynamic formation control protocols are proposed respectively, and the graph theory is used to prove that formation control protocols can realize system formation. Furthermore, the optimal control and cooperative control are introduced into the static and the dynamic formation control protocols, and the static cooperative optimal formation control protocol and the dynamic cooperative optimal formation control protocol are designed. Through MATLAB simulation, the static cooperative optimal control protocol and static formation control protocol are compared, and the dynamic cooperative optimal control protocol and dynamic formation control protocol are compared. By comparison, the state variables of the system can reach convergence quickly, and the system can complete formation in a short time, which verifies the effectiveness of the optimal theory and cooperative control.

Adaptive Dynamic Programming-based Adaptive Optimal Tracking Control of a Class of Strict-feedback Nonlinear System

Adaptive Dynamic Programming-based Adaptive Optimal Tracking Control of a Class of Strict-feedback Nonlinear System

Optimal control and cost-effectiveness analysis of an illicit drug use population dynamics

Optimal control and cost-effectiveness analysis of an illicit drug use population dynamics

Operational Absolutely Optimal Dynamic Control of the Stochastic Differential Plant’s State by Its Output

The problem of synthesizing the average-optimal control law for a dynamic plant subject to random disturbances, if its state variables are measured partially or with random errors, is considered. Using the method of a posteriori sufficient coordinates (SCs), the complexity of constructing the well-known interval-optimal Mortensen controller is described and a much simpler algorithm for finding its operational-optimal analog is obtained. The new controller does not require the solution of the corresponding Bellman equation in inverse time, since it is optimal in the sense of a time-varying criterion. This makes it possible to disregard information about the future behavior of the object and reduces the procedure for finding the dependence of a control on sufficient coordinates to direct-time integration of the Fokker–Planck–Kolmogorov equation and to solving a problem of parametric nonlinear programming. The application of the obtained algorithm is demonstrated by the example of a linear-quadratic-Gaussian problem, as a result of which a new operational version of the well-known separation theorem is formulated. It represents a stochastic control device as a combination of a linear Kalman–Bucy filter and a linear operational-optimal positional controller. The latter differs from the traditional interval-optimal controller by the well-known gain and does not require the solution of the corresponding matrix Riccati equation in inverse time

An Offline Closed-Form Optimal Predictive Power Management Strategy for Plug-In Hybrid Electric Vehicles

This article develops an optimal predictive power management strategy (OP-PMS) for plug-in hybrid electric vehicles (PHEVs) to manage the remaining battery level throughout a defined journey. Apart from using the battery before charging it again at the destination, this approach also supports transit through an Ultra Low Emission Zone (ULEZ), where a PHEV needs to operate in pure electric mode to avoid emissions. This type of PHEV power management strategy (PMS) design problem is a noncausal control problem, where the power demand of the remaining driving cycle and the final battery energy level targets influence the current power management action. Rather than solving the whole optimization problem online, this article presents a simplification that leads to a closed-form analytic solution with parameters that can be computed offline. This article makes three key contributions. First, a novel input-linearization method is developed, which converts the OP-PMS into a convex quadratic programming (QP) problem that captures the essential model nonlinearities using an input transformation and a quadratic cost function. Second, the influence of future power demands and final targets on current energy management policy is explicitly quantified from a dynamic optimal control perspective. Third, the noncausal convex QP is approximated with a closed-form analytic solution that is calculated offline. This leads to a real-time implementable OP-PMS with coefficients that can be precalculated and stored in the engine control unit. To demonstrate the viability of this approach, numerical examples are provided based on a generic PHEV model to verify the efficacy of the proposed OP-PMS.