Recent Progress in Reinforcement Learning and Adaptive Dynamic Programming for Advanced Control Applications

Reinforcement learning(RL) has roots in dynamic programming and it is called adaptive/approximate dynamic programming(ADP) within the control community. This paper reviews recent developments in ADP along with RL and its applications to various advanced control fields. First, the background of the development of ADP is described, emphasizing the significance of regulation and tracking control problems. Some effective offline and online algorithms for ADP/adaptive critic control are displayed, where the main results towards discrete-time systems and continuous-time systems are surveyed, respectively.Then, the research progress on adaptive critic control based on the event-triggered framework and under uncertain environment is discussed, respectively, where event-based design, robust stabilization, and game design are reviewed. Moreover, the extensions of ADP for addressing control problems under complex environment attract enormous attention. The ADP architecture is revisited under the perspective of data-driven and RL frameworks,showing how they promote ADP formulation significantly.Finally, several typical control applications with respect to RL and ADP are summarized, particularly in the fields of wastewater treatment processes and power systems, followed by some general prospects for future research. Overall, the comprehensive survey on ADP and RL for advanced control applications has d emonstrated its remarkable potential within the artificial intelligence era. In addition, it also plays a vital role in promoting environmental protection and industrial intelligence.

Adaptive Optimal Discrete-Time Output-Feedback Using an Internal Model Principle and Adaptive Dynamic Programming

In order to address the output feedback issue for linear discrete-time systems, this work suggests a brand-new adaptive dynamic programming(ADP) technique based on the internal model principle(IMP). The proposed method, termed as IMP-ADP, does not require complete state feedback-merely the measurement of input and output data. More specifically, based on the IMP, the output control problem can first be converted into a stabilization problem. We then design an observer to reproduce the full state of the system by measuring the inputs and outputs. Moreover, this technique includes both a policy iteration algorithm and a value iteration algorithm to determine the optimal feedback gain without using a dynamic system model. It is important that with this concept one does not need to solve the regulator equation. Finally, this control method was tested on an inverter system of grid-connected LCLs to demonstrate that the proposed method provides the desired performance in terms of both tracking and disturbance rejection.

Event-based performance guaranteed tracking control for constrained nonlinear system via adaptive dynamic programming method

An optimal tracking control problem for a class of nonlinear systems with guaranteed performance and asymmetric input constraints is discussed in this paper.The control policy is implemented by adaptive dynamic programming(ADP)algorithm under two event-based triggering mechanisms.It is often challenging to design an optimal control law due to the system deviation caused by asymmetric input constraints.First,a prescribed performance control technique is employed to guarantee the tracking errors within predetermined boundaries.Subsequently,considering the asymmetric input constraints,a discounted non-quadratic cost function is introduced.Moreover,in order to reduce controller updates,an event-triggered control law is developed for ADP algorithm.After that,to further simplify the complexity of controller design,this work is extended to a self-triggered case for relaxing the need for continuous signal monitoring by hardware devices.By employing the Lyapunov method,the uniform ultimate boundedness of all signals is proved to be guaranteed.Finally,a simulation example on a mass–spring–damper system subject to asymmetric input constraints is provided to validate the effectiveness of the proposed control scheme.

Decomposition of Mathematical Programming Models for Aircraft Wing Design Facilitating the Use of Dynamic Programming Approach

Aircraft designers strive to achieve optimal weight-reliability tradeoffs while designing an aircraft. Since aircraft wing skins account for more than fifty percent of their structural weight, aircraft wings must be designed with utmost care and attention in terms of material types and thickness configurations. In particular, the selection of thickness at each location of the aircraft wing skin is the most consequential task for aircraft designers. To accomplish this, we present discrete mathematical programming models to obtain optimal thicknesses either to minimize weight or to maximize reliability. We present theoretical results for the decomposition of these discrete mathematical programming models to reduce computer memory requirements and facilitate the use of dynamic programming for design purposes. In particular, a decomposed version of the weight minimization problem is solved for an aircraft wing with thirty locations (or panels) and fourteen thickness choices for each location to yield an optimal minimum weight design.

PDP: Parallel Dynamic Programming

Deep reinforcement learning is a focus research area in artificial intelligence. The principle of optimality in dynamic programming is a key to the success of reinforcement learning methods. The principle of adaptive dynamic programming(ADP)is first presented instead of direct dynamic programming(DP),and the inherent relationship between ADP and deep reinforcement learning is developed. Next, analytics intelligence, as the necessary requirement, for the real reinforcement learning, is discussed. Finally, the principle of the parallel dynamic programming, which integrates dynamic programming and analytics intelligence, is presented as the future computational intelligence.

Performance Potential-based Neuro-dynamic Programming for SMDPs

An alpha-uniformized Markov chain is defined by the concept of equivalent infinitesimalgenerator for a semi-Markov decision process (SMDP) with both average- and discounted-criteria.According to the relations of their performance measures and performance potentials, the optimiza-tion of an SMDP can be realized by simulating the chain. For the critic model of neuro-dynamicprogramming (NDP), a neuro-policy iteration (NPI) algorithm is presented, and the performanceerror bound is shown as there are approximate error and improvement error in each iteration step.The obtained results may be extended to Markov systems, and have much applicability. Finally, anumerical example is provided.

A stable implicit nodal integration-based particle finite element method(N-PFEM)for modelling saturated soil dynamics

In this study,we present a novel nodal integration-based particle finite element method(N-PFEM)designed for the dynamic analysis of saturated soils.Our approach incorporates the nodal integration technique into a generalised Hellinger-Reissner(HR)variational principle,creating an implicit PFEM formulation.To mitigate the volumetric locking issue in low-order elements,we employ a node-based strain smoothing technique.By discretising field variables at the centre of smoothing cells,we achieve nodal integration over cells,eliminating the need for sophisticated mapping operations after re-meshing in the PFEM.We express the discretised governing equations as a min-max optimisation problem,which is further reformulated as a standard second-order cone programming(SOCP)problem.Stresses,pore water pressure,and displacements are simultaneously determined using the advanced primal-dual interior point method.Consequently,our numerical model offers improved accuracy for stresses and pore water pressure compared to the displacement-based PFEM formulation.Numerical experiments demonstrate that the N-PFEM efficiently captures both transient and long-term hydro-mechanical behaviour of saturated soils with high accuracy,obviating the need for stabilisation or regularisation techniques commonly employed in other nodal integration-based PFEM approaches.This work holds significant implications for the development of robust and accurate numerical tools for studying saturated soil dynamics.

Leveraging on Flock Dynamics and Farmers’ Production Constraints in Designing Flock Health Program for Accelerated Goat Production

Compliance with appropriate flock health program is vital for preventing introduction and minimizing impact of diseases in goat farms. Unfortunately, most goat farms in Uganda, especially in the Albertine Graben Zone lack flock health program. The associated frequent outbreaks slow down effort aimed at commercializing goat production. In this study, we documented flock dynamics, identified and prioritized pressing challenges experienced by goat farms during the year 2022 and generated appropriate flock health program and packaged it for dissemination to farmers. Materials and Methods: Using a cross-sectional design, semi-structured questionnaire, data were collected and analyzed with MS Excel 2013. The data included: location and socio-demographics of household, farming system, flock dynamics, housing, feeding system, health management, challenges encountered by goat farm and suggested solutions. Results: Beginning January 2022 to December 2022, the number of goats reared in all the 45 sample farms increased from 2128 to 2220 goats. Results showed that 884 kids were produced and 88 breeding goats were introduced into the farms. Three hundred ninety-nine goats died due to mainly diseases and 435 goats got withdrawn through nondeath. The average farm level and overall mortality rate were 21 goats per 1000 goatmonths and 15 goats per 1000 goatmonths respectively. The most pressing challenges encountered by sample farms were death of goats especially due to diseases, poor access to veterinary extension services, high cost of inputs and feed scarcity. Solutions suggested by sample farms were improved access to veterinary services, improved housing, enhanced vaccination of goats against diseases, and enhanced grazing land management and feed conservation, all of which were incorporated into the flock health program. Conclusion and Recommendations: An appropriate flock health program was generated based on flock dynamics and production constraints which reveal high mortality and limited access to veterinary services respectively. Actors are recommended to promote adoption and adherence to the flock health program so as to increase goat production and access to wider market.

Residential Energy Scheduling for Variable Weather Solar Energy Based on Adaptive Dynamic Programming

The residential energy scheduling of solar energy is an important research area of smart grid. On the demand side, factors such as household loads, storage batteries, the outside public utility grid and renewable energy resources, are combined together as a nonlinear, time-varying, indefinite and complex system, which is difficult to manage or optimize. Many nations have already applied the residential real-time pricing to balance the burden on their grid. In order to enhance electricity efficiency of the residential micro grid, this paper presents an action dependent heuristic dynamic programming(ADHDP) method to solve the residential energy scheduling problem. The highlights of this paper are listed below. First,the weather-type classification is adopted to establish three types of programming models based on the features of the solar energy. In addition, the priorities of different energy resources are set to reduce the loss of electrical energy transmissions.Second, three ADHDP-based neural networks, which can update themselves during applications, are designed to manage the flows of electricity. Third, simulation results show that the proposed scheduling method has effectively reduced the total electricity cost and improved load balancing process. The comparison with the particle swarm optimization algorithm further proves that the present method has a promising effect on energy management to save cost.

Optimal Constrained Self-learning Battery Sequential Management in Microgrid Via Adaptive Dynamic Programming

This paper concerns a novel optimal self-learning battery sequential control scheme for smart home energy systems.The main idea is to use the adaptive dynamic programming(ADP) technique to obtain the optimal battery sequential control iteratively. First, the battery energy management system model is established, where the power efficiency of the battery is considered. Next, considering the power constraints of the battery, a new non-quadratic form performance index function is established, which guarantees that the value of the iterative control law cannot exceed the maximum charging/discharging power of the battery to extend the service life of the battery.Then, the convergence properties of the iterative ADP algorithm are analyzed, which guarantees that the iterative value function and the iterative control law both reach the optimums. Finally,simulation and comparison results are given to illustrate the performance of the presented method.

UAV flight strategy algorithm based on dynamic programming

Unmanned aerial vehicles(UAVs) may play an important role in data collection and offloading in vast areas deploying wireless sensor networks, and the UAV’s action strategy has a vital influence on achieving applicability and computational complexity. Dynamic programming(DP) has a good application in the path planning of UAV, but there are problems in the applicability of special terrain environment and the complexity of the algorithm.Based on the analysis of DP, this paper proposes a hierarchical directional DP(DDP) algorithm based on direction determination and hierarchical model. We compare our methods with Q-learning and DP algorithm by experiments, and the results show that our method can improve the terrain applicability, meanwhile greatly reduce the computational complexity.

Using approximate dynamic programming for multi-ESM scheduling to track ground moving targets

This paper researches the adaptive scheduling problem of multiple electronic support measures(multi-ESM) in a ground moving radar targets tracking application. It is a sequential decision-making problem in uncertain environment. For adaptive selection of appropriate ESMs, we generalize an approximate dynamic programming(ADP) framework to the dynamic case. We define the environment model and agent model, respectively. To handle the partially observable challenge, we apply the unsented Kalman filter(UKF) algorithm for belief state estimation. To reduce the computational burden, a simulation-based approach rollout with a redesigned base policy is proposed to approximate the long-term cumulative reward. Meanwhile, Monte Carlo sampling is combined into the rollout to estimate the expectation of the rewards. The experiments indicate that our method outperforms other strategies due to its better performance in larger-scale problems.

Approximate Dynamic Programming for Stochastic Resource Allocation Problems

A stochastic resource allocation model, based on the principles of Markov decision processes(MDPs), is proposed in this paper. In particular, a general-purpose framework is developed, which takes into account resource requests for both instant and future needs. The considered framework can handle two types of reservations(i.e., specified and unspecified time interval reservation requests), and implement an overbooking business strategy to further increase business revenues. The resulting dynamic pricing problems can be regarded as sequential decision-making problems under uncertainty, which is solved by means of stochastic dynamic programming(DP) based algorithms. In this regard, Bellman’s backward principle of optimality is exploited in order to provide all the implementation mechanisms for the proposed reservation pricing algorithm. The curse of dimensionality, as the inevitable issue of the DP both for instant resource requests and future resource reservations,occurs. In particular, an approximate dynamic programming(ADP) technique based on linear function approximations is applied to solve such scalability issues. Several examples are provided to show the effectiveness of the proposed approach.

A COMBINED PARAMETRIC QUADRATIC PROGRAMMING AND PRECISE INTEGRATION METHOD BASED DYNAMIC ANALYSIS OF ELASTIC-PLASTIC HARDENING/SOFTENING PROBLEMS

The objective of the paper is to develop a new algorithm for numerical solution of dynamic elastic-plastic strain hardening/softening problems. The gradient dependent model is adopted in the numerical model to overcome the result mesh-sensitivity problem in the dynamic strain softening or strain localization analysis. The equations for the dynamic elastic-plastic problems are derived in terms of the parametric variational principle, which is valid for associated, non-associated and strain softening plastic constitutive models in the finite element analysis. The precise integration method, which has been widely used for discretization in time domain of the linear problems, is introduced for the solution of dynamic nonlinear equations. The new algorithm proposed is based on the combination of the parametric quadratic programming method and the precise integration method and has all the advantages in both of the algorithms. Results of numerical examples demonstrate not only the validity, but also the advantages of the algorithm proposed for the numerical solution of nonlinear dynamic problems.

Optimal Control for a Class of Complex Singular System Based on Adaptive Dynamic Programming

This paper presents a new design approach to achieve decentralized optimal control of high-dimension complex singular systems with dynamic uncertainties. Based on robust adaptive dynamic programming(robust ADP) method, controllers for solving the singular systems optimal control problem are designed. The proposed algorithm can work well when the system model is not exactly known but the input and output data can be measured. The policy iteration of each controller only uses their own states and input information for learning,and do not need to know the whole system dynamics. Simulation results on the New England 10-machine 39-bus test system show the effectiveness of the designed controller.

Genetic programming for predictions of effectiveness of rolling dynamic compaction with dynamic cone penetrometer test results

Rolling dynamic compaction (RDC),which employs non-circular module towed behind a tractor,is an innovative soil compaction method that has proven to be successful in many ground improvement applications.RDC involves repeatedly delivering high-energy impact blows onto the ground surface,which improves soil density and thus soil strength and stiffness.However,there exists a lack of methods to predict the effectiveness of RDC in different ground conditions,which has become a major obstacle to its adoption.For this,in this context,a prediction model is developed based on linear genetic programming (LGP),which is one of the common approaches in application of artificial intelligence for nonlinear forecasting.The model is based on in situ density-related data in terms of dynamic cone penetrometer (DCP) results obtained from several projects that have employed the 4-sided,8-t impact roller (BH-1300).It is shown that the model is accurate and reliable over a range of soil types.Furthermore,a series of parametric studies confirms its robustness in generalizing data.In addition,the results of the comparative study indicate that the optimal LGP model has a better predictive performance than the existing artificial neural network (ANN) model developed earlier by the authors.

Parallel Control for Optimal Tracking via Adaptive Dynamic Programming

This paper studies the problem of optimal parallel tracking control for continuous-time general nonlinear systems.Unlike existing optimal state feedback control,the control input of the optimal parallel control is introduced into the feedback system.However,due to the introduction of control input into the feedback system,the optimal state feedback control methods can not be applied directly.To address this problem,an augmented system and an augmented performance index function are proposed firstly.Thus,the general nonlinear system is transformed into an affine nonlinear system.The difference between the optimal parallel control and the optimal state feedback control is analyzed theoretically.It is proven that the optimal parallel control with the augmented performance index function can be seen as the suboptimal state feedback control with the traditional performance index function.Moreover,an adaptive dynamic programming(ADP)technique is utilized to implement the optimal parallel tracking control using a critic neural network(NN)to approximate the value function online.The stability analysis of the closed-loop system is performed using the Lyapunov theory,and the tracking error and NN weights errors are uniformly ultimately bounded(UUB).Also,the optimal parallel controller guarantees the continuity of the control input under the circumstance that there are finite jump discontinuities in the reference signals.Finally,the effectiveness of the developed optimal parallel control method is verified in two cases.

Dynamic programming methodology for multi-criteria group decision-making under ordinal preferences

A method of minimizing rankings inconsistency is proposed for a decision-making problem with rankings of alternatives given by multiple decision makers according to multiple criteria. For each criteria, at first, the total inconsistency between the rankings of all alternatives for the group and the ones for every decision maker is defined after the decision maker weights in respect to the criteria are considered. Similarly, the total inconsistency between their final rankings for the group and the ones under every criteria is determined after the criteria weights are taken into account. Then two nonlinear integer programming models minimizing respectively the two total inconsistencies above are developed and then transformed to two dynamic programming models to obtain separately the rankings of all alternatives for the group with respect to each criteria and their final rankings. A supplier selection case illustrated the proposed method, and some discussions on the results verified its effectiveness. This work develops a new measurement of ordinal preferences’ inconsistency in multi-criteria group decision-making （MCGDM） and extends the cook-seiford social selection function to MCGDM considering weights of criteria and decision makers and can obtain unique ranking result.

Policy iteration optimal tracking control for chaotic systems by using an adaptive dynamic programming approach

A policy iteration algorithm of adaptive dynamic programming（ADP） is developed to solve the optimal tracking control for a class of discrete-time chaotic systems. By system transformations, the optimal tracking problem is transformed into an optimal regulation one. The policy iteration algorithm for discrete-time chaotic systems is first described. Then,the convergence and admissibility properties of the developed policy iteration algorithm are presented, which show that the transformed chaotic system can be stabilized under an arbitrary iterative control law and the iterative performance index function simultaneously converges to the optimum. By implementing the policy iteration algorithm via neural networks,the developed optimal tracking control scheme for chaotic systems is verified by a simulation.

CONTROLLING ROBOT MANIPULATORS BY DYNAMIC PROGRAMMING

A certain number of considerations should be taken into account in the dynamic control of robot manipulators as highly complex non-linear systems.In this article,we provide a detailed presentation of the mechanical and electrical impli- cations of robots equipped with DC motor actuators.This model takes into account all non-linear aspects of the system.Then,we develop computational algorithms for optimal control based on dynamic programming.The robot's trajectory must be predefined,but performance criteria and constraints applying to the system are not limited and we may adapt them freely to the robot and the task being studied.As an example,a manipulator arm with 3 degrees of freedom is analyzed.