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This paper presents an interior point method for pure state and mixed-constraint optimal control problems for dynamics, mixed constraints, and cost function all affine in the control variable. This method relies on resolving a sequence of two-point boundary value problems of differential and algebraic equations. This paper establishes a convergence result for primal and dual variables of the optimal control problem. A primal and a primal-dual solving algorithm are presented, and a challenging numerical example is treated for illustration. [ABSTRACT FROM AUTHOR]

The unsteady partial differential equations (UPDE) with convection term gives a clear descriptions for the solidification process of a slab in dynamic production of continuous casting. To give a suitable setting value of secondary cooling water flow rate for the dynamic control system, this study investigates an optimal control problem (OCP) of UPDE with convection term. Firstly, control vector discretization of OCP and the solution of UPDE are given. Secondly, due to the rapidity for gradient, this paper analyzes the expression of the gradient calculation method based on Hamiltonian function costate system by approximate treatment, matrix calculation and composite trapezoidal integral method. Thirdly, an improved three-term spectrum conjugate gradient algorithm (ITSCGA) is proposed to solve the OCP of UPDE, and the global convergence of the ITSCGA is demonstrated. Lastly, the performance of ITSCGA is demonstrated by experimental simulations. The results demonstrate that the ITSCGA provides a smaller temperature fluctuations, and improves the quality of a slab. [ABSTRACT FROM AUTHOR]

This paper deals with the orbit tracking and formation motion problems with optimal energies and reduced computational cost. First, the orbit tracking and formation motion are decomposed into movements in the normal and tangent directions of level orbits, respectively, and simultaneously, the optimal value functions in both directions are defined. Then, to reduce the computational cost, a switching threshold event‐triggered (STET) mechanism is designed. Based on the STET mechanism, the optimal value functions are constructed to evaluate the optimal energies of orbit tracking and formation motion. Critic neural networks are then designed to approximate the optimal value functions, which yield the optimal policies along the normal and tangent directions of desired orbits, that is, a so‐called switching threshold event‐triggered critic algorithm (STET‐C). Theoretical analysis of system convergence is given in detail. Finally, two comparison simulations are given. The former intends to verify the optimal energy of STET‐C compared to the feedback controllers. The latter shows that STET‐C significantly reduces the computational cost in contrast with the non‐triggered actor‐critic algorithm, non‐triggered critic algorithm, and the relative threshold event‐triggered critic algorithm. [ABSTRACT FROM AUTHOR]

Salp swarm algorithm (SSA) is an excellent meta‐heuristic algorithm, which has been widely used in the engineering field. However, there is still room for improvement in terms of convergence rate and solution accuracy. Therefore, this paper proposes an enhanced parallel salp swarm algorithm based on the Taguchi method (PTSSA). The parallel trick is to split the initial population uniformly into several subgroups and then exchange information among the subgroups after a fixed number of iterations, which speeds up the convergence. Communication strategies are an important component of parallelism techniques. The Taguchi method is widely used in the industry for optimizing product and process conditions. In this paper, the Taguchi method is adopted into the parallelization technique as a novel communication strategy, which improves the robustness and accuracy of the solution. The proposed algorithm was also tested under the CEC2013 test suite. Experimental results show that PTSSA is more competitive than some common algorithms. In addition, PTSSA is applied to optimize the operation of a heatless combined cooling‐power system. Simulation results show that the optimized operation provided by PTSSA is more stable and efficient in terms of operating cost reduction. [ABSTRACT FROM AUTHOR]

The force-balanced accelerometer (FBA), unlike other types of sensors, incorporates a closed-loop control. The efficacy of the system is contingent not solely on the hardware, but more critically on the formulation of the control algorithm. Conventional control strategies are usually designed for the purpose of response minimization of the sensitive elements, which limits the measurement accuracy and applicable frequency bandwidth of FBAs. In this paper, based on the model predictive control (MPC), a control algorithm of a force-balance accelerometer considering time delay is designed. The variable augmentation method is proposed to convert the force-balance control into an easy-handed measurement error minimization control problem. The discretization method is applied to deal with the time delay problem in the closed loop. The control algorithm is integrated into a practical FBA. The effectiveness of the proposed control is demonstrated through experiments conducted in an ultra-quiet chamber, as well as simulations. The results show that the closed loop in the FBA has a time delay 10 times of the control period, and, utilizing the proposed control, the acceleration signals can be accurately measured with a frequency range larger than 500 Hz. Meanwhile, the vibration response of the sensitive element of the controlled FBA is maintained at the level of microns, which guarantees a large measurement range of the FBA. [ABSTRACT FROM AUTHOR]

In this paper, elliptic control problems with the integral constraint on the gradient of the state and the box constraint on the control are considered. The optimality conditions for the problem are proved. To numerically solve the problem, a finite element duality-based inexact majorized accelerated block coordinate descent (FE-dABCD) algorithm is proposed. Specifically, both the state and the control are discretized by piecewise linear functions. An inexact majorized ABCD algorithm is employed to solve the discretized problem via its dual, which is a multi-block unconstrained convex optimization problem, but the primal variables are also generated in each iteration. Thanks to the inexactness of the FE-dABCD algorithm, the subproblems at each iteration are allowed to be solved inexactly. For the smooth subproblem, we use the preconditioned generalized minimal residual (GMRES) method to solve it. For the two nonsmooth subproblems, one of them has a closed form solution through introducing an appropriate proximal term, and another one is solved by the line search Newton's method. Based on these efficient strategies, we prove that our proposed FE-dABCD algorithm enjoys O (1 k 2 ) iteration complexity. Moreover, to make the algorithm more efficient and further reduce its computation cost, based on the mesh-independence of ABCD method, we propose an FE-dABCD algorithm with a warm-start strategy (wFE-dABCD). Some numerical experiments are done and the numerical results show the efficiency of the FE-dABCD algorithm and wFE-dABCD algorithm. [ABSTRACT FROM AUTHOR]

Two key challenges in optimal control include efficiently solving high-dimensional problems and handling optimal control problems with state-dependent running costs. In this paper, we consider a class of optimal control problems whose running costs consist of a quadratic on the control variable and a convex, non-negative, piecewise affine function on the state variable. We provide the analytical solution for this class of optimal control problems as well as a Hopf-type representation formula for the corresponding Hamilton-Jacobi partial differential equations. Finally, we propose efficient numerical algorithms based on our Hopf-type representation formula, convex optimization algorithms, and min-plus techniques. We present several high-dimensional numerical examples, which demonstrate that our algorithms overcome the curse of dimensionality. We also describe a field-programmable gate array (FPGA) implementation of our numerical solver whose latency scales linearly in the spatial dimension and that achieves approximately a 40 times speedup compared to a parallelized central processing unit (CPU) implementation. Thus, our numerical results demonstrate the promising performance boosts that FPGAs are able to achieve over CPUs. As such, our proposed methods have the potential to serve as a building block for solving more complicated high-dimensional optimal control problems in real-time. [ABSTRACT FROM AUTHOR]

This paper establishes an approximate optimal critic learning algorithm based on single neural network (NN) policy iteration (PI) aiming at solving for continuous-time (CT) 2-player zero-sum games (ZSGs). In fact, we have to face the problem that the errors will disturb the dynamics and in turn identifying dynamics will generate errors. In order to prevent the effect of errors, in this paper, a single NN-based online PI algorithm is developed for the CT system, which is disturbed nonlinear ZSG. With plenty of online data, the Hamilton–Jacobi–Isaacs equation can be solved without complete dynamics. Then by the least-squares method, we can obtain the NN weights. Moreover, in the process of dealing with the undisturbed system, we find the way that obtains NN weights in this paper is equal to the way that obtains the optimal solution by the Gauss–Newton method. Based on the convergence of the Gauss–Newton method, we can efficiently obtain the optimal controller for the undisturbed system by utilizing online data. After getting the controller of the undisturbed system, it is time to take disturbance into consideration, so that we design a robust control pair to overcome the disturbance. In order to demonstrate the effectiveness of this algorithm, we design a set of simulations. The results verify that we can solve the disturbed nonlinear ZSG by this algorithm. [ABSTRACT FROM AUTHOR]

This paper presents a novel adaptive dynamic programming (ADP) method to solve the optimal consensus problem for a class of discrete‐time multi‐agent systems with completely unknown dynamics. Different from the classical RL‐based optimal control algorithms based on one‐step temporal difference method, a multi‐step‐based (also call n‐step) policy gradient ADP (MS‐PGADP) algorithm, which have been proved to be more efficient owing to its faster propagation of the reward, is proposed to obtain the iterative control policies. Moreover, a novel Q‐function is defined, which estimates the performance of performing an action in the current state. Then, through the Lyapunov stability theorem and functional analysis, the proof of optimality of the performance index function is given and the stability of the error system is also proved. Furthermore, the actor‐critic neural networks are used to implement the proposed method. Inspired by deep Q network, the target network is also introduced to guarantee the stability of NNs in the process of training. Finally, two simulations are conducted to verify the effectiveness of the proposed algorithm. [ABSTRACT FROM AUTHOR]

In recent years, there has been an increasing demand for efficient and robust control algorithms to optimize the performance of autonomous systems. Traditional control techniques often struggle to handle the complexity and uncertainty associated with such systems. To address these challenges, hybrid neuro-fuzzy-genetic algorithms have emerged as a promising approach. This paper presents a comprehensive review of the application of hybrid neuro-fuzzy-genetic algorithms for optimal control of autonomous systems. The proposed algorithms combine the strengths of neural networks, fuzzy logic, and genetic algorithms to achieve adaptive and optimal control in real-time scenarios. The neurofuzzy component provides the ability to model and handle complex and uncertain systems, while the genetic algorithm component facilitates the optimization of control parameters. The combination of these techniques enables autonomous systems to adapt and optimize their control strategies based on changing environments and objectives. The paper discusses the underlying principles of hybrid neuro-fuzzy-genetic algorithms, their advantages, and challenges. It also provides a review of the state-of-the-art research in this field, highlighting successful applications and potential future directions. Overall, the integration of neuro-fuzzy-genetic algorithms in autonomous systems holds great promise for achieving optimal control in various domains, including robotics, aerospace, and autonomous vehicles. [ABSTRACT FROM AUTHOR]

In this paper, we consider an optimal control problem of nonlinear systems with mixed control variables and probability constraints. To obtain a numerical solution of this optimal control problem, our target is to formulate this problem as a constrained nonlinear parameter optimization problem (CNPOP), which can be solved by using any gradient-based numerical computation method. Firstly, some binary functions are introduced for each value of the discrete-valued control variable (DCV). Following that, we relax these binary functions and impose a penalty term on the relaxation such that the solution of the resulting relaxed problem (RP) can converge to the solution of the original problem as the penalty parameter increases. Secondly, we introduce a simple initial transformation for the probability constraints. Following that, an adaptive sample approximation method (ASAM) and a novel smooth approximation technique (NSAT) are adopted to formulate the probability constraints as some deterministic constraints. Thirdly, a control parameterization approach (CPA) is used to transform the deterministic problem (i.e., an infinite dimensional problem) into a finite dimensional CNPOP. Fourthly, in order to combine the advantages of limited memory Broyden-Fletcher-Goldfarb-Shanno (L-BFGS) algorithms and differential evolution (DE) algorithms, a L-BFGS-based DE (L-BFGS-DE) algorithm is proposed for solving the resulting approximation problem based on an improvied L-BFGS (IL-BFGS) method and an improved DE (IDE) algorithm. Following that, we establish the convergence result of the L-BFGS-DE algorithm. The L-BFGS-DE algorithm consists of two stages. The objectives of the first and second stages are to obtain a probable position of the global solution and to accelerate the convergence rate, respectively. In the IL-BFGS method, we propose a novel updating rule (NUR), which uses not only the gradient information of the objective function but also the value of the objective function. This will improved the performance of the IL-BFGS method. In the IDE algorithm, a novel adaptive parameter adjustment (NAPA) method, a novel population size decrease (NPSD) strategy, and an improved mutation (IM) scheme are proposed to improve its performance. Finally, an anti-cancer drug therapy problem (ADTP) is further extended to illustrate the effectiveness of the L-BFGS-DE algorithm by taking into account some probability constraints. Numerical results show that the L-BFGS-DE algorithm has good performance and can obtain a stable and robust performance when considering the small noise perturbations in initial state. [ABSTRACT FROM AUTHOR]

Minimum lap-time planning (MLTP) is a well-established problem in the race car industry to provide guidelines for drivers and optimize the vehicle's setup. In this paper, we tackle the 3D nature of the problem in its full extension, making no simplifying assumptions on the mechanics of the system. We propose a multibody vehicle model, described by rigorous dynamical equations. To effectively handle the resulting complexity, we devised an efficient direct dynamics computational method based on Featherstone's articulated-body algorithm (ABA). To solve the MLTP, we employed a direct-collocation technique, discretizing the problem so that all information of the 3D track is pre-processed and directly embedded into the discrete problem. This discretization approach turns out to be perfectly compatible with our vehicle model, leading to a solution in accessible computational time frames. The high level of detail of the model makes the proposed approach most useful for in-depth vehicle dynamics analyses on complex tracks. To substantiate the analysis, we provide a comparison with the results obtained by a double-track model on the Nürburgring Nordschleife circuit. Consistently with the average trend defined by the double track, the proposed model features a more dynamically rich behavior, realistically capturing the higher-order effects elicited by the sharp corners and the highly variable slope of the track. [ABSTRACT FROM AUTHOR]

This paper proposes and investigates a novel near-optimal finite-control-set model predictive control (NOP-MPC) algorithm to control the grid-connected, pulsewidth-modulator-driven voltage source converters with LCL filters. Exploiting the convex and elliptical paraboloid properties of the cost error, NOP-MPC adopts a systematic iterative algorithm within each control cycle to progressively synthesize finite sets of virtual voltage vectors (VVs) for the control optimization stage. The synthesis has the inherent features of respecting the converter voltage limits and converging the sets of VV candidates toward the global optimal point. The fixed-switching-frequency feature of NOP-MPC is expected to ease the LCL filter design. Effects of computational delay, pulsewidth modulation delay, and deadtime are considered and compensated successfully. A two-vector-variable cost function is used to actively damp the inherent LC resonance through an adjustable, weighting-factor-based damping level. This paper is substantiated by theoretical consideration, simulation and experimental results, parameter sensitivity study, and a comparative study with the standard finite-control-set model predictive control that uses only actual VVs. [ABSTRACT FROM AUTHOR]

This paper proposes a general framework for determining the effect of communication delays on the convergence of certain distributed frequency regulation (DFR) protocols for prosumer-based energy systems, where prosumers are serving as balancing areas. DFR relies on iterative and distributed optimization algorithms to obtain an optimal feedback law for frequency regulation. But, it is, in general, hard to know beforehand how many iterations suffice to ensure stability. This paper develops a framework to determine a lower bound on the number of iterations required for two distributed optimization protocols. This allows prosumers to determine whether they can compute stabilizing control strategies within an acceptable time frame by taking communication delays into account. The efficacy of the method is demonstrated on two realistic power systems. [ABSTRACT FROM PUBLISHER]

This paper examines the problem of optimizing hybrid electric vehicle (HEV) power management for fuel economy. This paper begins by presenting a pseudospectral algorithm to solve this optimization problem. Compared with traditional dynamic programming (DP)-based optimal power management approaches, this algorithm has two key advantages: It is numerically more efficient, and it furnishes both the optimal state and costate trajectories. Building on the second advantage, this paper proposes a two-level strategy for optimal power management in vehicles commuting along fixed routes. The upper level of the proposed strategy is a costate adaptation algorithm employing pseudospectral optimization, whereas the lower level is an instantaneous optimization controller employing Pontryagin's minimum principle (PMP). This paper shows its pseudospectral optimization algorithm and two-level strategy using numerical simulation for a series hybrid school bus. Parameters of the bus powertrain model are obtained from experimental component tests performed at the National Engineering Laboratory for Electric Vehicles, Beijing Institute of Technology. Simulation results show that the pseudospectral method reaches a solution close to DP with higher computational efficiency. Furthermore, the proposed two-level strategy is capable of adapting vehicle power management based on road-grade predictions, i.e., an attractive feature compared with more traditional online hybrid power management approaches such as the use of proportional integral derivative (PID) control for adaptive equivalent fuel consumption minimization [PID equivalent consumption minimization strategy (PID-ECMS)]. [ABSTRACT FROM PUBLISHER]

This paper mainly focuses on the optimal output feedback control problem for networked control systems (NCSs) involving multiplicative noises, packet dropouts, input delays and measurement delays. The main contributions of this paper can be concluded as follows. Firstly, different from the previous results, this paper overcomes the barrier of the packet dropouts and measurement delays. Based on the measurement data, the optimal estimator is given. Secondly, by using maximum principle, a sufficient and necessary condition for the optimal control problem is presented. Moreover, the explicit output feedback controller is derived with feedback gain based on the coupled Riccati difference equations. Numerical example is illustrated to show the effectiveness of the proposed algorithm. [ABSTRACT FROM AUTHOR]

Solving the optimal mean-field control problem usually requires complete system information. In this paper, a Q-learning algorithm is discussed to solve the optimal control problem of the unknown mean-field discrete-time stochastic system. First, through the corresponding transformation, we turn the stochastic mean-field control problem into a deterministic problem. Second, the H matrix is obtained through Q-function, and the control strategy relies only on the H matrix. Therefore, solving H matrix is equivalent to solving the mean-field optimal control. The proposed Q-learning method iteratively solves H matrix and gain matrix according to input system state information, without the need for system parameter knowledge. Next, it is proved that the control matrix sequence obtained by Q-learning converge to the optimal control, which shows theoretical feasibility of the Q-learning. Finally, two simulation cases verify the effectiveness of Q-learning algorithm. [ABSTRACT FROM AUTHOR]

This paper is concerned with the stabilization problem of a class of networked control systems, where the plant measurements and the control signals are transmitted over a network and encounter both time delays and packet losses. To deal with the nonzero disturbance rejection issue, two kinds of networked optimal state feedback integral control (SFIC) methods are proposed in this paper: One is a networked guaranteed-cost SFIC method, and the other one is an SFIC method based on estimation of a distribution algorithm. It has been shown that the proposed methods have better nonzero disturbance rejection capability and can achieve zero steady-state error. Simulation and experimental results are given to demonstrate the effectiveness and applicability of the proposed approach. [ABSTRACT FROM PUBLISHER]

The idea for this work starts from the situation in which a metaheuristic-based algorithm has already been developed in order to solve an optimal control problem. This algorithm yields an offline "optimal" solution. On the other hand, the Receding Horizon Control (RHC) structure can be implemented if a process model is available. This work underlines some of the practical aspects of joining the RHC to an existing metaheuristic-based algorithm in order to obtain a closed-loop control structure that can be further used in real-time control. The result is a systematic procedure that integrates a given metaheuristic-based algorithm into a RHC structure. [ABSTRACT FROM AUTHOR]

This paper investigates finite-horizon optimal control problem of continuous-time uncertain nonlinear systems. The uncertainty here refers to partially unknown system dynamics. Unlike the infinite-horizon, the difficulty of finite-horizon optimal control problem is that the Hamilton–Jacobi–Bellman (HJB) equation is time-varying and must meet certain terminal boundary constraints, which brings greater challenges. At the same time, the partially unknown system dynamics have also caused additional difficulties. The main innovation of this paper is the proposed cyclic fixed-finite-horizon-based reinforcement learning algorithm to approximately solve the time-varying HJB equation. The proposed algorithm mainly consists of two phases: the data collection phase over a fixed-finite-horizon and the parameters update phase. A least-squares method is used to correlate the two phases to obtain the optimal parameters by cyclic. Finally, simulation results are given to verify the effectiveness of the proposed cyclic fixed-finite-horizon-based reinforcement learning algorithm. [ABSTRACT FROM AUTHOR]

In this paper, a novel event-sampled robust optimal controller is proposed for a class of continuous-time constrained-input nonlinear systems with unknown dynamics. In order to solve the robust optimal control problem, an online data-driven identifier is established to construct the system dynamics, and an event-sampled critic-only adaptive dynamic programming method is developed to replace the conventional time-driven actor–critic structure. The designed online identification method runs during the solving process and is not applied as a priori part for the solutions, which simplifies the architecture and reduces computational load. The proposed robust optimal control algorithm tunes the parameters of critic-only neural network (NN) by event-triggering condition and runs in a plug-n-play framework without system functions, where fewer transmissions and less computation are required as all the measurements received simultaneously. Based on the novel design, the stability of system and the convergence of critic NN are demonstrated by Lyapunov theory, where the state is asymptotically stable and weight error is guaranteed to be uniformly ultimately bounded. Finally, the applications in a basic nonlinear system and the complex rotational–translational actuator problem demonstrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

This paper studies the optimal control problem for large-scale systems with unknown parameters and dynamics. By using robust adaptive dynamic programming (RADP) method, a decentralized optimal control design is given for large-scale systems with unmatched uncertainties. The convergence of the proposed RADP algorithm and the asymptotic stability of the closed-loop large-scale system are studied rigorously. Finally, a numerical example of a large-scale power system is adopted to illustrate the effectiveness of the obtained algorithm. [ABSTRACT FROM PUBLISHER]

We consider continuous linear programs over a continuous finite time horizon T, with a constant coefficient matrix, linear right hand side functions and linear cost coefficient functions. Specifically, we search for optimal solutions in the space of measures or of functions of bounded variation. These models generalize the separated continuous linear programming models and their various duals, as formulated in the past by Anderson, by Pullan, and by Weiss. In previous papers we formulated a symmetric dual and have shown strong duality. We also have presented a detailed description of optimal solutions and have defined a combinatorial analogue to basic solutions of standard LP. In this paper we present an algorithm which solves this class of problems in a finite bounded number of steps, using an analogue of the simplex method, in the space of measures. [ABSTRACT FROM AUTHOR]

The closed-loop optimal control systems using the receding horizon control (RHC) structure make predictions based on a process model (PM) to calculate the current control output. In many applications, the optimal prediction over the current prediction horizon is calculated using a metaheuristic algorithm, such as an evolutionary algorithm (EA). The EAs, as other population-based metaheuristics, have large computational complexity. When integrated into the controller, the EA is carried out at each sampling moment and subjected to a time constraint: the execution time should be smaller than the sampling period. This paper proposes a software module integrated into the controller, called at each sampling moment. The module estimates using the PM integration the future process states, over a short time horizon, for different control input values covering the given technological interval. Only a narrower interval is selected for a 'good' evolution of the process, based on the so-called 'state quality criterion'. The controller will consider only a shrunk control output range for the current sampling period. EA will search for its best prediction inside a smaller domain that does not cause the convergence to be affected. Simulations prove that the computational complexity of the controller will decrease. [ABSTRACT FROM AUTHOR]

This paper developes a novel model-free dual heuristic dynamic programming (DHP) algorithm combined with policy iteration and least square techniques to implement optimal consensus control of discrete-time multi-agent systems. The coupled Hamilton-Jacobi-Bellman (HJB) equations are required to be solved to achieve optimal consensus control, which is generally difficult especially under the case of unknown mathematical models. To overcome above difficulties, the DHP method is carried out by reinforcement learning utilizing online collected data rather than the accurate system dynamics. First, the performance index and corresponding Bellman equation are acquired. Each agent's value function has quadratic form. Then, a model network is employed to approximate the accurate system dynamics. The Q-function Bellman equation is obtained next. By taking the derivative of Q-function, the DHP method is applied to construct the update formula. Convergence and stability analysis of proposed algorithm are presented. Two simulation examples are provided to illustrate the validity of the proposed algorithm. [ABSTRACT FROM AUTHOR]

Routing algorithms in Delay Tolerant Networks (DTN) need nodes to forward the message to others based on the opportunistic contact. The contact depends on the beaconing rate of nodes, and bigger beaconing rate can bring more contacts. However, this needs more energy. In addition, bigger forwarding rate can make the message be transmitted much faster, but this also needs more energy. Therefore, how to control the forwarding and beaconing rates efficiently to get a trade-off between the expenditure (e.g., energy consumption) and efficiency is very important. This paper proposes a theoretical model to evaluate the performance of the epidemic routing (ER) algorithm under different forwarding and beaconing rates, and then formulates a joint optimization problem. Through Pontryagin's Maximum Principle, this paper obtains the optimal policy and proves that both the optimal forwarding and beaconing rates conform to the threshold form in certain cases. Simulations show the accuracy of the theoretical model. Extensive numerical results show that the optimal policy obtained in this paper is the best among all the policies in the numerical results. [ABSTRACT FROM AUTHOR]

Motivated by the increasing popularity of learning and predicting human user behavior in communication and computing systems, in this paper, we investigate the fundamental benefit of predictive scheduling, i.e., predicting and pre-serving arrivals, in controlled queueing systems. Based on a lookahead-window prediction model, we first establish a novel queue-equivalence between the predictive queueing system with a fully efficient scheduling scheme and an equivalent queueing system without prediction. This result allows us to analytically demonstrate that predictive scheduling necessarily improves system delay performance and drives it to zero with increasing prediction power. It also enables us to exactly determine the required prediction power for different systems and study its impact on tail delay. We then propose the Predictive Backpressure (PBP) algorithm for achieving optimal utility performance in such predictive systems. PBP efficiently incorporates prediction into stochastic system control and avoids the great complication due to the exponential state space growth in the prediction window size. We show that PBP achieves a utility performance that is within O(\epsilon) of the optimal, for any \epsilon > 0, while guaranteeing that the system delay distribution is a shifted-to-the-left version of that under the original Backpressure algorithm. Hence, the average delay under PBP is strictly better than that under Backpressure, and vanishes with increasing prediction window size. This implies that the resulting utility-delay tradeoff with predictive scheduling can beat the known optimal [O(\epsilon),O(\log(1/\epsilon))] tradeoff for systems without prediction. We also develop the Predictable-Only PBP (POPBP) algorithm and show that it effectively reduces packet delay in systems where traffic can only be predicted but not pre-served. [ABSTRACT FROM PUBLISHER]

In this paper, we present a game-theoretic model, a new algorithmic framework with convergence theory, and numerical examples for the solution of intersection management problems. In our model, we consider autonomous vehicles that can communicate with each other in order to find individual optimal driving strategies through an intersection, without colliding with other vehicles. This results in coupled optimal control problems and we consider a generalized Nash equilibrium reformulation of the problem. Herein, we have individual differential equations, state and control constraints and additionally nonconvex shared constraints. To handle the nonconvexity we consider a partial penalty approach. To solve the resulting standard Nash equilibrium problem, we propose a decomposition method, where the selection of the players is controlled through penalty terms. The proposed method allows the prevention of a priori introduced hierarchies. Using dynamic programming, we prove convergence of our algorithm. Finally, we present numerical studies that show the effectiveness of the approach. [ABSTRACT FROM AUTHOR]

Avionics and air traffic management (ATM) systems are evolving with the introduction of progressively higher levels of automation, toward attaining the ambitious operational, technical, and safety enhancements required to sustain the present growth of global air traffic. This paper presents novel 4-Dimensional Trajectory (4DT) functionalities that are being developed for integration in ATM and avionics systems to support trajectory based operations (TBO). The 4DT planning process, which is the main focus of the paper, is supported by a custom multiobjective variant of state-of-the-art optimal control algorithms, incorporating various operational, economic, and environmental factors. Capitalizing on the higher theoretical accuracy offered by optimal control algorithms compared to other methods, a key feature of the proposed approach is the introduction of a postprocessing stage to ensure that the mathematically optimal trajectories are translated into a set of standardized 4DT descriptors, which can be flown by state-of-the-art automatic flight control systems. Additionally, to support air-ground 4DT intent negotiation and validation in the TBO context, the 4DT postprocessing ensures that optimal trajectories are synthetically described by a limited number of parameters, minimizing the bandwidth requirements imposed on airborne data links. Simulation-based verification activities addressing operational efficiency improvements and computational performance in the terminal area ATM context support the viability of the proposed 4DT planning functionality for online tactical TBO. [ABSTRACT FROM AUTHOR]

This paper investigates a decomposition approach for binary optimization problems with nonlinear objectives and linear constraints. Our methodology relies on the partition of the objective function into separate low-dimensional dynamic programming (DP) models, each of which can be equivalently represented as a shortest-path problem in an underlying state-transition graph. We show that the associated transition graphs can be related by a mixed-integer linear program (MILP) so as to produce exact solutions to the original nonlinear problem. To address DPs with large state spaces, we present a general relaxation mechanism that dynamically aggregates states during the construction of the transition graphs. The resulting MILP provides both lower and upper bounds to the nonlinear function, and it may be embedded in branch-and-bound procedures to find provably optimal solutions. We describe how to specialize our technique for structured objectives (e.g., submodular functions) and consider three problems arising in revenue management, portfolio optimization, and healthcare. Numerical studies indicate that the proposed technique often outperforms state-of-the-art approaches by orders of magnitude in these applications. Data and the online appendix are available at https://doi.org/10.1287/mnsc.2017.2849. This paper was accepted by Yinyu Ye, optimization. [ABSTRACT FROM AUTHOR]

Purpose – The purpose of this paper is to propose an efficient algorithm for trajectory planning of unmanned aerial vehicles (UAVs) in 2D spaces. This paper has been motivated by the challenge to develop a fast trajectory planning algorithm for autonomous UAVs through mid-course waypoints (WPs). It is assumed that there is no prior knowledge of these WPs, and their configuration is computed as in-flight procedure. Design/methodology/approach – Since the off-line techniques cannot be applied, it is required to apply an online trajectory planning algorithm. For this reason, based on the optimal control and the geometry, each segment of trajectory is designed with respect to a local frame. The algorithm is implemented as a real-time manner in terms of the down-range variable. Findings – The proposed algorithm tries to find not only a feasible trajectory (the constraint includes the maximum heading angle rate) but also an optimal trajectory (the objective locally is to minimize the length of the path). This online trajectory planning algorithm gradually produces a smooth 2D trajectory aiming at reaching the mid-course WPs and the final target so that they are smoothly connected with each other. The mid-course WPs are described through the given down-range, cross-range, and heading angle. Originality/value – Based on geometrical principles, this algorithm is capable of re-planning the trajectory as in-flight manner, and the computational burden approaches the online capabilities for UAVs with high velocity. [ABSTRACT FROM AUTHOR]

This paper presents several modified subgradient extragradient methods with inertial effects to approximate solutions of variational inequality problems in real Hilbert spaces. The operators involved are either pseudomonotone Lipschitz continuous or pseudomonotone non-Lipschitz continuous. The advantage of the suggested algorithms is that they can work adaptively without the prior information of the Lipschitz constant of the mapping involved. Strong convergence theorems of the proposed algorithms are established under some suitable conditions. Finally, some numerical experiments are given to verify the advantages and efficiency of the proposed iterative algorithms with respect to previously known ones. [ABSTRACT FROM AUTHOR]

This paper focuses on the constraint handling for induction machines (IMs) using model predictive control (MPC) to enhance the optimality. Commonly, the constraints of IMs are represented by stator current and voltage limits, which are described as quadratic inequality in dq-frame. Due to the spherical feature, the constraints have to be replaced by approximation by polygon in order to get a standard form of quadratic programming (QP). In this paper, a novel approach is proposed to convert the quadratic inequalities into linear ones without approximation, whereat the inequality is parameter-varying. To tackle this parameter-varying inequality, the multiparametric quadratic program (mp-QP) algorithm for reference tracking is utilized and extended. To ensure the optimization problem solved in real time, an explicit MPC (EMPC) via mp-QP is applied instead of any online numerical solver. [ABSTRACT FROM PUBLISHER]

In this paper, we consider a joint pricing and dynamic production policy for perishable items without shortages. A unimodal time-varying demand function is assumed to be convex nonincreasing in sales price. We propose a dynamic optimization model to maximize total profit by allocating a limited production capacity and setting a suitable sales price. For a given sales price, the optimal production rate can be obtained by solving a dynamic optimization problem with Pontryagin’s maximum principle. By virtue of the relationships between price intervals and the corresponding optimal production policies, an effective algorithm is designed to generate the joint policy for a system with a general nonlinear demand function of price. For a linear demand function, it is shown that the objective function is concave in price and that there exists a unique optimal joint policy. Numerical examples are presented to illustrate the validity of the theoretical results, and several managerial implications in terms of the production and pricing of perishable items are provided. [ABSTRACT FROM AUTHOR]

The use of quaternions or quaternion error attitude control strategies for unmanned aerial vehicles (UAVs) is commonplace. Quaternion tracking error control is usually presented in rather theoretical works, where the control algorithm is almost exclusively chosen to be a suboptimal one. However, the application of optimal control techniques is usually associated to simplified attitude models frequently aimed at solving real-life problems. The work presented in this paper aims to formally merge the development of a complete theoretical quaternion error model with an optimal control strategy. Moreover, the application of optimal control algorithms to a fully defined quaternion error state-space model and the validation of the same in a real-time experimental setup is the focus of this research. The result is a novel controller named Optimal Quaternion Tracking of Attitude Error Linearization (OQTAL). The paper provides a comprehensive proof of stability, full simulation validation for a planetary landing gravity turn trajectory, and evidence of repeatable experimental work for a real-time quadrotor UAV on a motion capture testbed. OQTAL is compared with proven optimal forms of (PID) proportional-integral-derivative control and linear quadratic regulator control and is shown to have a 10%–20% reduction in error for the experimental setup trajectory tracking trials and an even larger tracking error reduction in the gravity turn simulation trials. Furthermore, for close tracking conditions, OQTAL behaves almost like a linear and time-invariant system, therefore requiring limited computation time for performing the trajectory tracking. [ABSTRACT FROM PUBLISHER]

The present paper is dedicated to the investigation of a predictive Equivalent Consumption Minimization Strategy. The objective is to determine the torque split between the internal combustion engine and the electric machine of a hybrid vehicle. The energy management is formulated as a receding optimization problem. To avoid a complex prediction of the vehicle speed and acceleration over time, the slow dynamic of their distribution is exploited. A rational tuning of the algorithm parameters is proposed as well as some improved implementations. The number of individual operations (additions, multiplications, interpolations, etc) required per seconds is discussed. Finally, the energy management algorithm energy consumption are assessed over different driving cycles, including one with a \boldsymbol 15406  ${km}$ length obtained using GPS measurements. A comparison with an adaptive Equivalent Consumption Minimization Strategy is provided. The predictive Equivalent Consumption Minimization Strategy allows controlling the state of charge close to a (possibly time varying) set point while providing low fuel consumption. [ABSTRACT FROM AUTHOR]

The problem of general non-linear stochastic optimal control with small Wiener noise is studied. The problem is approximated by a Markov Decision Process. Bellman Equation is solved using Value Iteration (VI) algorithm in the low rank Tensor Train format (TT-VI). In this paper a modification of the TT-VI algorithm called TT-Q-Iteration (TT-QI) is proposed by authors. In it, the nonlinear Bellman Optimality Operator is iteratively applied to the solution as a composition of internal Tensor Train algebraic operations and TT-CROSS algorithm. We show that it has lower asymptotic complexity per iteration than the method existing in the literature, provided that TT-ranks of transition probabilities are small. In test examples of an underpowered inverted pendulum and Dubins cars our method shows up to 3–10 times faster convergence in terms of wall clock time compared with the original method. [ABSTRACT FROM AUTHOR]

In this paper, an integral feedback and feed-forward (IFF) optimal controller with hard terminal constraints for missile formation reconfiguration is designed. The controller has quadric optimal performance for expected terminal errors, output, and control quantity. From the viewpoint of the kinematics relationship of a formation in the relative coordinate frame, the authors establish a precisely linearized relative motion model by transforming the control variables. This relative motion model can intuitively manifest the relationship of the relative motion in three directions in the relative coordinate frame. In order to solve the designed IFF optimal controller, detailed deductions for deriving the related Lagrange parameters are presented. A precise integration algorithm was adopted instead of using a traditional backward integration algorithm to calculate more precise solutions for the relevant parameters in the IFF optimal controller. A collision avoidance system with four spherical domains was proposed, and a modifying principle to avoid collision during formation reconfiguration was presented. Simulation results demonstrate that the presented IFF optimal controller is capable of implementing missile formation reconfiguration rapidly, stably, and accurately. It can additionally restrain invariant or slowly varying perturbations induced by the velocity of a leader missile. Furthermore, the collision avoidance system developed in this paper can enable missiles to avoid collision during formation reconfiguration. [ABSTRACT FROM AUTHOR]

This paper deals with collision avoidance for road vehicles when operating at the limits of available friction. For collision avoidance, a typical control approach is to: (a) define a reference geometric path that avoids collision; (b) apply low-level control to perform path following. However, there are a number of limitations in this approach, which are addressed in the current paper. First, it is typically unknown whether a predefined reference path is feasible or over-conservative. Secondly, the control scheme is not well suited to avoiding a moving object, e.g. another vehicle. Further: incorrect choice of reference path may degrade performance, fast adaptation to friction change is not easy to implement and the associated low-level control allocation may be computationally intensive. In this paper we use the general nonlinear optimal control formulation, include some simplifying assumptions and base optimal control on the minimization of an underlying Hamiltonian function. A particle model is used to define an initial reference in the form of a desired global mass-center acceleration vector. Beyond that, yaw moment is taken into account for the purpose of enhancing the stability of the vehicle. The Hamiltonian function is adapted as a linear function of tyre forces and can be minimized locally for individual wheels; this significantly reduces computational workload compared to the conventional approach of forcemoment allocation. Several combinations of actuators are studied to show the general applicability of the control algorithm based on a linear Hamiltonian function. The method has the potential to be used in future vehicle control systems across a wide range of safety applications and hence improve overall vehicle agility and improve safety. [ABSTRACT FROM AUTHOR]

This paper discusses the nonholonomic robotic systems whose motion constraints assume the Pfaffian form, and the equations of motion are represented by driftless control systems with outputs. By reference to the end point map of such a control system, we define the system's Jacobian and study Jacobian motion-planning algorithms. A new Lagrange-type Jacobian inverse, referred to as the General Lagrangian Jacobian Inverse (GLJI), is designed as the solution of an optimal control problem with a Lagrange-type objective function. Singularities of GLJI are examined. A special choice of the objective function illustrates features of GLJI. A new motion-planning algorithm based on GLJI is proposed. Theoretical arguments are illustrated with a motion-planning problem of a space robot. [ABSTRACT FROM PUBLISHER]

Abstract: This paper develops an online adaptive critic algorithm based on policy iteration for partially unknown nonlinear optimal control with infinite horizon cost function. In the proposed method, only a critic network is established, which eliminates the action network, to simplify its architecture. The online least squares support vector machine (LS‐SVM) is utilized to approximate the gradient of the associated cost function in the critic network by updating the input‐output data. Additionally, a data buffer memory is added to alleviate computational load. Finally, the feasibility of the online learning algorithm is demonstrated in simulation on two example systems. [ABSTRACT FROM AUTHOR]

In this paper, we present PARASOF, an algorithm for the solution of linear systems with BABD matrices on massively parallel computing systems like graphic processing units or GPUs. This algorithm is compared with the state-of-the-art algorithms, in particular SOF, from which it is inspired and takes the same stability properties. We detail its design and implementation issues and give the main figures of its theoretical and experimental performances. [ABSTRACT FROM AUTHOR]

This paper proposes a Takagi–Sugeno (T–S) fuzzy method to select cost function weights of finite control set model predictive DC–DC converter control algorithms. The proposed method updates the cost function weights at every sample time by using T–S type fuzzy rules derived from the common optimal control engineering knowledge that a state or input variable with an excessively large magnitude can be penalised by increasing the weight corresponding to the variable. The best control input is determined via the online optimisation of the T–S fuzzy cost function for all the possible control input sequences. This paper implements the proposed model predictive control algorithm in real time on a Texas Instruments TMS320F28335 floating-point Digital Signal Processor (DSP). Some experimental results are given to illuminate the practicality and effectiveness of the proposed control system under several operating conditions. The results verify that our method can yield not only good transient and steady-state responses (fast recovery time, small overshoot, zero steady-state error, etc.) but also insensitiveness to abrupt load or input voltage parameter variations. [ABSTRACT FROM PUBLISHER]

Recently Taylor^K-Kalman–Fourier filters were proposed for estimating dynamic phasors to provide instantaneous estimates and drastically reduce the total vector error by a factor of 10. However, they exhibit resonant frequencies at the edges of the pass band, and high-interharmonic gains. In this paper, the optimal linear quadratic (LQ) control is applied to design feedback filters referred to as Taylor^K-LQG-Fourier filters. This method reduces the interharmonic gains and the resonant frequency at the passband edges of the Taylor^K-Kalman–Fourier filter. The estimates from oscillating signals obtained through this optimal technique are quasi-instantaneous, and provide estimates of the instantaneous frequency, and its rate of change, preserving its synchrony with the signal for control applications. The effectiveness of the proposed algorithm is verified through simulations and experimental results. [ABSTRACT FROM PUBLISHER]