Computationally efficient nonlinear model predictive control relies on elaborate discrete-time optimal control problem (OCP) formulations trading off accuracy with respect to the continuous-time problem and associated computational burden. Such formulations, however, are in general not easy to implement within specialized software frameworks tailored to numerical optimal control. This paper introduces a new multi-phase OCP interface for the open-source software acados allowing to conveniently formulate such problems and generate fast solvers that can be used for nonlinear model predictive control (NMPC). While multi-phase OCP (MOCP) formulations occur naturally in many applications, this work focuses on MOCP formulations that can be used to efficiently approximate standard continuous-time OCPs in the context of NMPC. To this end, the paper discusses advanced control parametrizations, such as closed-loop costing and piecewise polynomials with varying degree, as well as partial tightening and formulations that leverage models of different fidelity. An introductory example is presented to showcase the usability of the new interface. Finally, three numerical experiments demonstrate that NMPC controllers based on multi-phase formulations can efficiently trade-off computation time and control performance.

Interdisciplinary integration is a superior method to improve the optimization algorithm. In this paper, control theory and optimization are combined, and the optimization algorithm is regarded as a control process. Based on the premise of optimal control, the state equation corresponding to Lagrange Algorithm is established with the Karush-Kuhn-Tucker (KKT) conditions as the objective. As an optimal control method, Linear Quadratic Regulator (LQR) is utilized to control the calculation process, and an innovative LQR-Lagrange Algorithm is proposed. The Lyapunov stability criterion is applied to analyze the convergence, and it is proved that the proposed LQR-Lagrange Algorithm is bound to converge as long as the parameter matrices and are positive definite. The analysis indicates that the influence of parameters in LQR-Lagrange Algorithm on the calculation speed is monotonic, and the elements in and has no effect on the convergence. Therefore, the proposed algorithm has a monotonic and user-friendly parameter tuning strategy. The significance and advantages of interdisciplinary integration with control theory and optimization are discussed in the end.

Because of the soft dynamic performance of the fuel cell stack, the battery is usually integrated in the power system in fuel cell hybrid electric vehicles. In this paper, a real time energy management strategy considering thermal constraints based on speed prediction with neuron network is proposed. The main principle of the proposed control strategy is to get the future power requirement with model predictive control based on the historic speed information, and then optimize the objective function according to the state variables. The objective function is set to minimize the equivalent fuel consumption of the vehicle and extend the life span of the fuel cell stack based on thermal constraints. Contrasting with the control strategy without thermal constraints under the WLTC driving cycle, the proposed energy management is 0.9% higher, but the temperature of the fuel cell stack and the battery can be limited within an appropriate range. The total equivalent fuel consumption is 3.9% lower than dynamic programming control strategy, which proves the availability of the proposed control strategy can reduce the equivalent fuel consumption while prolonging the fuel cell stack life span. Hardware in loop (HIL) experiment is implemented to testify the real time application of the proposed control strategy.

This article aims to address the optimization problems for continuous-time first-order and second-order multi-agent systems (MASs) with matrix-weighted networks. The matrix-weighted network is used to model the interdependence between agents’ multidimensional states, providing an effective approach to analyzing complex systems. The goal of optimization is that agents exponentially converge to the optimal value of the global cost function, which is formed by a sum of local cost functions. To achieve this goal, distributed optimization algorithms based on Hessian matrix and gradient information are constructed. Additionally, the edge-based event-triggered mechanism is utilized to avoid communicating with all neighbors at the time of event triggering while theoretically excluding Zeno behavior. The results show that the proposed algorithm can ensure that the intelligent body can achieve the optimization goal while reducing energy consumption. Eventually, an application is presented to substantiate the theoretical results.

Cooperative manipulators, vital for intricate tasks, are gaining widespread attention across industries. Recognizing their impact on power consumption, costs, and task outcomes, this paper emphasizes the critical study of control methods, actuator power consumption, and manipulator accuracy. Addressing these challenges, we propose a Neural Network-Sliding Mode Controller (NN-SMC) to optimize actuator power consumption and minimize errors in cooperative manipulators. Operating in trajectory and point-to-point modes, the NN-SMC dynamically generates real-time Switching Mode Controller (SMC) gains (L and K) for precise control. Stability is ensured by maintaining gains within permissible ranges. In point-to-point mode, the NN orchestrates an optimal path generation, along with tailored gains. To evaluate performance accurately, a novel control performance index is introduced. Experimental results on 3-DOF cooperative manipulators demonstrate a remarkable 28% increase in the control performance index for the trajectory mode and a substantial reduction in computational complexity for both modes. This work not only addresses inherent challenges in cooperative manipulators but also signifies a methodological advancement through the integration of neural network-based control, promising enhanced efficiency and stability.

This paper solves the robust tracking problem (RTP) for a type of partially unknown nonlinear systems with asymmetric constrained-input by utilizing an improved adaptive dynamic programming (ADP) method based on experience replay (ER) technique and critic-only neural network (NN). Initially, an identifier neural network (INN) is set to identify the unknown parts of the system dynamics. Subsequently, the tracking error and the desired trajectory are used to construct an augmented system, so that the robust tracking problem (RTP) is transformed into a constrained optimal control problem (OCP). It is proved that the designed control policy of OCP can make the tracking error to be uniformly ultimately bounded (UUB). Then, using the framework of ADP and critic-only NN to solve the derived Hamilton-Jacobi-Bellman equation (HJBE). The NN weight regulation law is partially derived by using gradient descent algorithm (GDA) and then is improved by using the ER technique and the Lyapunov stability theory, which no longer need the conditions of persistence of excitation (PE) and initial admissible control. Besides, the total system states and NN weights is proved to be closed stable by utilizing the Lyapunov technique. Finally, through two simulation examples, it is demonstrated that the proposed control scheme is effective.

The necessary conditions for the optimal control of partially observed, fully coupled forward-backward mean-field stochastic differential equations driven by Teugels martingales are discussed in this paper. In this context, we make the assumption that the forward diffusion coefficient and the martingale coefficient are independent of the control variable, and the control domain may not necessarily be convex. For this class of optimal control problems, we derive the stochastic maximum principle based on the classical method of spike variations and the filtering techniques. The adjoint processes that are related to the variational equations are determined by the solutions of proposed forward-backward stochastic differential equations in finite-dimensional spaces. Further, the Hamiltonian function is used to obtain the maximum principle for the optimality of the given control system. Our results are then applied to the mean-field type problem of linear quadratic stochastic optimization.

In this paper, the problem of state estimation for a fractional-order neural networks system with uncertainties is studied by a sampled-data controller. First, considering the convenience of digital field, such as anti-interference, not affected by noise, a novel sampled-data controller is designed for the fractional-order neural network system of uncertainties with changeable sampling time. In the light of the input delay approach, the sampled-data control system of fractional-order is simulated by the delay system. The main purpose of the presented method is to obtain a sampled-data controller gain K to estimate the state of neurons, which can guarantee the asymptotic stability of the closed-loop fractional-order system. Then, the fractional-order Razumishin theorem and linear matrix inequalities (LMIs) are utilized to derive the stable conditions. Improved delay-dependent and order-dependet stability conditions are given in the form of LMIs. Furthermore, the sampled-data controller can be acquired to promise the stability and stabilization for fractional-order system. Finally, two numerical examples are proposed to demonstrate the effectiveness and advantages of the provided method.

This paper studies the problem of optimal control with state constraints for mean-field type stochastic systems, which is governed by fully coupled forward-backward stochastic differential equations(FBSDE) with Teugels martingales. In this system, the coefficients contain not only the state processes but also its marginal distribution, and the cost function is of mean-field type as well. We use an equivalent backward formulation to deal with the terminal state constraint, and then we obtain a stochastic maximum principle by Ekeland’s variational principle. In addition, we discuss a stochastic LQ control problem with state constraints.

The purpose of this paper is to utilize adaptive dynamic programming to solve an optimal consensus problem for double-integrator multi-agent systems with completely unknown dynamics. In double-integrator multi-agent systems, flocking algorithms that neglect agents' inertial effect can cause unstable group behavior. Despite the fact that an inertias-independent protocol exists, the design of its control law is decided by dynamics and inertia. However, inertia in reality is difficult to measure accurately, therefore, the control gain in the consensus protocol was solved by developing adaptive dynamic programming to enable the double-integrator systems to ensure the consensus of the agents in the presence of entirely unknown dynamics. Firstly, we demonstrate in a typical example how flocking algorithms that ignore the inertial effect of agents can lead to unstable group behavior. And even though the protocol is independent of inertia, the control gain depends quite strongly on the inertia and dynamic of the agent. Then, to address these shortcomings, an online policy iteration-based adaptive dynamic programming is designed to tackle the challenge of double-integrator multi-agent systems without dynamics. Finally, simulation results are shown to prove how effective the proposed approach is.

In this paper, we study the optimal control of a discrete-time stochastic differential equation (SDE) of mean-field type, where the coefficients can depend on both a function of the law and the state of the process. We establish a new version of the maximum principle for discrete-time mean-field type stochastic optimal control problems. Moreover, the cost functional is also of the mean-field type. This maximum principle differs from the classical principle one since we introduce new discrete-time mean-field backward (matrix) stochastic equations. Based on the discrete-time mean-field backward stochastic equations where the adjoint equations turn out to be discrete backward SDEs with mean field, we obtain necessary first-order and sufficient optimality conditions for the stochastic discrete mean-field optimal control problem. To verify, we apply the result to production and consumption choice optimization problem.

It is well known that conservative mechanical systems exhibit local oscillatory behaviours due to their elastic and gravitational potentials, which completely characterise these periodic motions together with the inertial properties of the system. The classification of these periodic behaviours and their geometric characterisation are in an on-going secular debate, which recently led to the so-called eigenmanifold theory. The eigenmanifold characterises nonlinear oscillations as a generalisation of linear eigenspaces. With the motivation of performing periodic tasks efficiently, we use tools coming from this theory to construct an optimization problem aimed at inducing desired closed-loop oscillations through a state feedback law. We solve the constructed optimization problem via gradient-descent methods involving neural networks. Extensive simulations show the validity of the approach.

In this paper, an uncertain disturbance rejection control problem for the affine system in the presence of asymmetric input constraints is addressed using an event-triggered control method. The disturbance rejection control is converted to an H ∞ optimal control problem, and a Zero-sum game-based method is proposed to solve this H ∞ optimal control problem. To deal with the input constraints, a new cost function is proposed. The event-triggered controller is updated only when the triggering condition is satisfied, which can reduce the computational complexity.In order to obtain a controller that minimizes the performance index function in the worst-case disturbance, we use a critic-only network to solve the Hamilton-Jacobi-Isaacs(HJI) equation, and the critic network weight is tuned through a gradient descent method with the historical state data. The stability of the closed-loop system and the uniform ultimate boundedness of the critic network parameters are proved by the Lyapunov method. Two numerical examples are provided to verify the effectiveness of the proposed methods.