Optimal Motion Planning and Tracking Control for a...

Learning-based optimal cooperative control using edge-based triggering strategy

The optimal output tracking control problem for nonlinear large-scale dynamic systems is considered. A series-based approximate approach for designing the optimal controller is proposed with respect to quadratic performance indexes. By using the approach, the high order, coupling, nonlinear two-point boundary value problem is transformed into a sequence of linear decoupling two-point boundary value problems. By intercepting the frontal finite terms of the solution series, we obtained a suboptimal tracking control law. A simulation example illustrates the efficiency of the optimal output tracking control law designed.

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.

In this paper, we study optimal LQG tracking control problems for linear continuous-time hybrid systems. We adopt an approach to prepare some candidates of mode distributions and minimize value functions at each time for the systems and performance indices. By the approach, system states and mode distributions are simultaneously optimized so that the performance indices are minimized for available information of reference signals. We consider optimization problems for averaged systems and averaged performance indices throughout mode distributions. Finally we give numerical examples and verify that we can obtain both optimal tracking performance and optimal candidate of mode distributions by the algorithm presented in this paper.

With the increasing deployment of Unmanned Aerial Vehicle (UAV) swarms in uncertain and dynamically changing environments, optimal cooperative control has become essential for ensuring robust and efficient system coordination. To this end, this paper designs a data-driven optimal bipartite containment tracking control scheme for multi-UAV systems under compound uncertainties. A novel Dynamic Iteration Regulation Strategy (DIRS) is proposed, which enables real-time adjustment of the learning iteration step according to the task-specific demands. Compared with conventional fixed-step data-driven algorithms, the DIRS provides greater flexibility and computational efficiency, allowing for better trade-offs between the performance and cost. First, the optimal bipartite containment tracking control problem is formulated, and the associated coupled Hamilton–Jacobi–Bellman (HJB) equations are established. Then, a data-driven iterative policy learning algorithm equipped with the DIRS is developed to solve the optimal control law online. The stability and convergence of the proposed control scheme are rigorously analyzed. Furthermore, the control law is approximated via the neural network framework without requiring full knowledge of the model. Finally, numerical simulations are provided to demonstrate the effectiveness and robustness of the proposed DIRS-based optimal containment tracking scheme for multi-UAV systems, which can reduce the number of iterations by 88.27% compared to that for the conventional algorithm.

This paper presents an optimal trajectory tracking control algorithm for autonomous surface vessels (ASVs) using data-driven reinforcement learning (RL) to address challenges arising from model uncertainties and time-varying external disturbances in complex marine environments. To ensure robust performance under these conditions, we first employ the H ∞ control method. Then, we design a model-based RL algorithm to achieve the optimal trajectory tracking control law for the ASV despite uncertainties and disturbances. In addition, we extend the model-based RL algorithm to a model-free data-driven RL algorithm, removing the requirement for model of the ASV. The model-free algorithm directly learns the optimal control law from real-time data, providing a more flexible solution when the model of the ASV is unknown. Simulations are conducted to verify the proposed algorithms.

This paper dealt with design scheme of sliding mode optimal tracking control in which the hyperplane is designed to follow the desired trajectory without time-delay. At first, we designed the servo system by applying conventional optimal tracking control, H1 and H∞ optimal tracking control. Secondly, we show the design method of sliding mode optimal tracking control. Thirdly, we carried out the simulation to verify the validity of the design method. In the simulation, three patterns were examined by using H2 norm. The trajectory following and the robust performance in the difference of the design methods were clarified by the simulations. Finally, we applied these control methods to a quadruped locomotion robot.

Optimal tracking control with zero steady-state error for time-delay systems with sinusoidal disturbances

This paper studies the optimal output tracking control and stabilization for networked control systems with packet losses via output feedback control. Both finite-horizon and infinite-horizon cases are considered. For the finite-horizon case, the authors introduce an augmented system according to the state variable and the reference trajectory for the first time. Based on a set of difference Riccati equations, an optimal output feedback tracking controller is proposed by applying the stochastic maximum principle. And an optimal estimator is presented. For the infinite-horizon case, a necessary and sufficient condition for the stabilization of the system is provided. And an optimal output feedback stabilizing tracking controller is obtained by establishing a set of algebraic Riccati equations. Finally, numerical examples are given to verify the proposed results.

Surface cracks exist in many civil infrastructures such as road and bridge deck surfaces, parking lots, and building surfaces, etc. To prevent the crack growth and further deterioration, it is necessary to fill these cracks with appropriate materials on time. We present a robotic crack filling system that can effectively and efficiently deliver fluidic repairing materials to fill surface cracks. Motion planning and cracking filling control are the two main tasks presented in this paper. We present a graph-based crack coverage (GCC) algorithm to solve motion planning problem. The filling motion control is captured by a model predictive control (MPC) scheme given the mobile platform trajectory. We also develop a crack-filling robotic prototype. Simulation and experimental results are presented to demonstrate the system design and performance evaluation.

In this paper, near optimal tracking of a class of nonlinear systems is addressed. Adaptive (approximate) dynamic programming approach is used to calculate the optimal control in closed form. ADP (Adaptive (approximate) dynamic programming) has been widely used to resolve optimal regulation and tracking problems of nonlinear control systems. Despite advances in the so called supervised and unsupervised ADP techniques for optimal tracking, they have a main draw back. That is, the optimal controller needs to be recalculated for every particular reference trajectory. The main goal of this work is to address this issue for a class of nonlinear systems. Finally, this approach is applied on a Delta robot and the performance of the method is analyzed experimentally.

This study focuses on optimal motion planning for nonholonomic constraints mobile robot. We formulate the dynamics model of a differential-drive mobile robot by using Lagrangian mechanics, where the nonholonomic constraints are accurately described through differential equations. The optimal motion planning of the system is constructed as an optimal control problem which is then converted to a nonlinear programming problem by introducing trapezoidal collocation method, and the formulated nonlinear programming is solved by interior-point method. Compared with the prevailing methods in the field of motion planning, our proposed method can handle different kinds of path constraints, terminal conditions and collision-avoidance requirements. Simulation results indicate that the proposed approach can efficiently deal with various user-specified requirements with advantage of high computing efficiency.

In this paper, a comparison is addressed between two methods, that is, the optimal tracking control methods of unknown nonlinear systems with and without constrained input. Firstly, the optimal tracking problem for a class of affine nonlinear system is formulated. The tracking cost functions are also defined, both for the two methods. The two methods are proved to be equivalent as the actuator bound is large enough. Integral reinforcement learning (IRL) algorithm is employed to solve the optimal tracking problem by using only system data. To facilitate the implementation of the IRL algorithm, the actor-critic neural network technique and the least squares method are employed in approximating the unknown weights iteratively. In the simulation, a detailed comparison is given to demonstrate the relationship between the two methods in the aspects of control input and tracking cost value.

This chapter presents an optimal tracking control methodology for an offshore steel jacket platform subject to external wave force. Based on a dynamic model of an offshore steel jacket platform with an AMD mechanism and a linear exogenous system model of the external wave force on the offshore platform, an optimal tracking control scheme with feedforward compensation is proposed to attenuate wave-induced vibration of the offshore platform. A feedforward and feedback optimal tracking controller (FFOTC) can be obtained by solving an algebraic Riccati equation and a Sylvester equation, respectively. It is demonstrated that the wave-induced vibration amplitudes of the offshore platform under the FFOTC are much smaller than the ones under the feedback optimal tracking controller (FOTC) and the feedforward and feedback optimal controller (FFOC). Furthermore, the required control force under the FFOTC is smaller than the ones under the FOTC and the FFOC.

In this paper, the nonlinear optimal control problem is investigated for spacecraft formation flying with collision avoidance. Based on a nonlinear model of formation flying, two optimal tracking control laws are proposed to ensure the formation pattern converges to the predetermined configuration. The first optimal control law which combines Lyapunov optimizing control with a trajectory-following optimization technique is developed to solve the finite-time nonlinear optimal control problem. For the second controller, an extended [Formula: see text]-[Formula: see text] method is applied to design a closed-form feedback control scheme for nonlinear control problem of spacecraft formation flying with non-standard cost functions. By taking into account the flying safety, a repulsive control scheme is incorporated in the optimal controller to ensure collision avoidance and minimize the performance index. Finally, a numerical example is performed to demonstrate the effectiveness of the proposed approaches.